A FUNDAMENTAL STUDY OF THE EFFECTS OF APPLIED ELECTRIC FIELDS ON GAS-SOLID (DIELECTRIC) ADSORPTION By Arun V. Someshwar A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1982 F: -\s ‘u ‘4 aea ABSTRACT A FUNDAMENTAL STUDY OF THE EFFECTS OF APPLIED ELECTRIC FIELDS ON GAS-SOLID (DIELECTRIC) ADSORPTION By Arun V. Someshwar The effects of applied uniform and non-uniform electric fields on the adsorption characteristics of vapors in porous adsorbents are inves- tigated. The theoretical foundations to describe the thermodynamics of polarized layers and the irreversible thermodynamic formulations for surface and volume flow in porous media are laid out. A theoretical 'Single-Pore' model describing the adsorption kinetics in cylindrical, open pore adsorbent systems like silica gel, in the presence of applied electrostatic fields, is postulated. Given the pore and adsorbate char- acteristics, along with the diffusion coefficient and adsorption kinetics in the absence of the applied fields, this model predicts satisfactorily the observed enhancements in adsorption rates in the presence of the external fields. Various experiments conducted with porous adsorbents with only a few layers of adsorbate in the sample have confirmed the inability of applied electric fields to influence either gas—phase diffusion rates or surface diffusion rates. Experiments conducted with porous silica gel, wherein significant multilayer adsorption is known to have occurred, ~-_rc_-w F.l I l C). l f 0 r? O Arun V. Someshwar showed significant adsorption rate enhancements, both due to the polar- ized adsorbate and the presence of alkali ions on the adsorbent surface. Further experiments conducted with the silica gel-water vapor sys- tem have shown that (a) the extent of adsorption rate enhancement is not dependent on the magnitude of the macroscopic field gradient in the sample, and that (b) desorption kinetics from capillary porous media are essentially unaffected in electrostatic fields. The observation made in the literature that applied electric fields do not affect the adsorption behavior for non-polar adsorbates is confirmed by experiments with CZClu- silica gel. The phenomenon of relaxing, internal electric fields in moist capil- lary porous systems is proposed and the procedure to estimate the magni- tudes of the resulting internal field gradients is delineated. Preliminary experiments conducted with the fly ash-water vapor sys- tem have shown that the adsorption kinetics are essentially unaffected by applied electric fields in a humid environment (p/pS = 1). However, the adsorption equilibria are significantly affected in an unsaturated environment (p/ps = 2/3) and electrodynamic (with ionic current flow) fields. To my Mother -and- To my Father who had to bear so much ii ACKNOWLEDGEMENTS The author would like to express his sincere appreciation to Dr. Bruce W. Wilkinson for providing encouragement and support through every single phase of this work. His concern for this student will be long remembered. The author would also like to thank Drs. Carl Cooper, Charles Petty and MacKenzie Davis for their useful comments and criticisms. Special gratitude is offered to Dr. Carl C00per for providing this author with various opportunities during the early stages of graduate work. The excellent workmanship provided by the staff of the Engineering Workshop in fabricating the research equipment is much appreciated. The author gratefully acknowledges the financial support obtained from the National Science Foundation (CPE-8111276) and the Michigan State University Division of Engineering Research. The patience and perseverance of Karen Goodman in typing this thesis is gratefully acknowledged. iii IV‘ .. a.-. v\, b.‘ TABLE OF CONTENTS LIST OF TABLES . LIST OF FIGURES NOTATION . INTRODUCTION . I. 1 Motivation for this Research I. 2 Research Objective and Outline Chapter I SURVEY OF EXISTING LITERATURE . l l Field-Induced Effects in Solid-Gas Adsorption 1.2 Field-Induced Effects in Other Systems . II THERMODYNAMICS OF CHARGED AND POLARIZED LAYERS 2.1 Local Balance Thermodynamics in Electrochemical Systems 2.1(a) Ponderomotive Force . . 2.1(b) Conservation of Momentum and Energy 2.1(c) The Gibbs- Duhem Equation for Polarized Systems . . 2. 2 Thermodynamic Relations for Systems in which the Dielectric Constant Depends on the Macroscopic Field . . . 2. 2(a) Free Chemical Energy Density . 2.2(b) Entropy Densitys v . . . . 2.2(e) Internal Energy Density6 v . 2.2(d) Chemical Potential HY 2.2(e) Numerical Estimates . 2.3 Pressure and the Ponderomotive Force . . 2.3(a) Numerical Example for the Kelvin Pressure . 2.4 Distribution of Matter in the Interfacial Layers of Continuous Systems at Uniform Temperature . 2. 4(a) Kelvin Pressure Distribution: Mechanical Equilibrium . . 2.4(b) Equilibrium Distribution of Components in a Gaseous Mixture . iv , viii ix , xiii 15 16 16 17 19 21 22 22 23 23 23 26 28 28 29 29 Chapter 2.4(c) Polarization and Volume Effects in Liquids 2.4(d) Discontinuity of Pressure Across a Plane Interface Perpendicular to the Field . III GAS-SOLID ADSORPTION IN POROUS MEDIA 3.1 Thermodynamics of Adsorption in Porous Solids 3.1(a) Estimation of Surface Area for Porous Solids . . . . . 3.1(b) Estimation of 'Bound' Water and 'Capillary- Condensed' Water in Silica Gel . . 3.2 Surface and Volume Flow in Porous Media 3.2(a) Theoretical Formulation for Surface and Volume Flow 3.3 Irreversible Thermodynamic Formulation Extended to Porous Media in External Electric Fields IV ESTIMATION OF ELECTRIC FIELDS IN DIELECTRIC MEDIA . 4.1 The Electrostatic Field in Dielectric Media 4.1(a) Bed of Particles in Uniform External Field . . . . 4.1(b) Spherical Beads in Uniform External Field . . 4.1(e) Annular Sample Configuration in Cylindrical Field . . 4.1(d) Cylindrical Bed of Dielectric Specimen Coaxial with Cylindrical Electrode Geometry . . . 4.1(e) Charged Spherical Particles in Uniform Field . . . . . . 4.1(f) Bed of Spherical Particulates Subject to Uniform External Field 4.2 Dielectric Properties of Crystalline Powders 4. 3 Relaxation Fields: Estimation of Electric Fields in Moist, Capillary Porous Silica Gel . . 4.3(a) Dielectric Constant of Adsorbed Water in Silica Gel 4.3(b) Strategy for Internal Field Calculations . . 4.3(c) Comparison of Internal Field Gradients and External Field Gradients 3O 31 32 34 39 43 46 50 53 56 57 57 S8 60 61 63 64 66 69 7O 74 78 Chapter V EXPERIMENTAL VERIFICATION OF FIELD-INDUCED MASS TRANSFER EFFECTS 5 l Rationale Behind the Order of Experiments 5.2 Experimental Apparatus and Procedure . 5.2(a) Step— By- Step Procedure for Conducting Experiments . 5.3 Adsorption in Uniform, Applied Electric Fields . 5. 3(a) Spherical, Porous, Alundum Beads in Uniform Field . . . . 5.3(b) Bed of Silica Gel in Uniform, Applied Field . . . . . . 5.3(c) Bed of Spherical, Alundum Beads in Uniform Field . . . 5.3(d) Bed of Crushed Alumina Beads in Uniform Electric Field . 5.4 Adsorption in Cylindrical, Non-Uniform Electric Fields . . 5.4(a) Crushed Alumina in Annular Pan and Cylindrical Field 5.4(b) Crushed Alumina, CaC03 Powder, Porous Glass and Zeolite Beads in Strong Cylindrical Fields . . . 5.4(c) Alundum Catalyst Beads Strung on Filament Electrode . . 5.4(d) Water Vapor Adsorption in 'Drying Grade' Silica Gel . . . 5.4(e) Water Vapor Adsorption in S- 4133 (25 A0 dia. ) Silica Gel 5.4(f) Monolayer Adsorption in 8-2509 (60 Ao dia.) Silica Gel 5.4(g) Water Vapor Adsorption in Porous Alundum Catalyst Beads Strung on Ground Filament Electrode at p/pS = l and T = 25° C . . . 5.4(h) Water Vapor Adsorption in Crushed Alundum in the Presence of a Corona Field . . 5.5 Multilayer Adsorption in Cylindrical Electric Fields . . . 5.6 Further Experiments with Silica Gel S- 2509 (60 Ao dia. ) 5. 6(a) Non- Polar Adsorbate (C2C1;) and Silica Gel . 5.6(b) Effect of Decreasing the Gradient of External Field Squared, , but Maintaining the Average Field Strength Squared, . 5.6(c) Desorption Experiments: Water Vapor- Silica Gel . . 5.7 Preliminary Experiments with Treated Silica Gel S- 2509 . vi 80 81 84 87 89 89 90 93 95 95 95 98 99 99 104 106 106 108 110 112 112 114 116 119 c7. (n Chapter ‘VI MATHEMATICAL MODELING: MASS TRANSPORT IN A SINGLE, OPEN CAPILLARY PORE IN THE PRESENCE OF AN ELECTRIC FIELD . . . . . . . . . . . . . . . 6.1 The Mathematical Problem . . 6.2 Numerical Solution of the Second Order Partial Differential Equation (6.8) 6.3 Results of Numerical Calculations VII FLY ASH RESISTIVITY, CONDITIONING AND THE EFFECTS OF APPLIED ELECTRIC FIELDS 7 l Interparticle Field and Concentration Gradients 7.2 Preliminary Experiments with Fly Ash . VIII CONCLUSIONS AND RECOMMENDATIONS FOR CONTINUED RESEARCH 8.1 Conclusions . . 8.2 Recommendations for Continued Research . . 8.2(a) Further Experiments with Capillary Porous Materials . . . . 8.2(b) Experiments with Fly Ash . APPENDICES Appendix A ESTIMATION OF OVERALL ELECTRIC FIELDS . B ESTIMATION OF INTERNAL RELAXATION FIELDS C EXPERIMENTAL DATA 8 DATA ANALYSIS . D EQUIPMENT DESCRIPTIONS E COMPUTER PROGRAM FOR SINGLE-PORE MODEL BIBLIOGRAPHY . vii 122 122 129 131 138 143 147 151 151 154 155 157 161 174 181 200 204 216 LIST OF TABLES Influence of Field on the Theoretical Values of 2 e E [3%] and 20 1+ [31“] dEz mi 0 T,E ‘* . -> + Influence of Field on Entropy Density (T==25O C) Influence of Field on Free Energy Density and Internal Energy Density (T==25o C) Estimates of Overall Dielectric Constants and Macroscopic Electric Fields as a Function of W for Silica Gel S-2509 and Water Vapor System . . . . . . . . . . . . . . Estimates of e ., E ., E ., E . p1 p1 21 31 Estimation of Adsorption Rate Curve in the Presence of an Electric Field Comparison of Fields for Figures 5.18 and 5.20 . viii 24 25 25 76 77 135 170 .7(a) .7(b) LIST OF FIGURES Curves of moisture content W(%) in grade KSK-Z silica gel, as a function of time t (mins.) Sorption isotherms for plain and ion-saturated specimens of grade KSM-S silica gel without a field Sorption kinetics. Moisture content W(%) vs. time t (mins.) Adsorption-desorption isotherms of water vapor in KSS—4 Silica gel at various temperatures Percentage adsorption W vs. time t (min.) for KSS-4 silica gel at T = 2930 K . Adsorption rate dW/dt (%/min.) of water vapor by KSS-4 silica gel vs. moisture content W(%) . . . . . . . A type IV isotherm . a) Cylindrical meniscus; b) hemispherical meniscus . Adsorption isotherm for Silica Gel S-2509 B.E.T. plot x/y(l-x) vs. x for Silica Gel S-2509 . Comparison of A with available literature Ratio of bound energy to internal energy differentials (TAS/AU) of a moisture bond as a function of the moisture content in four Silica gels . Bound water vs. mean pore diameter . Monolayer amount adsorbed vs. mean pore diameter . Model capillary Bed of particles in uniform field Dielectric sphere in uniform field . Annular sample pan in cylindrical field ix 10 10 11 35 38 41 42 42 44 46 46 49 57 58 6O .7(a) .7(b) .7(c) .7(d) .10 .11 Cylindrical sample bed coaxial with cylindrical field . Charged particle in uniform external field Interparticle contact characteristics . Single cylindrical open pore with adsorbate . n-propyl alcohol-titania gel system . Relations between dielectric constants and sorbed amount of water (250 C) Spherical, porous dielectric particles in air; subjected to electric field . Schematic diagram for experiments . Sample pan configurations (other than that in Figure 5.1) Spherical porous alumina beads in uniform electric field Water vapor adsorption in drying grade silica gel in uniform, applied field . Water vapor adsorption on alundum beads in uniform electric field Water vapor adsorption on crushed A1203 in uniform electric field Water vapor adsorption in crushed alumina . Water vapor adsorption in crushed alumina . Water vapor adsorption in crushed alumina . Water vapor adsorption in crushed alumina . Water vapor adsorption on crushed A1203 in cylindrical field . . Water vapor adsorption on CaC03 powder in cylindrical field . Water vapor adsorption on porous glass in cylindrical field . Water vapor adsorption in zeolite catalyst beads in cylindrical field 62 63 65 69 71 72 74 86 86 91 92 94 94 96 96 97 97 100 100 101 101 .12 .l3(a) .13(b) .14 .15 .16 .17 .18 .19 .20 .21 .22 .23 Alundum beads strung on ground filament, p/ps==0.5, T=37°C,V=4KV. .. HZO-silica gel (D.G.) HZO-silica gel (D.G.) Adsorption of water vapor in Silica Gel S-4133 Monolayer adsorption in porous silica gel (S-2509)— H20 vapor adsorbate . Alundum beads strung on ground filament, p/ps==l.0, T=25°C,AV=6KV Water vapor adsorption in point-plane geometrical field--crushed alundum adsorbent Multilayer adsorption in capillary porous Silica Gel S-2509 in cylindrical electric field Adsorption of non-polar adsorbate C2C1L on Silica Gel S-2509 Adsorption of water vapor on Silica Gel S-2509 in the same average but smaller average . Desorption from a cylindrical pore Desorption kinetics, water vapor-Silica Gel S-2509 Water vapor adsorption in silica gel treated with HC1 and KCI solutions Single, cylindrical, open pore: (a) Knudsen and surface diffusion; (b) bulk adsorbate volume flow . Elemental mass balance Adsorption rate in single-pore model, with and without electrical field (theoretical curves) Rate of adsorption vs. amount adsorbed for single- pore model Integral curve to yield W' vs. t for Silica Gel S-2509 Predicted and experimental adsorption rate curves in silica gel—water vapor system Idealized array of uniform, spherical fly ash particles packed in a layer . . xi 102 103 103 105 107 108 109 111 113 115 117 118 120 123 125 132 134 134 136 140 \l .2(a) .2(b) Equilibrium curves for fly ash-argon (a); and fly ash-HZO-air (b) Geometrical properties of capillary condensed liquid at a point of contact between spherical particles . Interparticle contact dimensions Fly ash-H20 vapor, p/ps 2 2/3 . Fly ash-water vapor, p/ps = 1 Bed of ideal spheres Corona discharge through bed (negative corona) Annular pan with fly ash 1) H.V. Supply; 2) Multimeter; 3) D.C. Power Supply; 4) Variacs . . . . . . . . . . . . . . . . . . . . CAHN Gram Electrobalance Adsorption Chamber with Electrode Assembly Adsorbent Pans used in this work Adsorption Chamber in Water Bath with Weighing Chamber Overall view of all equipment . xii 140 141 144 148 148 157 158 158 201 201 202 202 203 206 II col «2 +71 'n +9- NOTATION Radius of interparticle contact circle. Area occupied by single adsorbed molecule. Specific surface area of adsorbent. B.E.T. parameter defined by Eq. (3.5). Polarizabilities defined by Eq. (4.11). Concentration of ith species. Diameter. Interelectrode distance in Figure 4.1. Diffusion coefficient. Internal energy density. Unit vector in z direction. Magnitude of electric field. Electric field vector. Free energy density. Force acting on molecule defined by Eqs. (1.1) and (1.2). Free energy. Pondermotive force defined in Section 2.1(a). Correlation factor. Gibbs function. Current density. Mass flux of diffusing species. Boltzmann's constant. xiii at (x) r4 Constant used in Eq. (3.15a). Langevin function of x. length of pore in adsorbent. Mean-free path on the surface of adsorbent. Mass of adsorbate in system. Molecular weight. Avogadro's number. Number of molecules per monolayer. Mass fraction of species y. Pressure. Vapor pressure at saturation. Specific polarization of a substance defined by Eq. (4.14). Polarization defined by Eq. (2.0). Heat flux defined in Section 2.1(b). Charge on particle at saturation defined by Eq. (4.5). Heat of adsorption. Heat flow vector defined in Section 2.1(b). Radial distance. Mean pore radius. Universal gas constant. Mean radius of curvature defined in Section 3.1(a). Radius. Entropy density. Entropy. Time. Thickness of bound adsorbate. Temperature. xiv Up(2) Cl +c: NI Gas—solid perturbation potential. Mean velocity of gas molecules. Internal Energy. Velocity due to external force defined by Eq. (1.3). Average drift velocity of diffusing species. Specific volume of surface adsorbed molecules. Applied voltage. Internal pore volume. Adsorbate content of Specimen Mass adsorbed in monolayer. Average charge per unit mass of body. Greek Letters 8 Ratio defined as r/a. Surface tension. Thickness of surface layer for surface diffusion. Volume fraction of 1th phase in adsorbent. Dielectric constant. Permittivity of vacuum or free space. Viscosity. Polar angle. Mean-free path. Phenomenological coefficient in Eq. (3.13). Magnitude of dipole moment. Chemical potential of 1th species. Dipole moment vector. Mass density. XV Average residence time of adsorbed molecule. Lingering time defined by Eq. (3.12). Time of oscillation defined by Eq. (3.8). Like To in Eq. (3.12). Relative vapor pressure. Scalar potential. Electric susceptibility. Barycentric velocity. Gibbs field potential in Section 3.1(a). xvi INTRODUCTION 1.1 Motivation for this Research In the technology of Electrostatic Precipitation, the phenomenon of 'back corona' or 'sparkover,‘ arising principally due to high ash or dust electrical resistivities, and the attendant problems with collec- tion efficiencies is very well documented [W2]. High ash resistivities owing primarily to the burning of low sulphur coal can lead to severe collection problems. For over a decade it has been known that the ash surface resistivity is sensitive to not only the chemical composition of the coal burned, but also to the composition of the flue-gas [W1,Bl]. The enhancement of water vapor concentrations in the gas, as well as the addition of small quantities of 'conditioning' agents such as sulphur- trioxide and some sodium compounds [W2] (which, in turn, bind the water more strongly on the particle surface), have been known to significantly lower ash resistivity. In their investigations of the sorption phenomena of water vapor on fly ash, Ditl and Coughlin [D1,D2] have ascribed the significant lowering of ash resistivity (for adsorbed amounts less than even a mono- layer) to ‘capillary condensation' in the ring-like inter-particle crev- ices. However, the problem of justifying the use of the 'Kelvin' equa- tion to account for the incipience of condensation in pore radii less than a few molecular diameters remains unresolved. In all the analysis carried out thus far to explain the sorption phenomena in the condition- ing process, the fact that the bed of fly ash is subjected to high 1 2 external electric fields and the charged nature of the particulates prior to precipitation is neglected. Extremely high and non-uniform electric fields are known to exist in the vicinity of the contact spots between particulates in a bed subjected to an external electric field [Ml]. Polar gases, and especially liquid-like adsorbates that are highly polarizable, experience additional thermodynamic forces in the presence of non-uniform electric and magnetic fields [D3]. The occurrence of alkali ions in fly ash [W2,Bl,B2] and their role in the sorption phe- nomena have been subjects of much recent study. However, the effects of the strong electric fields involved have so far escaped notice. With these specific goals in mind, the present research efforts are aimed at initiating an understanding of the fundamental concepts that underlie the effects of applied electric fields on the thermodynamics and kinetics of gas-solid adsorption. Both theoretical and experimental investiga- tions are attempted. An understanding of these 'electrical effects' could, of course, be utilized in all such processes where adsorption of gases or vapors takes place on electrically charged particles or parti- cles subject to strong electric fields. 1.2 Research Objective and Outline In this work the class of adsorbents used to study the electrical effects of gas-solid adsorption will be restricted to porous dielectrics. Conductors and semi-conductors will be excluded. The implications derived from porous dielectrics may, however, be extended to solid dielectrics. In the course of the experimental investigations, it was found that the electric field-induced effects in the sorption phenomena became significant only when multi-layer adsorption and/or capillary 3 condensation were known to take place. Monolayer adsorbed vapor was unaffected by ordinary laboratory fields (E < 1x10“ V/cm). Accordingly, the chief emphasis of this research work will be on studying the field- induced phenomena brought into play when significant amounts of polar- izable adsorbates are adsorbed. This study consists essentially of three parts. The first consists of laying out the theoretical foundations of adsorption in porous media and the related thermodynamic field-induced phenomena. Detailed analy— sis of how to estimate internal, local electric fields in an adsorbent- adsorbate system and the corresponding 'ponderomotive' forces is given. In the second section the various experimental investigations are out- lined, and the conclusions derived from each are recorded. Finally, the knowledge gained from the theoretical and experimental work already cited is applied to the problem of fly ash resistivity and conditioning in modern Electrostatic Precipitators. Appropriate recommendations for continued work with fly ash and other adsorbents (especially in the pres- ence of alkali ions) are made. CHAPTER I SURVEY OF EXISTING LITERATURE A polarizable molecule of 'effective' dipole moment u will experi- + ence a force when placed in a non-uniform electric field given by [H2] fp = u-VE (1.1) .+ ++ where £p = force per molecule VE = gradient of electric field .) This force will act in the direction of the maximum field intensity gradient. Besides the force on a polarizable molecule, a charged body (charged with either ions or electronic charges) will also experience a force given by fC = sz (1.2) + -+ where fC = force per unit volume of body + 3' = charge per unit mass of body 0 = density of body Several researchers have attempted to study the consequences of these two forces in solid-gas, solid-liquid, liquid-liquid and liquid- gas systems. In this chapter a detailed review of the effects of 4 5 external electric fields on the characteristics of gas-solid adsorption is made. Among solids only dielectrics are chosen, though the gaseous adsorption in metals and semi-conductors in the presence of an external field is also briefly touched upon. In the final section some instances where the external fields have been used to study liquid-liquid, liquid- gas systems are cited. 1.1 Field-Induced Effects in Solid-Gas Adsorption For some inexplicable reason, almost all of the research concerning the adsorption of gases and vapors on disperse dielectric solids in the presence of electric fields seems to have been carried out in the Soviet Union.+ Panchenko et a1. [P1 to P3, P5 to P11] have conducted experi- ments to study the adsorption of moisture on various kinds of silica gel, potato starch, cellulose-acetate and some natural polymers in the pres- ence of both sub-discharge and corona electric fields. In references [P3,P5,P6] the authors have studied the water vapor adsorption characteristics in two kinds of silica gel, KSM-S (mean pore radius = 12 A0) and KSK-Z (mean pore radius = 59 A0) in the presence of electric (both d.c. and a.c. z 50 Hz) and magnetic fields. Figure 1.1 shows the effect of cylindrical, non-uniform electric fields on the rate of water vapor adsorption in KSK-Z silica gel [P3]. The same authors studied the sorption kinetics of water-vapor in silica gel in the presence of uniform constant and uniform alternating (50 Hz) electric fields (with field strengths up to about 2 KV/cm) and .anch of the literature (none of which was felt to have any direct sig- Iiificance in this work, judging from the Short paragraphs in Chemical ,Abstracts) is in Russian and is unavailable in the MSU libraries. w 80 5 1\34 40 2 0 0 100 200 300 t Figure 1.1. Curves of moisture content W(%) in grade KSK-Z silica gel, as a function of time t (mins.): 1) without an electrical field; 2) U = 700 V; 3) U = 800 V; 4) U = 900 V; 5) U = 1,000 V. Relative pressure of water vapor ¢S = l, T = 293° K. failed to see any enhancement in the adsorption kinetics [P3]. Also, measurements made in non-uniform electric fields for the adsorption of carbon tetrachloride (dipole moment = 0, dielectric constant 2 2) in KSK-2 silica gel yielded no discernible effects. The low frequency (50 Hz) alternating fields were identical in their effects to the con- stant d.c. fields of similar intensities [P3], probably implying that the frequencies were yet too low to affect the adsorption. In non- uniform electric fields the authors also observed that the time required for attaining a given moisture content decreased linearly with increasing ‘voltage on the electrodes [P6]. The presence of magnetic or electric fields had no influence on the maximum hygroscopic moisture content of ‘the samples and did not change the shape of the adsorption or the desorp- 'tion branches of the isotherm [P6]. In [PS] the authors studied the txunperature effect on the sorption kinetics of water-vapor in Silica gel. They observed that an increase in the temperature from 2930 K to 3230 K weakens the field-induced phenomena. 7 The preceding authors also studied the effects of applied, non- uniform electric fields on the sorption kinetics of water-vapor in ion- saturated (K+, Ca++) silica gel KSM-S (mean pore radius = 12 A0) [P1]. The ions, especially bivalent Ca++, are assumed to provide additional sorption centers to enhance the adsorption. Further, the mobility of the hydrated ions is presumed to be Significantly enhanced in the presence of applied non-uniform fields, thereby influencing the adsorption kinetics. Figures 1.2 and 1.3 describe the equilibrium and kinetic characteristics of water-vapor sorption in ion-saturated silica gel KSM-S, respectively. As these figures clearly indicate, the applied non-uniform fields are seen to enhance both the maximum amount adsorbed, as well as the rate of adsorption in ion-saturated porous silica gel. W 4 5 60 1”7::: ./25;£%23 W ’___.... N' 40 3 Aéé 6O 77 . EEZI€E=EF‘ 4 l 40 20 I 20 0 , 0 0.4 0.8 1.2 ¢ 0 0 0.4 0.8 1.0 0 4O 80 120t Figure 1.2. Sorption isotherms for Figure 1,3_ Sorption kinetics. plain and ion-saturated specimens of Moisture content W(%) vs. time grade KSM-S silica gel without a + t (min.), T = 3030 K without a fleldz 1) plain KSM-S. 2) with K . field: 1) plain KSM-S, 2) with 3) w1th Caz ; in an electric field: K+ 3) with Ca2+° in an electric . . 2 ’ 9 4) W1th K . 5) WIth Ca . field: 4) plain KSM-S, 5) with K+, 6) with CaZI. 8 In [P10] the authors have investigated the effects of field inten— sity and homogeneity on the kinetics and statics of water-vapor adsorp- tion by silica gel KSM-S, sulfite cellulose and potato starch. The 'sub-discharge' electric fields had no effect on the maximum adsorption capacity of KSM-S. However, the capacity of cellulose and starch was reduced strongly. They concluded that the sub-discharge electric field shrinks the total pore volume by shifting the pore distribution to smaller radii. The adsorption kinetics were affected to different extents for the different adsorbents. In [M5] Mosievich has Studied the effects of applied electric fields on the internal mass transfer during sorption of moisture by natural polymers. Non-uniform fields increased the rate of adsorption, while uni- form fields of the same intensity had no effect on the rate. An increase in temperature weakened these effects. In [P11] the authors have researched the possibility of using a corona discharge to provide the electric field and the energy supply in the drying of a model capillary-porous body (KSM-S silica gel). Signif- icant enhancement is observed in the kinetic curves of drying, with the total duration of the process reduced by almost three fold in comparison with convective drying. An attempt is made to establish the physical mechanism underlying this phenomenon in [P12] (to be described soon). Panchenko et a1. [P2] have postulated a mechanism to help explain the field-induced effects on the internal mass transfer in porous bodies. They maintain that since a polar molecule of dipole moment R will experi- ence a force f in a non-uniform electric field (given by equation 1.1), this molecule will acquire a velocity component in the direction of increasing values of VE given by + u = Df/kT (1.3) -> -> where D = vapor diffusion coefficient k = Boltzmann's constant T = temperature To the normally existing diffusive flux, JV, is then added a con- vective flux, Je = 2C, and the total flux, J, becomes dC (E'V§)C J = Jv+ Je = "D a; 1 + kT(-dC/dx) (1.4) In the same work they have conducted experiments to yield the adsorption isotherms (Figure 1.4) and the adsorption kinetics (Figures 1.5, 1.6) for water-vapor adsorption in silica gel KSS-4 (mean pore radius==22Ap). Field gradients of up to VE = 8°5x10“ V/cm2 were used. As before, the adsorption isotherms were unaffected, while the kinetics were affected noticeably. They ascribe to the former result the fact that applied external fields are much less than the internal fields acting in the adsorbate-adsorbent system and governing the molecular bond energy. The latter result is attributed primarily to a mechanism explained by equa- tion (1.4) and also, possibly, to field effects on the surface transfer of adsorbed material. In [P9] the authors have reported an increasing amount of water adsorbed with increasing field gradients in the case of hydration of beads of a styrene-divinyl benzene (8%) copolymer modified by SOSH groups in the Na+, Cu2+ or Ca2+ form and at 2980 K. In [P8] the intensification of the drying process in bleached sulfite cellulose and starch, saturated 10 w 60 o a t b 40 l 20 0 , 0 20 40 60 80 p_.102 PS Figure 1.4. Adsorption-desorption isotherms of water vapor in KSS-4 silica gel at various temperatures: 1) 293° K, 2) 308° K; a) without a field, b) in an inhomogeneous elec- tric field (VE = 8-5xlo8 V/mz). -> 60 20 0 0 20 40 60 80 100 t Figure 1.5. Percentage adsorption W vs. time t (min.) for KSS-4 silica gel at T = 293° x. 1) Without a field; in- homogeneous electric fields: 2) VE = .76xlo8 V/mz, 3) 2.03x108, 4) 8.5xlo8 V/mz. 11 1.2 F3 0.8 0.4 O 20 40 60 W Figure 1.6. Adsorption rate dW/dt (%/min.) of water vapor by KSS-4 silica gel vs. moisture content W(%). 1) Without a field; in an inhomogenous electric field: 2) VB = .76x108 V/m2, 3) 2.03x108, 4) 8.5x108 V/mz. with EtOH and water (at 3330 K), was studied in the presence of a non— uniform field. The fields did not increase the material temperature nor cause any decomposition. In an attempt to define the physical mechanisms involved in the intensification of drying of moist capillary porous systems in corona discharges, the authors in [P12] have studied the effects of these dis- charge fields on the evaporation of water and aqueous KCl solution from quartz capillaries 2-30 pm in radius. Fields of the order of 2.7x10” V/cm and gradients of 9.9x10“ V/cm2 were created by a needle-plane electrode system. Appreciable increases in the rates of evaporation were observed, especially when the surrounding relative vapor pressures (p/ps) approached 1. The various factors that were cited as possible reasons for the observed enhancement are: (1) additional electroconvective flow Je (given by equation 1.4); (2) reduction in vapor pressure above the capillary mouth (where the corona needle is located), due to either a 12 screening of the capillary in the corona discharge zone by excess Space charge of high density [K3], or by sorption of vapor molecules on nuclei (ions) produced in the corona discharge [P12]; (3) liberation of Lentz- Joulean heat in the discharge gap (small). Further experiments to deter- mine the relative extents of mechanisms (1) and (2) revealed the domi- nance of (2) over (1). Besides the group of Panchenko et al., another Russian group, that of Kuliev et a1. [K4,K5,R2], have studied gas-solid adsorption in the presence of electric fields. In [K4] the authors have investigated the adsorption of p- and o-xylene and of H20 in silica gel KCM (at 3500 K) in an external electric field. They concluded that with increasing field potential, the adsorption on KCM increased with increasing adsorbate- molecular polarity and that on SKT was unaffected by the field. The silica gel KCM had apparently some concentration of foreign ions. In [K5] the same authors conduct adsorption studies with mixtures (1:1) of octane-octene, and p-xylene-o—xylene, on silica gel in the presence of a corona discharge field. The separation coefficient (relative concen- trations of adsorbate) was found to be two to three times higher in the presence of the field than without it. Rasulov et a1. [R2] studied the surface properties of adsorbents to elucidate the mechanism of processes which take place on solid surfaces in applied electric fields. The electrical conductivity of silica gel NS-62 and zeolite NaA was deter- mined during H20-vapor adsorption. The adsorption on NS-62 was observed to increase significantly in the field. Other than the work detailed above, no relevant information seems to be available relating the effects of external fields on the physical adsorption of gases on disperse, dielectric media. Considerable work, 13 however, has been carried out to study the effects of applied fields in the chemisorption of mostly non—polar gases on metallic and semi- conducting surfaces. The externally applied field is known to enhance or suppress (depending on the polarity) the movement of electrons to the surface and thus affect the electron transfer mechanism in chemi- sorption bond formation [S3]. Bennett [B7] has formulated a theoretical model with a quantum-mechanical approach to determine strong electric- field induced changes in the binding energy, equilibrium position and vibrational frequency of the adsorbate in chemisorption at a metal- vacuum interface. Lincoln and Olinger [Ll] observed an increase in the adsorption rate and quantity of CZH, on a porous nickel catalyst, but saw no change in the case of H2. Hoenig and Lane [H3] concluded that the adsorption of 02 on ZnO (known to take place by an electron transfer mechanism) could be suitably altered by imposing an appropriate electric field. The adsorption of 02 on W [D6], ZnO [D7], Ge [R3], of CO2 on ZnO [D7] and of Cs, Na, Li on W [T1] in an applied d.c. field were all seen to be significantly affected. 1.2 Field-Induced Effects in Other Systems In the areas of liquid-liquid and liquid-gas systems, considerable work has been done to study the effects of either applied electric fields or charged liquid droplets. Sawistowski and Banczyk [S4,B8] obtained a more than tenfold increase of the mass transfer coefficient for two- component systems during horizontal laminar flow of the phases and an electric field intensity of about lKV/cm. They also observed the forma- tion of additional turbulence near the interface, probably caused by electrodynamic forces acting on the liquid [R4]. Agaev and Abdullaev [Al] and Kowalski and Ziolkowski [K6] have independently utilized 14 electric fields in extraction columns with much success. Besides increased turbulence resulting from the application of non-uniform electric fields in association with inhomogeneous dielectric media [T2,GZ,SS,K8], the occurrence of an increased velocity and reduced interfacial tension of charged drops of the dispersed phase in relation to the continuous phase is exploited in various liquid-gas, liquid- liquid systems [89,K7,H4]. Further mention of the various interesting phenomena arising from electric fields applied to these systems is out- side of the scope of this work. CHAPTER II THERMODYNAMICS OF CHARGED AND POLARIZED LAYERS In a system containing polarizable constituents and unequally dis- tributed charges, classical thermodynamics are of dubious value. Prigogine [P13] was the first to derive a formulation of the thermo- dynamics of charged and polarized systems. He has shown that an elegant combination of the thermodynamics of irreversible processes and of the Maxwell—Lorentz electromagnetic theory, along with a lggal_rather than global character, yields information about thermodynamic functions and equilibrium conditions of charged and polarized matter under more general conditions than comprise the use of classical thermodynamics alone. Using the contributions of Prigogine, Mazur and Defay [P14,M6,D8], Sanfeld [ffifl has prepared an excellent monograph which makes a general survey of the thermodynamics of matter in a field. In this chapter some of the fundamental concepts developed by the above authors are presented. The significance of these concepts on the various aspects of this work is mentioned whenever applicable. Starting with the Kelvin concept of the 'ponderomotive' force, the laws of conser- vation of momentum and energy in charged and polarized systems are formu- lated. Next, the Gibbs-Duhem type of equation for these systems is derived. In Section 2.2 the effects of applied fields on various thermo- dynamic quantities in systems where the permittivity depends on the macroscopic field are investigated, both theoretically and with appro- priate numerical examples. In Section 2.3 the very interesting concepts 15 16 of 'pressure' in a dielectric and the ponderomotive force, according to the Kelvin and the Helmholtz approaches are presented. Also, the advan- tages of the Kelvin method over that of the Helmholtz method are noted. In the final section the distribution of matter in charged and polarized systems is discussed for various specific instances. 2.1 Local Balance Thermodynamics in Electrochemical Systems The phenomena due to electromagnetic forces are, in general, non- conservative. The basic conservation laws of momentum and energy are therefore reformulated to account for the presence of the electromagnetic fields. For the sake of convenience, the assumption that no magnetic fields are applied will be made here. The electric polarization P is defined as P = 60(8 - 1)E = x5 (2.0) where E = macroscopic electric field strength (V/cm) + e = dielectric constant (dimensionless) £0 = permittivity of free space (= 8'854x10-“2%2) = electric susceptibility = 60(8 - 1) = polarization per unit volume —grad 0 es +nl +w: :K II = scalar potential 2.1(a) Ponderomotive Force For a non-viscous fluid in the absence of gravity, the force acting upon each isotropic volume element 6V is 17 (F - grad p)6V + where F = electromagnetic force or ponderomotive force + In general, F = FL+ Fp + -> + where FL = 2(0 2')E = ozE = force on a volume element having 3 Y Y Y a realized charge zpdV and Fp = force on polarized volume element with electric moment PDV + If one follows Kelvin, one may define 2.1(b) Conservation of Momentum and Energy The dynamical equation for continuous media, viz., PEE.‘ F - grad p dt 3 (where w = barycentric velocity of the system, at a point) now becomes + pdg = pEE + P-Grad E - grad p (2-1) 31? -> —> —> Equation (2.1), when combined with the equation of continuity, viz., 9.9:-- at dive». 18 and after some vector manipulations [86, p. 20], yields the following macroscopic kinetic energy balance: dP (2.2) .. pEodt _ E03; - Engrad p where X'= %-(X is any arbitrary function) and the current density = EEIQY(wy-w) arises from the diffusion of charged components. Y e The energy term (%1xp24--§1§?) in equation (2.2) is not conservative i .p due to the source term d? —> . -oE..-E:-2gradp To get the conservation of energy balance equation, the internal energy balance is to be added to the kinetic energy balance equation (2.2). To make the total energy conservative, the internal energy den- sity ev is defined in such a way that, in addition to the usual convec- tive flow evg, the flow pg related to mechanical work, and the flow 3 related to pure heat flow, the above source term is added to get 3 ev dP . _, . —3t - -le(€v_L2 + g + p93) + DE (111 + E 1 + 9)) grad p (2.3) ++ Adding (2.2) and (2.3) and using the relations dE._ 8ev . pa? — 577 + d1v(gev) and 19 one gets the local formula for the first law of thermodynamics for charged and polarized systems, viz., ”0| - —- d E i 92-9.9 d_v .-» +2» dt‘dt'pdt +Edt+ 0 (2'4) 2.1(c) The Gibbs-Duhem Equation for Polarized Systems By assuming the polarization to be in statistical equilibrium with the field (i.e., i = 0) and by considering a one-component fluid without + viscosity, the following relations can be obtained: ds 1 d3 dt'Tdt and since i = 0 .+ dfV dP __- 91 ._z ‘ .— “CLO dt- SthIEdt+(f'—E>E+p)dt (2‘5) where the free energy density fv is defined by fv = ev - Tsv Since fV must be a state function of the volume element, one can write fv = fV(T’_I:2 p) with (2.6) 20 Prigogine, Mazur and Defay [Pl4,§l£fl have argued that equations (2.6) are valid even when irreversible processes occur, such as heat conduction or viscous dissipation. But polarization here is always con- sidered to be a reversible phenomenon. The entropy production by orien- tation of dipoles has been treated elsewhere [P15,P16,D3]. For a system of several components, one may rewrite (2.6) as fV = fv(T.§,ol, ...- 0C) (a) [My] [afv] (2'7) -- = -s (b) -——- = E (C) 8T V 3P . + £$pl""pc + T901, "pc Prigogine et 31. then define the mass chemical potential as follows: 8f v _ [.23—CT] '-' “Y (2-8) Y T.P.(o) + From (2.7) and (2.8) and using do Y _ . do _ . EE— - NYE (NY - mass fract1on) one gets dfv dP CIT + — (IO .___ = _ ___ ..__ = ——- 2. dt 5V dt *5 dt (fNy‘JyMt ( 9) Comparing (2.9) with (2.5), one obtains ZN_ =f+ V-E-F 2.10) Y YuY p + _) ( which is equivalent to the classical Gibbs function §'= f'+ p? for non- polarized systems. 21 From equations (2.7) and (2.8), a virtual variation of T,P,p1 . QC leads to 6f =—s dT ESP 2:— v v + + + + Y ydOY which, when combined with the differentiated form of (2.10) yields the Gibbs-Duhem equation for polarized systems: 6- T-P-E- '"= . p 5V6 + 6+ EdeuY O (2 11) In terms of gradients and at constant T, this may be rewritten as rad -P°radE-Z rad—=0 2.12 gp+g+Yng uY () Equation (2.12) is the fundamental relation describing the trans- port fluxes, both due to a pressure gradient and due to the gradient in the electric field. From an irreversible thermodynamical point of view, the mass fluxes in a system are proportional to the gradient of the chemical potentials. The relationship between the gradient in the chem- ical potential and the other driving forces in the system, given by equation (2.12), will form the starting point of all theoretical analy- sis used to describe the electric field-induced adsorption kinetic effects in this work. 2.2 Thermodynamic Relations for Systems in which the Dielectric Constant Depends on the Macroscopic Field In Section 2.1 the electric polarization P was defined as E = €o(€"1)§ The dielectric constant e is a function of E, the electric field. At low fields 3 may be assumed to vary linearly with E (i.e., E = 22 constant). However, at even moderate fields, 8 of a polar liquid becomes an explicit function of E, decreasing as E increases. + In general, a = €(T,C1,...CC,E) 2.2(a) Free Chemical Energy Density Equation (2.7c) may be written as E [353} where CY = pY/M is the molar _, SE 13C1,...Cc concentrat1on of spec1es y which, when integrated at T,C1,...Cc constant, yields P _ _ + . fv(T’:’Cl"'°°c) — v0(T,E — O,C1,...CC) + I E d3 (2.13) O,C On further expansion, one gets E-P e E2 . f =f ++++_9.J‘* SEE] dE2 (2.14) v v0 2 2 O,C 2 8E T,C'+ The last term corresponds to the contribution to fv, due to the varia- tion of e with E. .+ 2.2(b) Entropy Density sv Differentiation of (2.13) with respect to T, using (2.7b) gives: a 3 5V = SVO - [ET-JO C E d3] which may be further expanded to give 2 s :5 +3"—E 353 dE2 (2.15a) v v0 2 0C BTEC+ ’ +’ 23 01‘ C e E o .2 86 o + E 8 88 S = s + —— L I J - ——-f —-——{——l dE2 (2 15b v 2 8T ' ) V0 +[ §,C 2 O,C 2 8E aT}E,C T,C —) + Once again, the last term in (2.15b) corresponds to the contribution to 5V from the variation of (Be/3T) with respect to E. _) 2.2(e) Internal Energy Density ev From (2.14) and (2.15b) Since fv = ev - Tsv E-P Te e E2 <3 2 86 o + E 86 328 2 2 2 -> BI E,C 2 O,CZ 3E T,C DEBT C -> 2.2(d) Chemical Potential “y 8f From the definition “Y = [BEX- and equation (2.13), one gets Y T,P,(C) .—) e E2 O -> 38 2 " Y0 2 O,C aCY T,(C),E ‘* + (2.17a) which may be rewritten as E2 .- E:0 -> I: 328 2 + 2 J 2[3E3CY]T°§ (2'17b) Eo 2[3e O,C “Y = UYO - 75 EFL E (c) ’+’ 2-2(§l. Numerical Estimates In this section, some estimates are made of the deviations in entropy, free energy and internal energy densities for pure water at 25° C, due to a local electric field E. The effect of the electric field a, (Be/3T) and its resulting influence on the above thermodynamic quantities are also noted. 24 For a pure polar substance, Mandel [M7, eqn. (lll.3)] has proposed the expressio where n ONav 0L SgudE eoME ud 2kT + = molecular weight Avogadro's number = dipole moment in the bulk of the liquid correlation factor (2 2.55 for H20 at 25° C) Langevin function (L (x) = Cot hx— 1/x) Using this model for the dielectric constant, the following tables for pure water at 25° C can be prepared. Table 2.1. Influence of Field on the Theoretical Values of [ 2 35 6o .E as _ __ __ 2. 8T] Eand J, [3T] dE , from [86, p. 45] p. 0 T,E 4 -> -> at] o 80 E2 85] 2 ergs E V cm er K __.2' __. ’ l [e E (P ) 211e, Edam] 02+ 0 03., 1.2 x 105 -0.18 1.8 x 106 -0.16 3.0 x 106 -0.10 -l4.5 x 106 4.5 x 106 -0.057 -25.0 x 106 6.0 x 106 -0.034 -30.6 x 106 9.9 x 106 —0.014 -42.7 x 106 Table 2. as the field 1 clearly shows how the dependence of e on T drOps gradually intensity increases. This is in keeping with the physical ‘ 7' ~—-—- m 25 observation that the orientation of the dipoles increases with field intensity whilst disorder increases with temperature (i.e., the dis- ordering effect of temperature is partially corrected for by the field). Table 2.2. Influence of Field on Entropy Density (T = 25° C) Case I: e = €(T,C,E) Case 11: e = €(T,C,E = 0) 35 o erg sv‘svo E (V/cm) Case BT' (per K) sv - sv0 3 o -§————-x 100 0,; cm K V0 1 -0.1 —0.58 x 106 -1.48% 6 3 x 10 II —0.25 -l.00 x lo6 -2.57% 6 x 106 I -0.034 -l.22 x lo6 -3.12% 11 -0.25 -4.00 x 106 -10.26% I -0.014 -l.70 x 106 -4.36% 6 9'9 X 10 II -0.25 -10.9 x 106 -27.9 % Table 2.2 demonstrates how the action of the field is to reduce the deviation between sv and sv0 (i.e., ISv"5vol is greater for Case II than Case I). For water, sv0 = 3.9x107 erg/cm3 °K [cf., P17, p. 102]. Table 2.3. Influence of Field on Free Energy Density and Internal Energy Density (T = 25° C); from [S6, pp. 46, 48] er er §_(V/cm) Case fv - fv0 Efié- ev - evo 25% 6 I 2.07 x 10° .35 x 10° 3 x 10 II 3.09 x 10° .13 x 10° 5 I 4.26 x 10° .63 x 10° 6 X 10 II 12.34 x 10° .48 x 10° Once again, the effect of the field on e is such as to reduce the difference (fv - va); e.g., a reduction in (fV - fvo) of almost 49% 26 for E = 3 x 106 V/cm. However, as seen from Table 2.3, this saturation effect resulting from the external field increases the chemical internal energy deviation ev - evo, It may be noted at this point that fields encountered in the vicin- ity of ions and other highly charged colloidal particles may be of the order of 106 to 107 V/cm. However, ordinary applied fields used in the laboratory and in the practice of Electrostatic Precipitation, even when non-uniform, are typically of the order of 10“ V/cm. Thus, the effect of such fields on the magnitudes of the various thermodynamic quantities is rather negligible. 2.3 Pressure and the Ponderomotive Force The concepts outlined in the previous pages wherein, starting from a definition of the ponderomotive forces, one can derive thermodynamical quantities such as free energy, entropy, etc., are due to Kelvin. The Helmholtz method, on the other hand, consists in calculating first the free energy due to the field, and afterwards, the work and the pondero- motive forces (indirectly) in the case of a reversible transformation. Nevertheless, the results derived from both methods are in perfect agree- ment. In the Helmholtz method the pressure in the dielectric (in a field) p is the same as p0, the pressure with no field. The pondero- motive force F is given by H 1 2 1 2 ax] In the Kelvin method F is defined as + FK = P-Grad E (2.19) -> -> -> 27 and the pressure p is given in terms of the Helmholtz pressure pO by the relation [86] E:0 2 80 E2 88 p-po-E— --J .H 2 ‘* 2 o,c Y Y 39y T,E,C .+ _ 2 e dE (2.20) For weak fields (E-i 3x10“ V/cm)€ is almost independent of E, and + for a single component system (2.20) reduces to (2.21) Thus, the definitions of pressure and the ponderomotive force in an electric field are quite arbitrary, as long as the 'sum of the mechanical actions exerted on the dielectric is invariant.‘+ Neverthe- less, the Kelvin method based on the hypothesis of forces is found to be more convenient for at least two reasons: First, it leads to a uniform chemical potential for dielectrics in mechanical equilibrium and at uniform temperature; i.e., it can be easily seen from equation (2.12) that the mechanical equilibrium condition 3 grad p - Grad (5;?) = 0 ++ also implies the chemical equilibrium constraint (grad u)T = 0 Secondly, the Kelvin method can be easily extended to irreversible processes, whereas the Helmholtz method can only be applied to reversible transformations. DeGroot and Mazur [D3, p. 395] give an example of the physical meaning of p (Kelvin) by considering the equilibrium conditions +In other words, 5 - grad (p) should be the same [56, p. 56]. 28 between two isotropic systems with different susceptibilities, thereby suggesting that the Kelvin pressure even has physical significance. The pressure pO in the absence of an electromagnetic field arises as a consequence of the kinetic energy and the short-range interactions between the constituent particles of the medium. If an electromagnetic field is applied, additional interactions of electromagnetic origin arise. These result in long-range forces (ponderomotive forces) and modify short-range interactions, and thus, the pressure [S6]. 2.3(a) Numerical Example for the Kelvin Pressure For pure water at T = 250 C, using Kirkwood's [K9] model for a pure polar liquid and equation (2.20), Sanfehi [S6, p. 60] has esti- mated for the pressure deviation po - p = 1.4 atm at E = 1.2x106 V/cm —+ Once again, for the weaker fields around E = l x 10“ V/cm, one gets .+ a rather small deviation pO - p = 1.07x1o'“ atm Note that in either case the effect of the electric field is such as to reduce the pressure. 2.4 Distribution of Matter in the Interfacial Layers of Continuous Systems at Uniform Temperature In this final section, appropriate equations to estimate (a) the hydrostatic pressure difference between two points of the system, (b) the concentration profile of components in a gaseous mixture, (c) the 'polarization' and 'volume' effect in liquids, and (d) the discontinuity of pressure in a surface layer perpendicular to the applied field, are 29 presented. 2.4(a) Kelvin Pressure Distribution: Mechanical Equilibrium From (2.1) and the relation div(€E) = é—Eb, one gets for the dis- + o tribution of the Kelvin pressure . E:0 2 grad p — EOE d1v(e§) +~3T(€- 1) grad E (2.22) Thus, a knowledge of the geometry of the charged and/or polarized surface, the E field profile and the dependence of the dielectric con- stant e on E, can enable one to estimate the 'pressure profile' in the vicinity of such surfaces. As a = l for most gases and vapors and > 1 for liquids, in the absence of real charges (Z=wx)only the profile in the latter will generally be other than flat (for fields 5.3 1x105 V/cm). In Chapter 7 use shall be made of equation (2.22) in estimating the pressure (and, therefore, the concentration) profile in the vicinity of the interparticle contacts in a bed of fly ash. 2.4(b) Equilibrium Distribution of Components in a Gaseous Mixture For a gaseous mixture of two components 1 and 2 at constant temper- ature, the condition of thermodynamic equilibrium in a charged and polarized layer, viz., u1 = Tl-1 and 112 = 172 [where the prime designates the bulk of the medium (E = O, p = p' = p0) and uY is the electrochemical potential] leads to the equation [816, p. 76] fN fN :52 10 1 10 1 o 88 3s = . , exp 'EET J+ {{55—) - [6E7] }d§2 (2.23) f20N2 f2oN2 02C 1 C2 2 C1 where fYo = local activity coefficient of component Y at §==0 NY = local mole fraction of v V I If f20 = £20 and f10 = f10 and if component 1 is more polarizable than component 2, i.e. [as] 2, [as] 8C1 8C2 , the integral in (2.23) becomes positive and consequently, for large values of ae/acY and E, molecules of 1 will fill the charged layer to an appreciable extent. 2.4(c) Polarization and Volume Effects in Liquids Sanfeld [S6, p. 80] has derived an expression for the distribution oftmm>uncharged constituents l and 2 in the diffuse layer created by I I ions in a solution. As in the above case, if f10 = f10 and f20 = f20 , he has shown that O 2 e E * I- 0+ ** * 3222 E:;" exp 2RT { 2e(v20 -leo) + ac, a 2} (2.24) *3? where v = standard molar specific volume extrapolated to zero pressure Y0 at temperature T in dilute solution. For 1 being more polarizable than 2, i.e. g; >’ Be ac1 ac2 ’ 31 the polarization effect, as was seen in 2.4(b), is such as to increase 1 in the diffuse layer. However, the volume effect (v:: - v::) is able to either increase or counteract the polarization effect. Large compo- nents, as can be easily seen from equation (2.24), will tend to avoid the layer. For a mixture of methanol and acetone in electrolytic dilute aqueous solution, methanol concentrates in the layer and the volume effect is even greater than the polarization effect. On the other hand, for a mixture of methanol and urea, the polarization term is greater than the volume term and urea tends to concentrate in the diffuse double layer [S6, p. 81]. 2.4(d) Discontinuity of Pressure Across a Plane Interface Perpendicular to the Field The pressure difference across a surface of discontinuity between two fluids 1 and 2 is given by [86, p. 181] - - 152 E"- -€—° £2 - 132 2 25 where 61, 62, El, E2 are the dielectric constants and the fields perpen- dicular to the interface in fluids 1 and 2. If 1 is water and 2 is air, then since 6151 = €2§2 and 52 > El’ it can be seen from equation (2.25) that p2-> p1, or the pressure imme- diately above the water is less than that in the air. The field thus acts as a dryer, reducing the vapor pressure immediately above the water surface. It is this effect that the authors in [P12] allude to when describing the increased evaporation rate of water from a quartz capil- lary in the presence of a needle corona discharge. CHAPTER III GAS-SOLID ADSORPTION IN POROUS MEDIA The adsorption of gases and vapors on solids is indeed a very vast topic. In this study only solid dielectrics (or insulators) will be considered. The electrical field-induced effects in the adsorption of gases on conductors (W, Cu, etc.) and semi-conductors (ZnO, etc.) are primarily due to the electronic nature of the gas-solid interactions, and these will not be considered here. The subject of gas—solid adsorp- tion with the solid being a dielectric, is in itself quite diverse. However, as various experiments have clearly demonstrated in this work, the formation of a monolayer in gas—solid adsorption is generally unaf- fected by imposed electric fields of magnitudes less than about 10 KV/cm. This may be due to the fact that the ordinary forces of diffusion oper- ative in the formation of a monolayer are too high when compared with the additional field-induced thermodynamic forces. Multilayer adsorp- tion and/or capillary condensation appears to be a prerequisite before appreciable effects of applied electric fields can be noticed. Of course, for situations in which either extremely high fields exist at the solid- gas interface or when the adsorption forces are relatively weak, the influence of applied electric fields on the extent and rate of monolayer formation cannot be ruled out. In this study fields of magnitudes generally found in the ESP are applied, fields whose upper limit is fixed by the occurrence of such 32 33 phenomena as dielectric breakdown, back-corona, etc. Porous dielectric media constitute a large percentage of solid dielectrics that one encounters in the practical world. The adsorption in porous media, especially at high relative partial pressures, leads to multilayer for- mation and/or capillary condensation. Fly ash, powdered alumina, porous glass, silica gel, beds of dusts from various cleaning operations, etc., may be classified as porous media. In this study, though experiments have been conducted on various porous, disperse, and dielectric media, the primary emphasis will be on capillary porous silica gel. The reason for this is threefold: (a) the internal structure of silica gel is pretty well understood; (b) the adsorptive forces are strong enough to lead to multilayer adsorption and capillary condensation; and, finally, (c) dielectric studies, as also studies reporting the influence of elec- tric field effects on water-vapor adsorption in silica gel at a relative saturation of = l, have been reported in the literature [Pl,P2,P3,Kl,M2]. This last factor makes it convenient to refute and justify preconceived ideas and conclusions already arrived at by some authors, and also to propose concepts which are compatible with all available literature. To understand the nature of the field-induced effects on the thermo- dynamics and the kinetics of gas adsorption in porous media, one needs to fully comprehend these phenomena in the absence of the external fields. In Section 3.1 the thermodynamics of adsorption in porous media is briefly investigated, with particular reference to silica gel. In Sec- tion 3.2 the concepts of surface and volume flow in porous media are defined and, once again, the particular reference to silica gel is made. In the final section the irreversible thermodynamic formulation for mass transfer in porous media developed in Section 3.2 is extended to systems 34 polarized under the influence of external electric fields. 3.1 Thermodynamics of Adsorption in Porous Solids The Brunauer-Emmett-Teller (B.E.T.) [B3] theory is generally accepted as providing an accurate description of that part of the adsorption isotherm represented by two or three layers of adsorbate. Surface area calculations based on the B.E.T. monolayer capacity for relative pressures less than about .35 are even today considered to be the most accurate estimates available [81]. However, for thick films, the B.E.T. theory becomes increasingly inaccurate. The primary reason for this failure is attributed to the assumption that gas-solid inter- action energies for molecules beyond the monolayer are zero [81]. By considering an external potential field to account for the solid-gas interactions, the Frenkel-Halsey-Hill (F.H.H.) theory appears to des- cribe the problem of very thick films most successfully. The adsorption on very finely divided or porous solids, however, cannot be adequately described by either of these theories. The behavior of adsorbates in porous systems is dominated by effects resulting from the curvature of the solid surfaces and of the adsorbed fluid, especially as saturation is reached. Of the five classes of adsorption isotherms in the B.E.T. classifi- cation, the adsorption on porous systems most often falls under the category of class IVfi- Figure 3.1 shows a typical type IV adsorption isotherm. +More specifically, type IV isotherms are encountered in solids whose pores have diameters in the range of tens to hundreds of angstrom units [61, p. 123]. 3S H K 3 1. g G "-4 p Q. 1... O m 3 F E D l 1.0 Relative Pressure (p/ps) Figure 3.1. A type IV isotherm. Along low pressure branch DEF, monolayer adsorption is assumed to take place. Opinions differ as to the exact course of events along branch FGH. The most widely accepted view is that a multilayer is grad— ually built up and that more or less normal liquid-vapor menisci are formed [GI]. At H the pores are filled with a liquid-like adsorbate, and the flat branch HK refers to the negligible adsorption in the out- side of the grains. During the desorption process the menisci persist, becoming concave towards the vapor, and the desorption branch HLF is traversed. Evaporation occurs at lower partial pressures and adsorption hysterisis is observed. Most researchers agree that the desorption branch, especially for high partial pressures, is most adequately described by the Kelvin equa- 1. tion +A more rigorous relation would have an additional potential energy term Up(z) in the right-hand side to account for the external field created by the solid surface [81]. 36 2 RT 1n (pO/P) = 2?, C056 (3.1) m where p = adsorption pressure Y = surface tension of liquid-like adsorbate vfi = specific volume of adsorbate 6 = liquid-solid contact angle Rm = mean radius of curvature p5 = saturation vapor pressure This equation is obtained by the combination of the well-known Laplace equation 2 l l pV - p = Y[—- + —-]Cose R1 R2 (3.2) (where pV and p2 are the pressures in the vapor and liquid across a curved surface of tension with curvatures R1 and R2, 2/Rm = l/R1 + l/Rz, Y is the surface tension) with the thermodynamic relation v duv = RT log P—- o = 6n“ = v“(pg - pV) (3.3) P The Kelvin mechanism implies extremely large negative adsorbate pressures. For example, Y = 72 dynes/cm for water at T = 2980 K, and for a cylindrical pore of mean radius of curvature Rm 2 30 A0 and C056 = 1, equation (3.2) gives for the pressure in the liquid about p£ = -474 atm. Along increasing pressure paths, nearly all adsorbents show considerable expansion [F1, p. 55]. This implies negative adsorb- ent and positive adsorbate pressures, and thus, very little of the Kelvin mechanism would seem to be applicable along the path of 37 adsorption. Rather than large, negative pressures as required by the Kelvin mechanism, Flood [Fl, p. 47] has offered the following explana- tion to justify the hypothesis that the adsorbate layer farthest from the pore walls does, indeed, experience pressures similar to that in the gas phase (along the adsorption path only). The Gibbs field potential of any thin layer of liquid-like adsorbate can be considered to be the sum of the potentials Qsa + Qaa’ the former arising from interactions with the solid surface, the latter from field forces of neighboring adsorbate layers. In the middle of the layer Qaa would approach zero, whereas in the liquid-like layer most remote from the solid a positive Qaa should result, just as the last dense layer of the bulk liquid-vapor interface. As saturation is approached along reasonably reversible increasing pressure paths, the net Gibbs potential Qaa + Qsa of the layer most remote from the solid should approach zero. Consequently, the pressure of this region should be about the same as the saturation pressure. The pressure in this layer will thus be much less than the pressure of the underlying layers, and this layer cannot be considered a surface of tension at all. Other authors [C1,Sl] have attempted to treat the adsorption in cylindrical pores as capillary condensation, but with the meniscus being cylindrical in shape rather than spherical (see Figure 3.2). They arrive at a Kelvin—type relation for the gas pressure pad’ beyond which the pore will fill spontaneously 2 = ;Yl_ RT 1n (pad/p5) (Ro'tc) (3.4) Here tc = thickness of adsorbate at which the change in Up(t) (the gas- solid perturbation energy) with t becomes smaller than sz/(Ro—tc)2; 38 i.e., beyond tC adsorption leads to a decrease in chemical potential and, therefore, becomes spontaneous [81]. This sort of adsorption mech- anism, nevertheless, requires extremely high, negative adsorbate pres- sures, due to the formation of curved surfaces of tension. To form isothermally a number of menisci having relatively high surface tensions and having a large total surface area, considerable pv work must be done on the system to cause condensation and to form the large excess Helm~ holtz potential of these surfaces of tension [F1, p. 56]. /////// Figure 3.2. a) Cylindrical meniscus; b) hemispherical meniscus. From the above discussion it would seem that adsorption along increasing pressure paths is essentially a multilayer adsorption phenom- enon with normal adsorbate-gas interfaces (rather than curved surfaces of tension). The pressure in the adsorbate is positive, being extremely large in regions close to the solid surface where the gas-solid pertur- bation energy (Up(z)) is significant, and decreasing rapidly with dis- tance z from the pore wall (Up(z)wumfioa .m> sz onAOmwm ucsoem ”mommnm How mofififlm pom ShoguOmfi :ofiumhomc< .m.m ohswfim o.H .o 4 N . A r oumeflumo wouuflm o>p=u C) m M ‘— UHQHM CZ 000 o o ADV w >0; u>< Ema figs .33.: MS i 3%. E S .amm .10.. 9 3 p. X .00 T. AU no 42 .07? .06. ">2 I Cl .05 >. c-l '04’ Slope = [ymc] = .1383 .03» Intercept = ———-= .01575 Ymc .02 c = 9.781 .01 b ym = 8.491 0 1 . . i O O l 2.2 0.3 0.4 X = P/PS Figure 3.4. B.E.T. plot x/y(l-x) vs. x for Silica Gel S-2509. 70- CA S g 60’ "-4 -o m ‘3‘ 50» o 5.4 o D. 40» A Reference [D4] .1 k’—*’ 6: <3 b N O 10’ This work # A L 4 p Figure 3.5. 8 10 mz/g x 10-2 4 6 1’ " A (specific area) Comparison of A with available literature. 43 where Vm = internal pore volume of gel From the experiments conducted in this work for S-2509 gel, ~ .70 cc . ~ gm_ ~ 0 Vm - gm adsorbent (u51ng pHgO — 1 CC), and hence rm - 30.7 A . Dushenko et al. [D4] have conducted a careful investigation of the interaction of moisture with four different silica gels (with varying mean pore diameters). Figure 3.5 is a plot of B.E.T. surface area vs. mean pore diameter for the four gels. Note that the area and mean pore radius obtained from this work fits quite well with their work. The pore size distribution of capillary porous materials can be obtained fairly easily by the application of the Kelvin equation to the desorption branches of the isotherms. With silica gels the distributions are generally quite narrow, indicating that pores with diameters equal to the mean pore diameter are of the dominant variety. 3.1(b) Estimation of 'Bound' Water and 'Capillary-Condensed' Water in Silica Gel Both dielectric studies [K1] and calorimetric studies [P4] have demonstrated that water adsorbed on the surface of silica gel exists in three distinct states. The first is the monolayer-adsorbed water; the second is the 'bound' or 'adsorbed' water (which, in a sense, has greater degree of freedom of rotation, yet is bound or influenced by the solid surface forces); and finally, the capillary-condensed water which has most of the essential qualities of free, bulk water. Panchenko et a1. [P4] have conducted calorimetric experiments to determine the bound energy TAS of the adsorption bond given by TAS = AU - AF 44 where T = temperature AS entropy of the bond between moisture and specimen AU = internal energy of the bond between moisture and specimen determined as the difference between the specific heat of isothermal evaporation of moisture and that of free water at the same temperature AF = free energy of the bond determined from the desorption branches of the isotherms for various temperatures and moisture content levels Figure 3.6 illustrates the variation of the ratio TAS/AU as a function of the moisture content for four different silica gels [D4]. TAS 12 Y // %— r-""""". ----- Corresponds to 1 approximate transition of adsorptive to capillary-condensed adsorbate KSM-S 0.4 1 M2 S-A 0 0 32 64 96 U Figure 3.6. Ratio of bound energy to internal energy differentials (TAS/AU) of a moisture bond as a function of the moisture content in four silica gels: l) 2930 K, 2) 3080 K. 45 Figure 3.6 shows very clearly the transition of one form of mois- ture bond to another; i.e., the energy fraction differential TAS/AU is very sensitive to the change of forces (adsorptive into capillary) which retain moisture in a colloidal dispersion. Dielectric studies of water- vapor adsorption on silica gel have also confirmed this observation [K1]. Figure 3.7(a) gives a plot of the bound water vs. mean pore radius for the four silica gels investigated in [D4,P4]. Using rm = 30.7 A0 for the silica gel sample S-2509 used here, one gets bound water = 13.9 gms/lOO gms adsorbent Hence, water adsorbed beyond the monolayer is = (13.9-6.49) = 7.41 gms/100 gms adsorbent, or approximately a second layer. The fact that adsorbed water only extends to about two layers of adsorbate con- firms the hypothesis that surface forces extend only to the first few layers adsorbed. Figure 3.7(b) gives the variation of monolayer—adsorbed water (gms/gm adsorbent) with the average pore radius in the four silica gels [D4]. Estimates obtained for Silica Gel S-2509 fit reasonably well with the curve obtained. The object of estimating the monolayer adsorbed water, the bound water and the remaining capillary-condensed water (70-l3.9 = 56.1 gms/ gm adsorbent) will become clear when these transitions are used to esti- mate the polarizabilities of the various 'water qualities' in Chapter 4. 3.2 Surface and Volume Flow in Porous Media The basic mechanisms for gas flow in capillaries include molecular streaming (Knudsen flow), streamline or viscous flow (Poiseuille flow), turbulent flow, and orifice flow. The last two, namely, turbulent flow (high velocities) and orifice flow (smooth, short capillaries), are 46 O‘ 0 U1 0 This work A O ——/&——-Pore Radius (A0) '5’ 8 ' 1 l I I I l I l l l I l l I l l H O p—————-——- O 4 8 12 16 20 W 0 Bound Water 6(W) Figure 3.7(a). Bound water vs. mean pore diameter [D4]. 60. SO- 20’ This work ——-——¢-——- Pore Radius (A0) M O 9’ 10’ O 4 A 4 J x 0 4 8 12 16 20 ————¢——-.— gms adsorbed ym gm adsorbent Figure 3.7(b). Monolayer amount adsorbed vs. mean pore diameter [D4]. 47 relatively unimportant in porous media. Molecular streaming represents a limiting situation in which the mean-free path A_of the flowing molecules is much greater than either the diameter or the length of the capillary [B5]. The mean—free path of gaseous molecules at 1 atm and room temperature lies between 500 A0 and 1000 A0. Thus, in capillary tubes narrower than 500 A0, Knudsen diffu- sion is expected to be predominant. If the average time that molecules colliding with the wall spend at the wall,'r,were taken to be zero, then the diffusion coefficient D is given by [DS] D = ——- (3.7) where d = diameter of capillary — 8RT 1/2 u = mean velocity of gas molecule = 757 M = molecular weight T is generally of the form [D5, p. 30] T = To exp(Q/RT) (3.8) where To = time of oscillation of the molecules in the adsorbed state (10'12 to 10‘1“ secs) Q = heat of adsorption The adsorption time T is usually very significant and the diffusion coefficient is much reduced according to the relation [D5] 2dzfi' D = 6(d451) (3.9) 48 During the time T, if surface migration is possible, then the diffusion coefficient is enhanced. Two main mechanisms for surface diffusion have been postulated. Clausing [C2] considered a two- dimensional diffusion caused by surface migration. In his model the diffusion coefficient is given by 2d23+ 31E,“ (U) 2 D = __ (3.10) 6(d+ut) where E5 is the mean-free path on the surface. If the molecules of the two-dimensional gas behave as 'hopping' molecules, the diffusion coefficient is given by [D5] 2d2_' 2_’ ' u+3ta u/ZT (3.11) 6(d+UT) D: _ c where a is the hopping distance (2 3x10 8 cm) and T is the lingering time given by [D5, p. 96] I T = To' exp(AQa/RT) (3.12) I - with To being similar to To described above (2 10 13 secs), and AQa being the energy of activation for hopping (some fraction of heat of adsorption). In this work the hopping mechanism shall be adopted as indicative of the surface diffusion of water-vapor molecules in capillary porous silica gel.+ ~ +When the gas flow is by Knudsen diffusion, the 'random' or the 'mechan— iJStic' hopping model has been most widely used [G3,H5,P18,S7,W3,T3] to describe the surface flow mechanism. 49 .JZ = CV = -C>\E (3.13) where C is the concentration of the diffusing species. For a model capillary, an open, cylindrical one is considered in Figure 3.8, shown below. k l--Knudsen diffusion W 2--surface diffusion 3--volume or bulk flow —-—- W Figure 3.8. Model capillary. Transport in such a capillary can occur in the following ways [B5,DS]: l) Knudsen diffusion brought about by molecules banging against the capillary walls, then bouncing back, and so on; 2) Knudsen diffusion with simultaneous surface diffusion (by, say, the hopping mechanism) during the time intervals T in which the diffusing molecules are tempo- rarily adsorbed; and finally, 3) simultaneous bulk volume flow due to pressure gradients in the adsorbed layers. For gaseous diffusion at constant T (no external fields) du = vdp As already pointed out in Section (3.1) surface diffusion totally dominates the gas phase diffusion phenomena. Hence, dus = vsdpS where v5 = specific volume of surface adsorbed molecules, and dpS = pressure differential along surface for 'hopping' molecules. From (3.13L then, 50 For water-vapor adsorption Q = 10 Kcal/gmole, AQa = 2.0 Kcal/gmole (estimate) and from equations (3.08) and (3.12) - v _ - 2x10 5 secs; T = 2.9x10 12 secs ,4 2 for I? E’ 5.87x10“ cm/sec For a capillary with diameter d 2 60x10“8 cm, one can see from estimating the magnitudes of the first and second terms in equation (3.11) that the surface diffusion contribution to D far exceeds the Knudsenian diffusion term. Thus, surface diffusion by either the hop- ping mechanism, or any other mechanism, usually fully accounts for the diffusion coefficient in capillaries when adsorption in the pore is sig- nificant. 3.2(a) Theoretical Formulation for Surface and Volume Flow The penetration of molecules into micro-capillaries may be treated as a diffusion problem. The irreversible thermodynamic formulation to describe the transport process is as follows. For a single substance diffusing in an immobile medium, if the force acting per molecule is proportional to the chemical potential dU gradient -255’ the average drift velocity of the molecule is - d_u v — -Adz where A is the phenomenological coefficient. Then the total flux in the z direction is given by 51 J52 = —CAvS E33 (3.14) dz At this point, one needs to take a closer look at two things: first, what is the pressure gradient that the surface-hopping molecules experience?, and second, what is the concentration of these hOpping molecules? The pressure in the adsorbed layers, over and above that due to ordinary intermolecular attractions, arises from the gas-solid pertur- bation energy Up(£) [81]. As mentioned earlier, this energy may be neglected beyond the first few adsorbed layers. The pressures in the first and second layer are, however, extremely large. From the discus- sion in Section 3.1(a), it seems reasonable to assume that beyond the 'bound' layers the pressure exerted on the hopping molecules in the layer farthest from the solid surface is about the same as the gas- phase pressure, and the pressure gradient for the surface-diffusing mol- ecules is the same as it would be in the gaseous phase. Thus, dps z dpg z %}-dcg for C5 > csb where Cg concentration of diffusing species in gas phase concentration of adsorbate 'bound' to surface. Csb The concentration of the hopping molecules may be taken as being proportional to the gas-phase concentration Cg. This is true as the number of molecules hitting any surface is proportional to the partial pressure of that species in the gas phase [D5] and is much larger than the rate at which the molecules are adsorbed. Thus, 52 C 2 KCg (K = constant) and from (3.14) we then have dC ~_ BI.._& Jsz — KACgvS N1 dz (3.15a) = -D dC s__3. dz (3.15b) where the surface diffusion coefficient Ds is defined as _ _R_T_ -' Ds - KAvs bl Cg - K Cg (3.16) Equation (3.15b) suggests that the diffusion of molecules along the surface of adsorbate in capillaries may be given by a Fickian model, with the diffusion coefficient dependent on the gas—phase concentration. For bulk volume flow in adsorbed layers, the most general form of Darcy's equation for a homogeneous fluid may be written [BS] K10 c111c JC = T —d-Z— (3.17) where duC = vcdpC , with vC = specific volume of adsorbate dpC = average pressure differential in adsorbed layer K = coefficient (empirical) p = density of fluid n = viscosity of fluid 53 Thus, J = ——— v ———- (3.18) The average pressure gradient in the adsorbed layers is very large. However, most of the large pressures are very close to the solid surface with the layers farthest from the surface experiencing a pressure simi— lar to that in the bulk fluid at the given temperature [F1]. In attempt- ing to fit the theoretical concepts with the data obtained from the experiments with silica gel (in Chapter VI), the contribution to the overall mass transfer in fine pores from bulk volume flow was found to be very small. This may be attributed to the more ordered structure of the adsorbed species [Kl], as also due to strong solid-adsorbate inter- actions in the silica gel-H20 system. Of course, as saturation is reached and the cross-sectional area for gaseous diffusion gets to be exceedingly small, bulk volume flow achieves increasing importance in the mass transfer phenomena. 3.3 Irreversible Thermodynamic Formulation Extended to Porous Media in External Electric Fields The Gibbs-Duhem equation for polarized systems has been derived in Section 2.1(c): grad p - E°grad E — ng grad E; = 0 (2.12) For a single-component system one may write the '2' component of equa- tion (2.12) as 54 where e d —-d§ JZ = -Ac v i - P- (3.19) For surface diffusion in a cylindrical pore dC dE e z - El __8 - _M_ . + st KACgvs M d2 RT .1: dz] (3'20) and from (3.16) and (2.0) (3.21) dC M eO(€ -1) dE2 J : -D _g _ _ :— ___: z 5 dz RT 2 dz In equation (3.21) a few of the terms need further elucidation. Es is the dielectric strength of the surface adsorbed molecules. E rep- resents the field that the hopping molecules see during their motion. As the hopping molecules are neither in the bulk adsorbate phase or fully in the gas phase, the exact magnitude of E is difficult to estimate. In this work 5 is assumed to be the field estimated (in Chapter IV) in the gas phase 58' The term p in (3.19) stands for the Kelvin pressure. However, as pointed out in Chapter II, for fields E‘s 1x10“ V/cm (rough estimate for values of 58 in the silica gel bed from Chapter IV) the pressure remains fairly unaffected and the ideal gas relation pg==Cg‘%; holds. Similarly, for the bulk volume flow in a pore -K1p dpC __dE J - ———-v - P- T 2 n C dz .+ dz (3.22) -K1 dp dE .. ___ 13,—) T] d2 «)dZ In (3.22) the electric field E = EC’ or the field in the adsorbed phase. Also, dpC = pressure differential in the adsorbate. As EC < Eg+ and dpC > dpg, one can easily see that the E field-induced effects will be much larger in the case of surface diffusion than for volume flow. Further clarification (fifthis and other field related observations made up to this point will be dealt with in Chapter V. The various physical characteristics of silica gel necessary to evaluate the theoretical model presented in Chapter VI have been esti- mated in this chapter. The fundamental relationships for the mass fluxes, with and without the applied electric fields, have been derived for cap- illary porous adsorbents. Once the various internal and external elec- tric fields have been estimated in the next chapter, all necessary information for solving the mathematical model proposed in Chapter VI becomes available. +The field in a dielectric in contact with air or vacuum is always lesser in intensity than the field in the latter. CHAPTER IV ESTIMATION OF ELECTRIC FIELDS IN DIELECTRIC MEDIA The Kelvin Ponderomotive Force was defined in Chapter II as F = P-VE (2.19) ++ where P = 60(e-l)§ is the polarization of the medium and V5 is the gradient of the electric field (a tensor). It seems imperative, then, that in the absence of any real charges or ions in the system a non-uniform field distribution (at least locally) needs to exist in order for the above force to be effective. Non- uniform fields are created by various configurations, both of the elec- trodes and the adsorbent system under investigation. In this chapter the various electric field distributions encountered for the several electrode and adsorbent sample geometries are briefly described. Com- parisons are made of the relative magnitudes of the ponderomotive forces in each case. Detailed derivations are worked out in Appendix A. In Section 4.2 a popular method for estimating the dielectric properties of crystalline powders and the electric fields in the various phases of an adsorbent-adsorbate system is outlined. In Section 4.3 the phenomenon of relaxation fields, as encountered in moist capillary porous silica gel, is postulated by this author. Numerical estimates for the 'internal' field distribution are also given. 56 57 4.1 The Electrostatic Field in Dielectric Media Six major field configurations are described in this section. The first four refer to experiments conducted in this work, and the last two have direct bearing on the fly ash situation in ESPs. 4.1(a) Bed of Particles in Uniform External Field Figure 4.1 describes a bed of homogeneous (or near homogeneous), disperse dielectric placed in a uniform, external electric field. [7/l7/////]///[[LbQ7£A———1 r AV --- —r Figure 4.1. Bed of particles in uniform field. If the particles are fairly small and the bed has fairly uniform dielectric properties (even during adsorption), the field in the bed is uniform and is given by AV Ebed = E3137- (4-1) a = dielectric constant of the bed AV = voltage applied between parallel plate electrodes di = inter-electrode distance E2 = unit vector in z direction For typical values used in this work of AV = 10 KV, d 2 2.5 inches and e = 2 (dry silica gel) If dielect' multila; dependil in the 1 parts of uniform. used as field co 4.101) . ~L~—.:;_ Sphe k‘een a p; the Sphex The much Tedu 58 E 2 .79(KV/cm) + If only monolayer adsorption is known to take place, then the dielectric properties in the bed will change very little. If, however, multilayer adsorption and/or condensation is known to occur, then, depending on the adsorbate characteristics and the diffusion resistances in the bed, the adsorbate concentrations can differ widely in various parts of the bed and concurrently, the internal field can become non- uniform. In this work crushed alumina, silica gel and fly ash were used as adsorbents and water—vapor as adsorbate for this particular field configuration with AV = 10 KV and dit=2.5 inches. 4.1(b) Spherical Beads in Uniform External Field Spherical, catalyst-grade, porous alumina particles are placed bet— ween a parallel plate capacitor. The field in the immediate vicinity of the spherical particle is non-uniform (see Figure 4.2 below). 1]! IHHHH [HHHH Figure 4.2. Dielectric sphere in uniform field. The Kelvin force on a dipole molecule of moment p (at the particle surface) is given by (see Appendix A.l) fr=R = (lieff'VE) |r=R which reduces to 59 2 -3(€-l E0“ . fR = —IUEP2 x E€+232 x (2€Cosze-Sin26) (4.2) where E0 = applied field 0 = polar angle 8 = dielectric constant of particle uZE _ . . _ —) ”eff — effective dipole moment - 3kT' I? For a = 5, E0 (10 KV/2.5"), u = 6.18x10_28 Ccm, T = 2980 K, k = 1.38x1o'23 CV/°l( fR = -3.8xlO-23x f(0,e) (Newtons) where f(e,e) 26C0520-Sin26. For 6 = 5, f(0,€) is given below: 6 O 30 6O 90 120 1 18 (deg.) 50 O f(0,€) 10.0 7.25 1.75 -1.0 1.75 7.25 10.0 i The average gradient of the field squaredT is given by favg (V52) 2 R = 9.37xlO7(V2/cm3) avg u2/6kT at r=R Also E = E x -—§—- ’ +2 +0 (8+2) The internal field E2 is uniform and ceases to be so only when sig- _) nificant adsorption can take place in the particle and the adsorbate 1”In all comparisons of electric fields the gradient of the field squared, VEZ, is taken, as the ponderomotive force is given by F = €o(€-l)VE2/2. ltd-IL; 60 concentration decreases significantly as the center of the sphere is reached. For porous alumina particles with fine pores, the field in the particle may be expected to be uniform. 4.1(e) Annular Sample Configuration in Cylindrical Field An annular pan (made of metallic screen material) containing the disperse, dielectric specimen was placed concentric with a cylindrical wire—cylinder electrode system (see Figure 4.3 below). —-~—_———~—- (114—.1. Figure 4.3. Annular sample pan in cylindrical field. The electrical field distribution has radial symmetry and the gra- dient of the field squared in the adsorbent phase 'a' for this geometry is given by (see Appendix A.2) 2 VE2 = dE2 = (Vz-Vl) 2 dr -(lnR2/R1)2x'r3 (4'3) where 8 AV R o ’R R a 1 — ln(R1/Ri) a /ln{[§3} [—1-$% } 1 < l < II R 2 1n{(R1/Ri)AV (Rz/RO)V1}/ln E; 1 AV = voltage applied across electrodes Ea = dielectric constant of adsorbent 50 = dielectric constant of air (or vacuum) 2 1 R1, R1, R2, and R0 are described in Figure 4.3 .75 cm and For AV = 6000 v, ea 2 3, R1 = .0794 cm, R1 = .3 cm, R2 R0 = 1.25 cm -2 VB2 = (932.23)2 x-;§(VQ/cm3) and 2 ~ 7 2 3 VEavg — -l.47lx10 (V /cm ) The field here is non-uniform and depends on the radius r. However, as can be seen from the expression for VEZ, most of the non-uniformity is around the central electrode, and therefore, does not involve the cylindrical annular sample holder. 4.1(d) Cylindrical Bed of Dielectric Specimen Coaxial with Cylindrical Electrode Geometry The sample pan containing the adsorbate is cylindrical in shape, with a fine wire running through its axis and base. The wire serves as the ground electrode and a surrounding cylindrical screen serves as the H.V. electrode (see Figure 4.4). 62 ___—_-——q Figure 4.4. Cylindrical sample bed coaxial with cylindrical field. Once again, the field is radial in nature with the gradient of the field squared, given by (see Appendix A.3) 2 2 vs; = dEr _ (AV) 2 IE7 '(1nR'/Ri+e;a1nRO/R‘)2'“3 (4 4) H I For AV 2 6000 V, Ri = .0089 cm, R = .16 cm, R0 = 1.25 cm, Ca 2 1.50 (for dry silica gel) VE2 2 -2.02x106/r3(V2/cm3) and VE2 2 -l.68x101°(V2/cm3) avg The average gradient of the field squared in this geometry is seen to be about three orders of magnitude greater than in the annular geom- etry of Figure 4.3. The central electrode is a fine wire, thus account- ing for high fields and field gradients in its immediate vicinity. The average field strength in this geometry for the above parameters and a Of course, as adsorption proceeds, the fields (especially in the case of porous silica gel) get exceedingly complex, varying all along 63 a single internal pore. A method to estimate the internal pore fields during adsorption is proposed in Sections 4.2 and 4.3. 4.1(e) Charged Spherical Particles in Uniform Field Fly ash particulates encountered in an ESP are charged to satura- tion by a stream of ions. The field around a fully-charged particle is shown in the figure below. Figure 4.5. Charged particle in uni- form external field. The field on the particle surface for n/Z §_0 5_n is zero (due to opposing effects of the surface charge and the applied field), while the field on the surfacefor'0_g 0 < n/2 is given by [R1, p. 199] e-l Ro3 qs E — EOCOSB [2[€+2];§ + I] + W (4.5) where q5 = maximum free charge on particle = 12(€/€+2)TTEOR02Eo c = dielectric constant of particle 64 R 0 particle radius EO charging field For R0 2 20x10-6 m, E0 = 3x103 V/cm, e 2 4 (typical values for fly ash particulates in ESPs) avg E 2 9.82x103(V/cm) r=RO and 2 avg SEE 2 1.79x1011(v2/cm3) dI‘ r=RO Thus, though the field at the particle surface is not very signifi- cant, the gradient of the field squared is quite steep. A surface adsorbed dipole molecule (dipole moment us) on this charged particle will experience an additional binding force f = ps°dE/dr due to the field gradient. 4.1(f) Bed of Spherical Particulates Subject to Uniform External Field A bed of fly ash particulates may be assumed to consist of spherical particles neatly arranged in a cubic array. If such a bed is subject to a uniform external electric field, the typical interparticle contact (shown below) will experience very high non-uniform fields in its immedi- ate vicinity [M2,82]. The electric field along the plane of contact (in direction r) is estimated to be [$2] (B_Z 1.0) (4.7) where 65 V = voltage drop per contact a = radius of contact circle R0 = radius of particle B = r/a (dimensionless distance, 8 Z_1) Figure 4.6. Interparticle contact characteristics. Using typical values encountered in an ESP Ro/a = 100, V = 12.5 volts/contact, a = .10x10-6 m, one obtains the following field distri- bution B + 2 5 10 20 50 100 Er 8.3x107 1.0x107 2.5x106 6.3x105 1x105 2.5x10“ (V/cm) 2 dBr 1.85x1021 9.04x1o18 2.58x1017 7.87x1015 8.0x1013 2.5x1012 (Vz/cm3) dr A field intensity of 5x105 V/cm is of the order of the breakdown strength of air, and consequently, field intensities > 5x10s V/cm (for B 5_22) imply a 'gap charge emission' phenomena. This breakdown is res- ponsible for the non-linear current-voltage characteristics observed with a bed of fly ash [M2]. The field intensity ES(0) along the particle surface has also been + estimz where the f0. 4.6). In Solid p to eSti all mac aSSumpt 66 estimated as [82] 55(6) = Ea/(-(ln E33-)Sin28) (4.8) where Ea layer average field = AV/h AV voltage drop across an ash layer of thickness h Using typical values AV = 2 KV, h = .32 cm, RO/a = 100, one gets the following field variations along the particle surface (see Figure 4.6). e 3 1 5 10 40 90 (deg-) §s(e) 3.8x106 1.5x105 3.9x10“ 2.9x103 1.2x103 (V/cm) 1aegm) 0"?T 3.44x1018 1.1x1015 3.47x1013 3.89x101° 0.0 (V2/cm3) 0 4.2 Dielectric Properties of Crystalline Powders In an adsorbate-adsorbent system, there exists three phases: the solid phase, the adsorbate phase and the gaseous phase. The procedure to estimate the dielectric properties of the three phases and the over- all macroscopic dielectric constant for the powder involves certain assumptions. The method of Bottcher [B6] (in particular, its extension as developed by McIntosh and his associates [M2,M4]) is considered to be most easily adapted to heterogeneous adsorptive systems. Bottcher's method is based on the following assumptions [M3, p. 12- 17]: 1) The average internal field in the heterogeneous dielectric, and in any phase thereof, is given by the factor (c+2)/3 times the macro- sc0pic field. e is the appropriate dielectric constant. I‘J vidual 1 a) bv addir polar122 internal 5) usual f: field, 1 dielect: 6) adsorbat Frc retiCal Where tl gaseous 67 2) The average internal field is given by the addition of the indi- vidual internal fields on a volume-fraction basis. 3) The overall polarization of the composite system is also given by adding the individual polarizations on a volume-fraction basis. 4) The polarization of each phase is related to its volume average polarizability by the relation Pi = ciEi, where Ei is the average internal field of the ith phase. 5) The macroscopic field in voids or interstices is given by the usual formula for spherical voids, E = 38/(2€+€3) times the applied 3 field, where 6 refers to the composite dielectric constant and £3 to the dielectric constant of the interstices. 6) The average field within the solid phase does not alter with adsorbate concentration in the composite system. From the above assumptions, all of which are based on some theo- retical basis, the following equations are obtained: I I E(€+2) = E1 01 + E2 62 + E3 63 (4.9) 3 I I I E(e-l) = C15151 + c262E2 + c363E3 (4.10) 40 where the subscripts l, 2, and 3 refer to the solid, adsorbate, and gaseous matter, respectively. 5i = volume fraction of ith phase I £1 = average internal field in phase i given by E1. = (81+2)Ei (Ei = macroscopic field in phase 1) 3 c the average polarizability in the ith phase, is given by is 68 3(ei-l) Ci = 4n(€i+2) (4.11) From equation (4.10) one has for the initial condition (62==0 or no adsorbate) o 61E1 = (e -l)E/4'rTc1 (4.12) since 62 = 0 and c3 2 0 (polarizability of gas phase 2 0). 60 = dielectric constant of composite material when 62==0 Thus, from assumption (6), when the applied field is E, the field in the solid phase is always given by (4.12), irrespective of whether 62 = 0 or not. In cases where E itself is decreasing with adsorption, _) an additional assumption that equation (4.12) still holds is made here. From (4.9) and (4.10) and with the help of (4.12), one arrives at the relation (2+2) 3353 _ (e°-1) , (e-e°) 3 ’(2e+1)’ 4nc1 4pc (4.13) 2 where 83 has been taken to be 2 1 (gas phase). Thus, a knowledge of the variation of the composite dielectric constant e as a function of the amount adsorbed, and of 61, the solid dielectric constant, yields 82, the average dielectric constant of the adsorbate phase. Conversely, if the permittivity of the adsorbed phase is known, an approximate estimate of the overall dielectric constant may be obtained. Once the dielectric constants are obtained, the evaluation of the average fields in the various phases can be easily carried out from equations (4.9), (4.10) and (4.12). If the adsorbed phase is a multi- layer, very often distinct phases in the adsorbed phase are known to 69 exist (see Section 4.3). In such a case, equations (4.9) and (4.10) may be reapplied to the adsorbed phase to yield the electric fields in the respective adsorbed intra-phases.+ The electric fields in equations (4.9) and (4.10) are, in general, not uniform. For example, if one wishes to estimate the dielectric properties of a powder subjected to a cylindrical external field, the overall macroscopic field becomes radial in nature (as seen in Section 4.1(c)). The local fields depend on both the overall field and the local environment. In the next section an approximate methodology for estimating the local and global electric fields as a function of applied voltage, adsorption amount and powder characteristics is proposed. 4.3 Relaxation Fields: Estimation of Electric Fields in Moist, Capillary Porous Silica Gel Due to the cylindrical shapes of pores in silica gel, and the rather long, narrow pore structures, the adsorption of water vapor in silica gel may be represented by diffusion-controlled mass transfer phenomena in open, cylindrical pores (see Figure 4.7 below): W/fl/W _. A‘— Figure 4.7. Single cylindrical open pore with adsorbate. v +Calculations show that this procedure yields almost the same values for the average field as when equations (4.9) and (4.10) were not reapplied. 1.- 'I) tend to center. monolay and tap vary al existin 4.3(a) Th the ear amFl al tign of with am this W0 70 As adsorption is taking place, the regions close to the pore mouths tend to have a greater concentration of adsorbate than those deep in the center. Owing to the different dielectric constants associated with monolayer adsorbate, bound layer adsorbate, condensed layer adsorbate and vapor phase adsorbate (to be seen shortly), the local fields will vary all along the pore. In general, the fields at the pore mouths will be smaller (due to higher average dielectric constants) than the fields at the middle of the pore. Consequently, a local field gradient is set up with the gradient pointing towards the center of the pore. This field gradient, and the corresponding ponderomotive force, will vary continu- ously with the adsorption process. Thus, the fields in the pore will, so to say, relax with the progress of adsorption. In this work, it is seen that the internal field gradients produced by such relaxation, though depending on the magnitude of the overall external applied field are, nevertheless, much larger than the macroscopic field gradients existing in the bulk adsorbent sample. 4.3(a) Dielectric Constant of Adsorbed Water in Silica Gel The dielectric behavior of porous adsorbents has been studied since the early 19405. Higuti [H1] examined the behavior of n-propyl and iso- amyl alcohols adsorbed in titanium oxide gel. In Figure 4.8 the varia- tion of the capacitance (or dielectric constant) of the porous sample, with amount adsorbed, is shown. Three linear regions were reported in this work. m 71 2.5 I I I l I 2.0- AC (arbitrary units) / 1 1 1 L 0 50 100 150 200 250 300 Amount Adsorbed, mg/g Frequency, 1.5 Mcps Figure 4.8. n-propyl alcohol- titania gel system. Kurosaki [K1] investigated the silica gel-water system. He also reported three linear regions for the variation of sample dielectric constant with amount adsorbed (see Figure 4.9). The discontinuity in the slope from the first to the second region is considered by most to be proof that the monolayer has been completed [M3, p. 67]. The third linear region is not observed with most adsorbates. With water vapor adsorbed on silica gel, Kurosaki has given as a possible explanation the existence of very strongly developed hydrogen bonds in the adsorbate for this third linear region. All researchers agree that the plots are linear. This experimental result shows that the dielectric property of an amount of adsorbate added is independent of the amount already pres- ent [M3, p. 67], which then implies that the adsorbate in the two or three regions described above have more or less uniform dielectric con- stants (at least within a linear region). 72 I w i g 1 :3 2.6~ I - I m I I ' 5 2 4 I I I L.) b | . 3 n—l :1: 42—— 3—F: t.) 2.2. I : g I . v—4 | 0 .2 2.0 I . 1 e I I ; g 1.8 I I z 8 I | . 8: I ' <1 1.6 ' : ; I 1.4 I i O l. 1 4 l J 4 O 20 4O 6O 80 100 120 Water Content (mg/g) Figure 4.9. Relations between dielec— tric constants and sorbed amount of water (25° C): A. 5001«:;B. 1,000 kc. The Onsager-Kirkwood formula [K2] yields the following relationship between the specific polarization of a substance Pk and its dielectric constant e p _ (€—l)(2€+1) k - 98p (4.14) p = density of substance When water is adsorbed on to, say, silica gel, the differential specific polarization of water can be shown [Kl] to be 3- = ifk_= (282+1)(3€/3W) W SW 9820 (4.15) where 73 AW = small amount of water added to the composite dielectric e = dielectric constant of composite dielectric p 2 density of moist composite dielectric P; = differential specific polarization of adsorbed water Using the experimental results obtained in the silica gel-H20 vapor system Kurosaki has obtained for the three regions described above Region 1 Region 2 Region 3 P' 2 1 8-11 2 23 w If one uses the Onsager-Kirkwood formula for the adsorbate only (an assumption), one then obtains a rough estimate for the adsorbate dielectric constants Es Region 1 Region 2 Region 3 Es 2 1.05 243.26 2 104 The dielectric constant of pure liquid water at 250 C is 2 80, and of pure ice 2 100. Thus, region 3 corresponds to an 'ice-like structure' arising from tightly bonded 'clusters' of water molecules [Kl]. Similar ice—like structures have been observed with water-vapor adsorbed on a — Fe203 [21]. In this work the transition from region 2 to 3 will be taken to imply that adsorptive forces (bound layer) have been converted to bulk liquid intermolecular forces (condensed layer). This fits very well the numerical estimates of Kurosaki's work and the estimates of bound water in Figure 3.7(a). Zettlemoyer [Z1,22] has suggested a doubly hydrogen bonded monolayer, singly bonded second layer and ordered 'ice- like' multilayer for water adsorbed on oxide surfaces, which is consis- tent with the analysis presented here. 74 4.3(b) Strategypfor Internal Field Calculations Detailed numerical calculations are described in Appendix B. The procedure outlined below (estimating local fields) is divided into two parts. Part I To Obtain Overall Dielectric Constant and Electric Field 1) Knowing W (gms adsorbed/gm adsorbent), the assumption that the water is adsorbed uniformly in the whole silica gel bed is made. Next, the average dielectric constant of adsorbate (volume average of the three layers) is estimated, and using equation (4.13), the average dielectric constant of each spherical silica gel particle, E = 8p, is obtained. 2) The whole bed is treated as composed of silica particles of dielectric constant 8p interspersed with air (see Figure 4.10). N '50 C 32%: 9 3‘28 . 0.. .Q H ‘ C 9‘ :r.‘ 003'}: fi *3! .1 1'1?! 0 2:8 'Lo Q ‘0 ‘ 2.129 {9 933 -fll0 HRH":- .1 o (1313' . $)‘. .. eb . 6‘ ‘~ C.‘ 69° . Qw' I :2 C .. 7“. ‘38 . . Figure 4.10. Spherical, porous dielectric particles in air; subjected to electric field. Using equation (4.13) with 41Tc1 = 3(ep-l)/(ep+2) and 41Tc2 = 0 (only two phases here), one gets 6, the overall dielectric constant of 75 the bed as a function of W. 3) The overall electric field for the field geometry shown in Figure 4.10 is obtained from equation (4.4) as AV E = x r (lnRo/Ri+€lnR/Ro) l ;' (4.4) Part II To Obtain Local Dielectric Constant and Local Field 4) The average macroscopic field in a particle, Ep, is obtained from applying equations (4.9) and (4.10). 5) As the adsorbate concentration is, in reality, non-uniform all along the particle (decreasing as the center of the particle is approached), the local field will be different from the average particle field. The field inside a spherical particle subjected to an external field E is given by (see Section 4.2) + E = -—§—— E (4.16) +p €p+2 + The assumption is made here that the local field Epi is related to the average field Ep in the particle by the relation .+ E ( . = + 4.17 +p1 2) §p(€p 2) ( ) E .‘I' 131 based on the above observation (equation 4.16). 6) Using Bottcher's method (equation 4.13) for a small local seg- ment, one can estimate Epi’ the local particle dielectric constant (knowing the local adsorbate concentration Ci)- Next, using Ep from (4) and Ep from(l) along with equation (4.17), the local average particle field E . is obta —>p1 76 ined. 7) Finally, by applying (4.9) and (4.10) to the small local section of adsorbent, E . +21 the gas phase, re The followin and E31, the local average fields in the adsorbate and + spectively, are estimated. g tables give some numerical estimates of the local and global fields calculated. Table stants 4.1. Estimates of Overall Dielectric Con- and Macroscopic Electric Fields as a Function of W for Silica Gel S-2509 and Water Vapor System w gngds €2an ep 5 Er (V) Epr (V) .10 15.88 3.53 2.08 837.2 678.7 .20 48.09 9.63 4.18 522.6 364.2 .30 66.73 19.94 7.39 331.71 211.9 .40 76.04 31.85 10.98 237.3 145.3 .50 81.65 44.12 14.63 182.0 108.9 .60 85.36 47.12 18.48 146.8 86.5 .70 88.03 70.11 22.30 123.1 71.8 av e 8 Table 4.1 11 bed rises with W, gms adsorbed/gm adsorbent dry average dielectric constant of adsorbed phase average overall dielectric constant of bed average overall electric field = g-(B = f(€)) radial position in bed average electric field in silica gel particle lustrates how the overall dielectric constant of the and correspondingly, how the field in the bed 77 decreases. The variation of a with W is approximately linear (within the respective adsorbate regions), which confirms the experimental observations made earlier. For a given W, Table 4.2 gives the adsorbate concentration profile in a typical pore (obtained from computer calculations in Chapter VI) and the corresponding Epi (local dielectric constant), Epi (local aver— age field), 521 (field in adsorbate) and E31 (field in vapor space in pore). . = gm adsorbed Table 4.2. Estlmates of Epi’ Epi’ E21, E3i for W .3085 gm adsorbent’ eavg = 20.95, (Epr)avg = 206.2 V (from Table 4.1) c + 0 .24 .25 .26 .49 .50 .51 Ci .9888 .3556 .3497 .3441 .2744 .2741 .274 epi 69.22 14.42 13.98 13.57 9.12 8.91 8.91 (Epir) 66.45 284.73 296.1 303.9 425.6 433.8 433.8 (Ezir) 85.02 263.8 281.7 292.4 396.5 392.8 392.8 (E3ir) 99.7 412.8 428.8 439.65 563.9 557.9 557.9 C = %, z = distance in pore, L = length of pore, Ci = dimensionless adsorbate concentration. Thus, when the amount of adsorbate in the silica gel bed is about 30.85 gm/lOO gm dry adsorbent, a typical pore will have the adsorbate phase and the gas phase field increasing towards the center of the pore (C 2 .50). All the fields up to now have been obtained as a product of E and r, the latter being the radial position in the bed of particles. To obtain an average estimate of the field distribution, r is taken to 78 correspond to the radial position of the average field squared . This is due to the ponderomotive force being defined as E = B'VEi = é-eo(€s-1)V|Ei|2 and the observation that by 'gradient of the field squared' (VEiZ) is .meant the gradient in the internal pore fields. The latter depend on the magnitudes of the overall field squared (E2) and not on the gradient of the overall field squared (VEZ). 4.3(c) Comparison of Internal Field Gradients and External Field Gradients For a cylindrical bed of silica gel subject to a cylindrical elec- trical field as in Figure (4.10), the gradient of the overall (field)2 is given by differentiating equation (4.4) 2 dEr = (AV)2 x 2 --' 2 "3 dr (lnRO/Ri+elnR/Ro) r (4.18) For R0 = .16 cm, Ri = .0089 cm, R = 1.25 cm, AV 2 6000 V, e = 7.70 and W = .3085, the average component of the ponderomotive force _ 60(6-1) gp? . . (F - 2 dr ) IS given by = 60002 x 4 dr (1n(.16/.0089)+7.7x1n(1.25/.16))2 (.167;.00897) 1 - 1 .0089 .16 OT 2 (92-) = 1.71x109(V2/cm3) dr overall For the internal field gradients, for example, at C = 0.25 (L==.Ol693 cm) from Table 4.2 (for same R0, Ri’ R, AV, e and W as above) 79 defii { 292.4 2 _ 263.8 2} dr .0667 7.0667 .02x.01693 = 1.06x101°(V2/cm3) and dE2. { 439.65 2 _ 412.8 2} 7.0667_ 7.0667 .02x.01693 = 1.519x101°(V2/em3) where ravg 2 .0667 cm is substituted for the radial position of the average field squared (see Appendix B.2). Thus, it can be seen that the internal field. gradients set up by the relaxing fields are much larger (one order of magnitude, in this case) than the overall external field gradients. In essence, then, it would seem that the field-induced effects should be observed in moist silica gel, even with uniform externally-applied electric fields of mag- nitudes comparable with those calculated for non-uniform fields. More on this in Chapter V, Section 5.6(b). CHAPTER V EXPERIMENTAL VERIFICATION OF FIELD-INDUCED MASS TRANSFER EFFECTS In this chapter the various experiments conducted in the M.S.U. laboratory to study the effects of both uniform and non-uniform, externally-applied electric fields are presented. In Section 5.1 a brief outline of the rationale that determined the sequence of experi- ments conducted is given. In Section 5.2 the apparatus used in these experiments, the schematic diagram and a step-by-step procedure for conducting the experiments are illustrated. Section 5.3 deals with the application of uniform electric fields to various adsorbents and adsor- bent geometries. In Section 5.4 the effects of non-uniform applied fields to several adsorbents are described in the context of water- vapor adsorption. Both 5.3 and 5.4 deal with a maximum of two to three layers of adsorbed gas. Section 5.5 involves multilayer adsorption and/or capillary condensation in porous silica gel in the presence of non-uniform, cylindrical fields. Section 5.6 covers various interesting sub-topics such as the adsorption of non-polar adsorbates, the field- induced effects on the desorption process in silica gel, the relative significance of internal and external field gradients, etc. Finally, in Section 5.7, preliminary experiments conducted with silica gels treated with concentrated HCl, and also impregnated with traces of K+ ions, are presented. 80 81 5.1 Rationale Behind the Order of Experiments At the outset of the experimental investigations, available liter- ature [P2] seemed to suggest that the kinetics of gas(polar)-solid adsorption was enhanced or depressed due to an additional electro- convective vapor-phase flux, defined in equation (1.4) as Je = D (u-VE) C (1.4) -> kT -> —> where p is the molecular dipole moment and a vector. For a gas not subjected to any external field, its effective dipole moment (even when the gas is polar, like water-vapor) is zero. When a fairly strong field is applied, however, the polar molecules assume an effective dipole moment in the direction of the field which for most laboratory fields encountered (E _<__1x106 V/cm) is given by [R5, p. 108] 2 _ U E Eeff — 3kT' (5'1) The magnitude of “eff for E of, say, 1x10“ (V/cm), is about four .+ orders of magnitude smaller than u itself, and numerical estimates of the electro-convective flux using “eff yield negligible increases over + the ordinary concentration gradient-driven diffusive fluxes, i.e. 101 NE) C/D pg kT +eff 3x << 1 Consequently, if the electro-convective flux of equation (1.4) above were indeed the correct mechanism for increased mass transfer rates, then the value of.p in this equation should be other than that of Eeff' Equation (5.1) is arrived at by assuming a Boltzmann distribution for the potential energy of permanent gas dipoles and estimating the average 82 value of the effective dipole moment (component in field direction) [R5, p. 107]. If, however, the time scale over which the force acting upon a dipole gas molecule is much smaller than the time scale over which an equilibrium Boltzmann distribution is applicable, then the instantaneous force on a dipole is much larger (as, then, =10 though ueff the direction of the force is absolutely random. This could conceivably lead to an increase in 'local turbulence,‘ and therefore an increase in the mass transfer rates. With these rather 'undeveloped' ideas in mind, the adsorption of water-vapor in individual, spherical, catalyst-grade alundum (A1203) particles in uniform external fields were initiated. Also, the adsorption of HZO—vapor in the same field in a bed of silica gel particles was studied to observe, if possible, any increases of mass transfer rates due to the presumed 'electro-turbulence' phenomenon. At this point all the experiments were conducted at a relative water-vapor pressure p/ps 2 2/3 (at which pressure no condensation is expected) and T=37° C. More experiments were undertaken with uniform fields applied across beds of alundum particles and crushed alumina. No significant effects were observed with the applied uniform fields under the above conditions. The kinetics of adsorption was next studied in cylindrical annular sample pans containing, mainly, crushed alumina particles (non- spherical). Cylindrical fields across a wire cylinder geometry were applied. The reasoning behind using an annular pan went as follows: the gradient of the electric field in a wire-cylinder geometry always points towards the central wire (see Figure 4.3 for geometry details). If the electro—convective flux given by equation (1.4) is indeed the correct transport mechanism, then, blocking the inner face of the annu- lar pan (see Figures 4.3 and 5.2(c)) would simulate a closed pore 83 adsorbent sample. Thus, according to reference [P2], this should lead to an acceleration of adsorption kinetics and an exponential equilibrium concentration distribution limited only by the Kelvin concentration for condensation. On the other hand, blocking the outer face of the pan should lead to a deceleration of the adsorption kinetics, due to the ponderomotive forces acting towards the mouth of the closed pore system (i.e., away from the sample). With both faces unblocked, only adsorp- tion kinetics should be affected and not the equilibria. In spite of the cylindrical fields imposed on the sample in annular pans, no appreciable changes in the adsorption kinetics or equilibria were observed, and it was concluded that somehow much higher fields and field gradients were essential before any effects could be expected. To this end, cylindrical sample pans with a fine metallic filament run- ning through their axis of symmetry were constructed. The fine wire was grounded when the pan was positioned directly over the grounded elec- trode. A cylindrical screen formed the High-Voltage electrode (see Figure 4.4). In this way, very high fields and field gradients exist- ing in the immediate vicinity of the filament electrode were utilized. Crushed alumina, porous glass, CaCO3 powder, alundum beads individually strung on the central filament, zeolite catalyst beads and 'drying grade' silica gel were used as adsorbents and water—vapor as adsorbate (with relative vapor pressures varying from 0.5 to 1) in this electrode- sample configuration. The extent of adsorption was as yet at most two or three layers. In spite of fairly high fields and field gradients employed, no discernible effects could be detected in either the rate of adsorption or the maximum hygroscopic moisture content in the various porous adsorbents, except drying grade silica gel. In the latter, small 84 increases in the rates of adsorption were observed, especially as the relative vapor pressure was increased towards p/pS 2 1. In order to conduct more careful investigations into the observed enhancements of adsorption rates in drying grade silica gel, highly porous samples of Silica Gel S-2509 and S-4l33 (from SIGMA Chemical Company) were pro- cured. Significant capillary condensation was observed in S-2509, owing to the large pore diameters. At this point, it was realized that multi- layer adsorption and/or condensation was essential to notice appreciable electric field-induced effects. Various related experiments were then carried out with Silica Gel S-2509 as adsorbent, and water-vapor (u = 1.85 debye) as adsorbate. Besides the field configurations men- tioned above, a point-plane field was also briefly tested in the adsorp- tion of water-vapor in crushed alumina particles. Finally, preliminary experiments were conducted with silica gel, first treated with HCl to remove any foreign ions in the gel, and next, treated with a saturated . . + . KCl solution to introduce some K ions. 5.2 Experimental Apparatus and Procedure The gravimetric method was adopted to study the gaseous adsorption + A CAHN of water-vapor in the various disperse, dielectric adsorbents. Gram Electrobalance (see Appendix D) was modified to perform remote weighing. Figure 5.1 is a schematic diagram illustrating the experimental +An indirect volumetric technique would probably have been better suited to conduct these experiments, especially in the light of the various problems associated with weighing a sample when the latter is subject to an electric field. However, the Gram Electrobalance was the only measur- ing equipment available at the outset. 85 set-up. A rectangular plexi-glass box served as the adsorption chamber. The chamber was immersed in a constant temperature water bath. The elec- trode geometry and sample pan configurations used in this work are des- cribed in Figure 5.1 and also in Figures 5.2(a), (b) and (c). The sample was suspended from the central hook of the electrobalance during weigh- ing. The balance was located directly above the chamber and outside the water bath. A 'Spellman' high voltage D.C. supply was used to provide the required voltage across the electrodes. A 'Simpson' ultra-high sen- sitivity multimeter was used to measure the leakage current through the electrodes. Dry nitrogen brought up to the bath temperature by heating coils was passed through two separate lines. The NZ passing through one remained dry as it entered the adsorption chamber, while the N2 passing through the other picked up moisture (became saturated with it) as it bubbled through pure distilled water contained in bubbling bottles. The relative flow rates could be adjusted to control the humidity of the entering N2 stream. Using the gravimetric method to measure the progress of adsorption in the presence of strong electric fields can cause innumerable 'back- ground' problems. The pan material, the string from which the pan is hung, the distance of pan from the electrodes, the pan geometries and charging characteristics, etc., all have to be taken into account for a 'background-free' reproducible reading. 'Strip Teeze' teflon tape (dielectric constant low) was found to be best suited to serve as the string on which the adsorbent sample was suspended. For the uniform field electrode geometry polystyrene foam (dielectric constant 2 l) was found to serve best as the sample pan without distorting the field Teflon Tape —" Electro- P Sample Pan 43“R> - IEJ‘vfl wi th '35.. :1}?! Adsorbent r“"‘ 86 Balance BNSSNGNRQN .1 v.--.,‘ «'1‘..\'» Adsorption Chamber {IL-_— 7 H.V. Supply _WéLtel Level- Dry N 2 Figure 5.1. Schematic diagram for experiments. Will/III. m1 W (a) Uniform Field (b) Cylindrical Field (E) cylindrical Fiel I l I I I l l L Figure 5.2. Sample pan configurations (other than that in Fig. 5.1) 87 characteristics. In the case of the cylindrical fields, metallic screen material formed concentric constant voltage surfaces, thus leaving the cylindrical applied fields unaffected. 5.2(a) Step-By-Step Procedure for Conducting Experiments The procedure followed in conducting all the experiments consisted of essentially two parts: Part 1 Preparation for Start of Experiment a) The water bath was filled with water until the entire adsorption chamber was submerged. The temperature control knob was set at the required bath temperature (either 250 C or 370 C in this work). b) The power to the microbalance was switched on and so was the current for the two N2 heaters. c) If the adsorbent was to be desorbed by passing dry N2 at the adsorption temperature (as for all cases except silica gel in this work), then dry N2 was passed into the adsorption chamber with the adsorbent in the sample pan. If silica gel was the adsorbent, the dry, water-free silica gel was removed from the oven (at 2 1100 C) and placed inside a dessicator at room temperature for about one-half hour prior to the start of an experiment. In this case, the N2 fed to the chamber (without the adsorbent but with the sample pan, etc.) was moist and of the same humid- ity as that required for the experiment. d) The microbalance was zeroed and calibrated and the adsorbent sample (or the sample pan only) allowed to come to temperature and con- centration equilibrium with the N2 environment (2 1 hour). e) The weight of the dry adsorbent sample (or the wet sample pan) 88 was recorded as the initial reading. Part 11 During the Experiments f) For the case with the dry adsorbent sample at time t = 0, the moist N2 was started through the bubblers and the required voltage applied across the electrodes. For the case of silica gel, the adsorbent sample pan was removed from the chamber and the dry, room temperature adsorbent immediately filled into the narrow, cylindrical sample pan. The pan was then lowered back into the wet adsorption chamber and the time recorded as t = 0. In both the cases, the field was applied only after the sample pan was unhooked from the balance and placed firmly in the required configuration. In the cylindrical field case, proper care was taken to ensure that the sample pan was concentric with the wire cylinder electrode geometry and that, in the case of the filament elec- trode, the latter was in good contact with the grounded terminal. g) For silica gel the reading on the balance was recorded after one minute, the pan unhooked and placed in the chamber securely, and then the H.V. started. h) After four minutes, the voltage was turned off (for 2 1 minute) and the reading at t = 5 minutes was recorded. From this reading and the readings at t = 1 minute and t = 0 minutes, the weight of the dry silica gel sample was estimated (see Appendix C.20). i) At successive intervals of time (e.g., at t = 15, 30, 45, minutes) the voltage was turned off for one minute and the adsorbent weight recorded. The time for which the adsorbent sample was not sub- jected to the field in this weighing procedure ranged from about 4 to 8% of the total time. This on-off procedure was essential to ensure that 89 the weighings were not affected by the imposed fields. j) All experiments were repeated for the blank data, i.e., the data without any adsorbent in the sample pan. The actual amount adsorbed was then obtained by subtracting the blank readings for both the 'no-field' and 'with-field’ case. k) The zero was periodically checked for error. Calibration error was usually found to be negligible when a 'stabilized line source' was used to power the balance. 5.3 Adsopption in Uniform, Applied Electric Fields In the following experiments a uniform field was created between two parallel plates two and one-half inches apart, and across which a 10 KV voltage drop was maintained (see Figures 5.1 and 5.23). 5.3(a) Spherical, Porous, Alundum Beads in Uniform Field Spherical beads of catalyst-grade porous alumina of about .25 to .30 cm. diameter were stuck on a rectangular strip of polystyrene foam and suspended from the balance as shown in Figure 5.2(a). The tempera- ture of the bath was maintained at T = 370 C and the relative humidity of the moist N2 was about 67%. Only monolayer adsorption is expected in the fine pores of this catalyst at p/ps 2 .67. The nature of the fields and field-induced forces in this geometry was discussed briefly in Section 4.1(b). The average of the field gradient squared++ existing at the spherical particle surface has been shown in Appendix A.1 to be In some cases the pan experienced a push from the surroundings during weighing, possibly due to residual charges left by the field. ++§ = 80(8-1)VE2/2 and hence, the comparison of VEZ. 90 about VE:Vg 2 1.1lx107 (Vz/cma) and the average field at the surface Eavg 2 2.19 (KV/cm). The internal field is uniform and of smaller mag- nitude than the external applied field. Figure 5.3 is a plot of the experimental data obtained. Within experimental error, no change is observed either in the adsorption kin- etics or the maximum amount adsorbed. As discussed in Chapter IV, Sec- tion 4.3(a), molecules adsorbed in the monolayer have very low dielectric constants (or low polarizabilities) and, consequently, the effect of field-induced forces on surface diffusion in the monolayer is negligible. This and the added factor of relatively low fields and field gradients could account for the lack of any observed effects in these experiments. 5.3(b) Bed of Silica Gel in Uniform, Applied Field Drying grade silica gel (6—16 mesh, 'Baker Analyzed' Reagent) was crushed and placed in a cylindrical polystyrene foam pan of length = 0.5 cm and diameter = 1.2 cm (see Figure 5.1). The gel was placed over- night in an oven at 115° C and degassed under vacuum for 2 2 hours just before being introduced into the adsorption chamber. Dry N2 was passed through the chamber for 2 1 hour, or until the sample could be assumed to have come to equilibrium with the bath temperature (= 37° C). At the start of experiments, the N2 flow rates were adjusted to give p/ps 2 2/3 and a voltage drOp of AV = 10 KV was applied across the electrodes. Results of water-vapor adsorption in drying grade silica gel at 37° C, p/pS 2 2/3 and AV = 10 KV are shown in Figure 5.4. On the y axis is plotted the ratio of the weight of water-vapor adsorbed to the dry sample weight, W, and on the x axis is time, t. As shown in Section 4.1(a), the average field in the sample is about E 2 .79 V/cm (when sample is —). adsorbed) m (mg. 12 IO 91 "X from Electrobalance ’0‘”. I no. .00 NO field 5 xxixxfl M)KV 0 15 T45 60 75 30 -—4r—O- t (mins.) Figure 5.3. Spherical porous alumina beads in uniform electric field--adsorption of water vapor, T = 370 C, p/pS = 2/3, AV = 10 KV. 92 .>¥ OH 1 >< .M\N u ma\a .0 Own n & ”waofim vowfimgm .Enomfics :a How mowfiwm owmhw wcflxuw :2 :OMHQHomvm uomm> Houmz .v.m ensued 795.5 u. III+| own SN 3: omfi ONH om oo om o 4‘ 1 9 1 II 1 d J o w h e 2 .m .2. EU W.O H a Eu NA 0 w .W HE w I x u. 40H I ma figs 6%. >x OH .35.: u ma OH O 0.000 3 .m z b x x 2 low .m w. x .mm OOIXM 93 dry). Once again, within experimental error, no discernible effects are observed due to the imposed uniform field. However, it is not essential to conclude from this that uniform applied fields have no effect on the adsorption kinetics, as has been suggested by some authors [P3,P5,P6]. Rather, as discussed later in Section 5.6(b), the magnitudes of the applied fields (zuui therefore the applied voltage drops) have to be much larger in order to expect any field-induced effects. In comparison, the average field magnitudes for non-uniform applied fields are much larger for similar applied voltage drops, AV. Also, from a knowledge of the maximum adsorption capacity of this silica gel and comparisons with other silica gels mentioned in Chapter 111, it may be concluded that only three or four layers of adsorbate are formed. Surface diffusion, which predominates in such fine pored solids, may thus be expected to be influ- enced very little. §i33(c) Bed of Spherical, Alundum lieads in Uniform Field The interparticle contact points between spherical particles exper- juence extremely high, non-uniform electric fields [Ml]. To investigate tflie effects of such fields on the adsorption characteristics, spherical (:atalyst A1203 particles used in Section 5.3(a) were piled one upon the (Ither to form a bed of spheres. This bed was subjected to a uniform fiield of AV 2 10 KV and the environment was maintained at p/ps 2 2/3, 7F = 37° C. The experiments were conducted just as in 5.3(a). Figure 55.5 shows the adsorption kinetics for this system with and without the fiield. The results imply that the above mentioned non-uniform fields Eire obviously too 'local' to affect appreciably the adsorption in the internal pores of alundum catalyst beads. m (mg.) “10118-1 94 12I 10» * f ‘ 3“ " n :2 I " " 8- I " o000° No field g XIII" 10 KV 6I 1‘ -=- i 4. 5 2. a C A L A A 4 0 50 100 150 200 250 ’1, a. t (mins.) Figure 5.5. Water vapor adsorption on alundum beads in uniform electric field, AV = 10 KV, T = 37° c, p/pS 2 2/3. 24 I 0000. NO field '8’ a I! II It 10 KV 16- o. ‘. v "V ' g1 ‘ o 4 8» “ .§ K I? OH 4 A A 4 A 0 50 100 150 200 250 _Q/__... t (mins .) Figure 5.6. Water vapor adsorption on crushed A1203 in uniform electric field, AV 2 10 KV, T = 370 c, p/ps 2 2/3. 95 5.3(d) Bed of Crushed Alumina Beads in Uniform Electric Field In Figure 5.6 is represented the experimental data for water vapor adsorption in crushed A1203 particles in the presence of a uniform external field of AV 2 10 KV, T = 37° C, p/pS 2 2/3. Once again, no appreciable effects are observed. 5.4 Adsorption in Cylindrical, Non— Uniform Electric Fields In the following experiments a cylindrical field was created between a thin rod (or filament) and a cylindrical screen. Two sample pan geom- etries were utilized. In the first, an annular pan (see Figure 5.2(c) and also Figure 4.3) made of metal screen was filled with the adsorbent, and the central electrode was a thin metal rod of radius = 1/32 inch. In the second, a cylindrical metal (screen) or polystyrene foam pan with a fine filament (r = .0089 cm) passing through the axis of the pan and :5erving as the grounded electrode (see Figures 5.2(b) and 4.4) was filled wvith the adsorbent. In both cases the High-Voltage electrode was a (:ylindrical, metal screen of diameter = 2.5 cm. 33:4(a) Crushed Alumina in Annular flan and Cylindrical Field The adsorption of water-vapor in crushed alumina in the presence of E1 cylindrical field (AV 2 5.5 to 6 KV across electrodes) was studied in fibur different configurations. In Figure 5.7(a) the only face of the Etnnular pan open to adsorption was the top face. In 5.7(b) the inner Corlindrical face was open with the other faces being blocked. In Figure 55.7(c) only the outer cylindrical face was open to adsorption. Finally, iJl Figure 5.7(d) both the cylindrical faces were open with the top and IDottom faces closed off. In all four cases field calculations in Appendix 96 30. r? o- .... No field 2; 25. “V'U‘6KV . ,. r " V ' ' g i l E g * 20. 5‘" ' I I . “‘I. 3 I , .15.; : | "Q; 10' I I ‘ p?" a | 5. I 0 1 . 41 g. 0 40 80 120 160 200 —7/—- t (mins.) Figure 5.7(a). Water vapor adsorption in crushed alumina. I; 2 ----2- No field :0 25. uni-25.5 KV , g 5 x E k f 20' g I I . "" | 15 ' a I t 'I‘ I 10 r 2 I 9 I 5 I O i o . . 1 . 11__s 0 40 80 120 160 200 __v_.. t (mins.) Figure 5.7(b). Water vapor adsorption in crushed alumina. 97 30* ...... No field *7 In”! 5.5 KV E0 25. o x ’ 'x . ’1' E t 20' r * 15' .x I I 10L ." .IIHI—llllfi I I 5» 0 4 J L n 4 0 25 50 75 100 125 ——-p——- t (mins.) Figure 5.7(c). Water vapor adsorption in crushed alumina. too... O KV 9 at “In" 6 KV «r Y X ’7 25’ .x l °° k 5 v E 20. x’ {I 15» 0X 10- & SI 0 . A 0 40 200 Figure 5.7(d). Water vapor adsorption in crushed alumina. 98 A give estimates of VE:Vg = 1.97x107 (Vz/cma) and Eavg 2 1.78 KV/cm. At the time these experiments were undertaken, one was still looking for the electro-convective vapor-phase flux of equation (1.4) (described earlier in this chapter). The exact significance of the dipole moment and the Boltzmann equilibrium distribution was still not very clear. If instead of ”eff (= uZE/3kT) one used u for the magnitude of p’in equation (1.4) with the resulting direction of the force being random, one would then expect some sort of a local turbulence phenomenon. It was to observe this phenomenon, if possible, that the experiment in Figure 5.7(a) was conducted. From the results in that figure, it appears as though the Boltzmann equilibrium distribution is valid and the electro- turbulence phenomenonisu therefore, non-existent.+ In Figures 5.7(b), (c) and (d) the objective was to simulate a closed-pore model, as men— tioned earlier. Once again, it is obvious from the results obtained that the fields to which the adsorbents are subjected are too weak to have any effect on the gaseous diffusion of water vapor. In the following experi— Inents available field strengths are further increased and so is the sur- 'rounding vapor pressure. 5.4(b) Crushed Alumina, CaCOa Powder, Porous Glass and Zeolite Beads in Strong Cylindrical Fields Figures 5.8, 5.9 and 5.10 represent the adsorption kinetics of Ivater vapor in crushed, porous A1203 particles, CaCO3 powder and porous .fRough calculations made later for the comparison of time scales over ‘which collisions occur with those over which the electrical forces act, indicated that the former were much smaller than the latter, thus justi- fying the use of the Boltzmann equilibrium distribution. 99 glass, respectively, in the presence of a non-uniform cylindrical field. The sample pan-electrode geometry is described in Figure 5.2(b). Field calculations give (for a dry sample bed) VE:v 2 3.46x108 (VZ/cm3) and 8 Eavg 2 1.74 KV/cm. In these experiments p/pS 2 2/3 and T = 37 ° c. With- in experimental accuracy no appreciable effects are observed due to the imposed electric fields. Field gradients are as yet quite low and the amount adsorbed at p/ps 2 2/3 is limited to the first few bound layers. Figure 5.11 shows the kinetics for water-vapor adsorption in zeolite, catalyst beads (Linde Type 3A, 1/16" pellets) at p/ps 2 1/2 and T==37O C. Fields estimated in this case were about VE:vg 2 10.2x108 (VZ/cm3) and E 2 2.98 KV/cm. Once again, insufficient adsorption at p/ps 2 1/2 +avg may be cited as the major cause of insignificant field-induced effects. 5.4(c) Alundum Catalyst Beads Strung on Filament Electrode Three cylindrical porous alundum catalyst beads were strung on the central ground electrode filament used in the previous experiments. A O voltage drop of AV = 4 KV was applied with p/pS 2 1/2 and T = 37 C. In this configuration the average fields experienced by the beads (estimated in Appendix A.3) are VE2 ~ 9 2 3 2 . avg - 1.90x10 (V /cm ), Ea 4 KV/cm. Figure V8 5.12 depicts the amount adsorbed m (in mg.) vs. time t (in mins.) for this system. Again, the applied fields (higher than before) have no discernible effect on the monolayer formation rate. 5.4(d) Water Vapor Adsorption in _jDryipg Grade' Silica Gel The adsorption rate of water vapor in silica gel has been known to be enhanced in the presence of strong, non-uniform electric fields [P1, P2,P3,P5]. Having observed no discernible effects with unsaturated N2 100 30 ’7 . . 4:: 8 "' E; 25 _ .. .... No field gr V 111111131: 3 KV a E p a. 20. t x k 15 I ‘f 10. 'x 5 . g 0 J 1 1 1 g. 0 30 60 90 120 150 —+’t (mins.) Figure 5.8. Water vapor adsorption on crushed A1203 in cylin- drical field, p/pS 2 2/3, T = 370 C. 4.5 - . * ' x X 3.75. ,7 o i " 2: , 3 no . f3 x g 3.0» d = 1 cm E i l I III _ I I 2.25, 0000.0 NO fleld I ' I signal 3 KV I g C I 1.5. III—Ill .—- l I I— : I .75' l é I I "' I 0 ’1 A A l J 0 25 50 75 100 125 ___4——.- t (mins.) Figure 5.9. Water vapor adsorption on CaCO3 powder in cylin— drical field, p/pS = 2/3, T = 37° C. 101 12 10h ‘ :at ‘ -——4-—.- m (mg) o~ a: ii fl” k o o o o o 0 NO field [*4 | 4 , I a It: II II 3 KV II II I I ‘ I . I I I 2b —-IL— | I ‘5" I d = 1 cm 0 A I J 4* 4 0 25 50 75 100 125 4& *’ t (mins.) Figure 5.10. Water vapor adsorption on porous glass in cylin- drical field, p/ps = 2/3, T = 37° C. x K . .15. K ' g 9 ‘ i Q m.10' ‘. | ' 2° * I ' 25 g ~q“-++-1 I 53 a I I X , I 3 '1 I IS I l .05» ‘ ‘ ...... No field , I (1 .nnxAv=4I 1. Q Oh? ' mmNo field a f, ' ..... 4 KV I, 3 3 "i” 6.5 KV 4‘ I I O . | I .2? I I—HI-‘II . I g I ' '-.=' I ' = .7 cm. .1. fi ? 00 4b 86 150 160 200 ¢ "" t(mins.) Figure 5.13(a). H20 - silica gel (D.G.), p/ps 2 1, T 25 C, AV = 4, 6.5 KV. .sI : , I ’5 so I II I '-1. I z I w nun-0N0 field ,2. d 32 ufixsul6.5 KV .v 2" .1I I {I 0 L - L % 3 20 4O 6O 80 100 "—f—"’ t (mins.) Figure 5.13(b). AV = 6.5 KV H20 - silica gel (D.G.), p/pS = l, T 104 = 1.24x1010 (Vz/cma) and Eavg = 10.23 KV/cm. Significant enhancement in the rate of adsorption is observed in this case. However, owing to the non-uniformity of the crushing process (to facilitate packing the gel into the narrow pan) and the resultant differences in the available sur- face areas and pore volumes for adsorption (each sample used only once), much scatter is observed in the data. To rectiifirthis,‘uniform-sized, fine, chromatographic silica gels were procured and used in the following experiments. For the sample electrode configurations in Figure 5.13(a) and (b), experiments were also conducted in such a way as to take only one reading after a sufficient length of time, both with and without an electric field applied. The object here was to verify whether the off-on proce— dure for the applied field was resulting in depolarization of the polar- ized adsorbate, and thus preventing any significant field-induced effects from occurring. The results in Appendix C.ll suggest that this was not the case. In view of the relaxation time for polarization for water being of the order of 10'11 secs., polarization is essentially instan- taneous in the adsorbate and the above result is to be expected. 5.4(e) Water Vapor Adsorption in S-4133 (25 A0 dia.) Silica Gel Adsorption of water vapor was studied in uniform sized (70-140u) chromatographic silica gel with approximate mean pore diameter of 25 AO (made by SIGMA). The cylindrical screen pan dimensions were d = .35 cm., 2 = 2.5 cm. For applied voltages of AV = 6 KV, fields estimated in Appendix A.3 for this geometry give Vfiévg = 1.43x101° (Vz/cma) and E = 11.01 KV/cm. Figure 5.14 represents the adsorption kinetics for +avg this system. The enhancement in the rate of adsorption is clearly W 105 .40p ( ‘ .0 f I. ': . .32I AR : O O x l‘ I 0 I .' ' I . I .24 I FHHHI'“ I X I I I! I I I I ~% I .16- d = .35 cm. &' O 00.00. NO fiEId ; "”l“*6KV .08- v I 0 . , - a 0 3O 60 90 120 150 ——'9—. t (mins .) Figure 5.14. Adsorption of water vapor in Silica Gel S-4133 (25 A0 M.P.D.), AV = 6 KV, T = 25° C, p/pS = 1. 106 indicated by the data obtained. A maximum amount of about 35% by weight of dry sample is adsorbed. For a mean pore diameter of about 25 A0, the monolayer amount adsorbed corresponds to about 11.5% of dry sample weight (see Figure 3.7b). Thus, only three to four layers of adsorbate may be expected in this sample. 5.4(f) Monolayer Adsorption in S-2509 (60 A0 dia.) Silica Gel Chromatographic grade Silica Gel S-2509 (63-2000) with mean pore diameter around 60 A0 was placed in a highly unsaturated (p/ps 2 1/3) humid environment at 250 C. In Section 5.5 the maximum water capacity of this gel is seen to be around 70% by weight of dry gel and the mono- layer capacity around 6.5%. In Figure 5.15 the adsorption kinetics show a maximum of around 8% by weight, which corresponds to a little over a monolayer. Fields of the same magnitude as in the previous section yield no discernible effects in monolayer adsorption kinetics. More on this in Chapter VIII. 5.4(g) Water Vapor Adsorption in Porous Alundum Catalyst Beads Strung on Ground Filament Electrode at p/ps 2 1 and T = 250 C The experiment described in Section 5.4(c) is repeated here, but 0 C. The for a saturated, moist N2 environment (p/pS 2 1) and T = 25 beads of diameter 2 .35 cm are subjected to even higher fields of _ 2 2 9 2 a 2 AV - 6 KV, VEavg 4.28x10 (V /cm ), Eavg 6.02 KV/cm. The results of the adsorption kinetics are shown in Figure 5.16. The fact that even such high fields and moist surroundings fail to produce any discernible effects in the rates indicate mainly that the field effects on the first few bound layers of adsorbate are negligible for the given field :V ~5.6I:..~IA..IT.~.. .3: t 2 107 8 X I , . X g . : ' x' i O. a. 6* ‘ x I P I ’2 5 | I EL 0 I ~ . -LII» o a. I I .o E I II <3 I O U) 4. I I In x I “$63) I: I l OE . co cm. E ’P 2 3 000.00 No field 2L “xfllx 6 KV or— I . 1 A #n O 20 4o 60 80 100 ——¢—‘- t (mins .) Figure 5.15. Monolayer adsorption in porous silica gel (S-2509)- H20 vapor adsorbate - AV = 6 KV, p/pS 2 1/3, T = 25° C. 108 20' ox’ . *' O ,2 x 'o _ ' g 16 o.’ I ' 8 I 'I * m 'o-o .—| '3 12- * I -«- -— l 62) a? I, .--l E ' ' V 8- t I I E go... No field d = .35 cm. 4’ .. xxxx6KV * 0 . . . 1 . O 50 100 150 200 250 —4—-b t (mins.) Figure 5.16. Alundum beads strung on ground filament, p/p 2 1.0, T = 250 c, AV = 6 KV. S strengths. The pores in the catalyst beads are extremely fine, leading to only a few layers of adsorbate at saturation. 5.4(h) Water Vapor Adsorption in Crushed Alundum in the Presence of a Corona Field The lower plate of the parallel plate capacitor described in Fig- ures 5.1 and 5.2(a) was removed and a needle electrode inserted in the center, as shown in Figure 5.17. In this point-plane electrode configu- ration was placed a shallow polystyrene foam pan filled with crushed alundum. The pan was suspended just above the needle tip. The results of water-vapor adsorption at T = 370 C, p/pS 2 2/3, withzuuiwithout the external field are represented in Figure 5.17. A slight dielectrophor- etic push on the pan due to the field was observed during the experiments. The push varied linearly with the amount of adsorbate in the system. The data in Figure 5.17 are plotted after accounting for this push. There seems to be a definite, though small, increase in the rate, as well as a 10 SL8 I? r. . 3: V adsorbed) ”(6* m (mg. 12. 10. .0» 3 III AV =ESKV 1" 0. " '1 0N0 fleld O O. t" A 109 ~vu++ 1+ P 004 o...” X!!! X XWith field — _ £- 0 . 4 n A O 30 6O 90 120 ___—v-fl 1: (mins .) Figure 5.17. Water vapor adsorption in point—plane geometrical field--crushed alundum adsorbent. 110 extent of adsorption in this system. The voltage drop across the point and plane was AV = 5 KV and the point-plane gap was about 1 inch. Further, careful experiments have to be conducted to verify the claim made in the literature [P11,P12,K5] that corona discharge fields affect adsorption-desorption kinetics appreciably. 5.5 Multilayer Adsorption in Cylindrical Electric Fields Figure 5.18 represents the adsorption kinetics of water vapor adsorbed in Silica Gel S-2509 (M.P.D. 2 60 A0) already used in 5.4(f), however at conditions of p/pS 2 l. The large pore diameters of this gel allow for multilayer adsorption and/or condensation. Monolayer adsorbed water accounts for about 6.49% by weight of dry sample (see Section 3.13) Bound layer adsorbate accounts for 2 13.9% by weight (Section 3.1b). The mean pore radius for this gel is calculated in Section 3.1(a) to be 2 30.7 A0. Beyond 13.9% by weight adsorbate, the remaining 56.1% by weight corresponds to free, multilayer adsorbed water. Figure 5.18 indi- cates a significant enhancement in the adsorption kinetics of this sample, reducing the time required for saturation (WS 2 70% by weight) by almost 20%. Fields existing in the dry bed are estimated to be about Vfizvg 2 1.68x1010 (Vz/cma), Eavg 2 11.89 KV/cm. In Figure 3.3 the adsorp- tion isotherm for this silica gel was plotted, both with and without the applied non-uniform field. As observed in [P2], the isotherm is unaf- fected by the field indicating that the adsorptive forces are much stronger than the ponderomotive forces. In Chapter VI a theoretical model is proposed for the multilayer adsorption of a vapor in a single, open, cylindrical capillary pore with and without applied electric fields, and the results obtained therein are used to predict the adsorption 111 .nfidflm HdQMHHUdHQ Hdouuecufixo a. .>¥ o u >< .u omm I A .H.umd\d .Ao< oo I .o.d.zv momNIm ado ddufium madden sudHHuddd a. :oMBQHOmud udxdfiuufisz .wfi.m dusmud 2.22.25 5 IIIT ooe omm com omm com omfi ooH om o I J a I d 1 q q - O .m.a .mH . .m.m~ _ . . u .om . . a. dill. ._ I . v __ . . .m.am — 0 fl 4 . .mq HE o>uso umom . a. 1 >5. 0 I Z xxxxx .93 fifimww DZ .00. 00 .oo . .. . xx 0 k Amufio M 112 kinetics in the silica gel-water vapor system. 5.6 Further Experiments with Silica Gel S-2509 (60 AO dia.) In this section, various experiments aimed at verifying proposed notions of the field-induced forces and also experiments to further probe the exact nature of the field and its effects on both adsorption and desorption phenomena are discussed. 5.6(a) Non-Polar Adsorbate (CIClI) and Silica Gel Ethylene tetrachloride (dipole moment = 0, dielectric constant 2 2) was chosen as an excellent representative of the non-polar adsorbate o C.+ Figure group. CZClI was adsorbed in Silica Gel S-2509 at T = 25 5.19 represents the adsorption kinetics for this system. As seen in this figure, the kinetics are essentially unchanged, although the maximum amount adsorbed (2 106% by weight of dry sample) corresponds to capillary condensed liquid. The adsorption time is much smaller (2 60 mins.) than for water vapor (2 5 hrs.) in the same adsorbent, owing to the higher molecular weight and greater saturation partial pressure of C2Clu at 250 C. Working with CCln (same dielectric properties as CZClI), the adsorption time was found to be even smaller (2 30 mins.), owing to the still higher partial pressures at T = 250 C; and thus the experiments were, as such, found to be inconclusive, owing to the scarcity of experi- mental points obtainable. In references [P2,P3,P6] CCll+ was used to +Tetrachloroethy1ene is toxic in nature, and therefore the entire experi- ment was conducted under a hood with the air suction being turned on at all times except when readings were being taken (to avoid external effects on weighing). W (gm/gm sample) x 100 113 IZOI . C x . § Q X 100I . x. 000000. No field 6 KV 80’ ‘ fi'BI‘fL$ . I 1' I 60. I . HIP-III" I ' I I *- I I _,. I I 40 ‘ d = .32 cm 20- 01‘ i - . 0 15 3O 45 6O 75 —-%-—- t (mins .) 4 Figure 5.19. Adsorption of non-polar adsorbate CZCII on Silica Gel S-2509, p/ps = 1, T = 25° C, AV = 6 KV. 114 demonstrate the inability of applied fields to affect the adsorption kinetics of non-polar adsorbates. In the light of the above—mentioned observation, this seems hardly justifiable. 5.6(b) Effect of Decreasing the Gradient of External Field Squared, In the course of carrying out the calculations for the external field gradients (in the silica gel sample) as a function of adsorbate concentration, it was observed that the magnitudes of the macroscopic gradient of the externally applied field squared (VEZ) were not suffi- cient to account for the observed enhancement in the adsorption kinetics. Further analysis showed that the internal field gradients in the fine micro-pores (resulting from fields relaxing as adsorption in the pores proceeds towards saturation) were much higher than the above-mentioned external, overall field gradients (shown in Section 4.3c). To verify the validity of this calculation, an adsorption pan was constructed as before, but instead of a fine filament (r 2 .0089 cm), a thick metallic wire (r 2 .0348 cm) formed the grounded, central electrode. In this fashion by increasing the applied voltage somewhat (see Appendix A.4), the average of the field squared was maintained essentially the same but the average gradient of the field squared was reduced by almost one-third the value estimated for the original pan geometry. The experimental results for the adsorption kinetics are represented in Figure 5.20. The rate of adsorption in the presence of the field changes very little due to the reduction of the overall average . For similar average s in the two cases compared, the adsorption kinetics are essentially similar. This seems to justify the assumption that in estimating the 115 HoHHmEm cow .ANmDV ommno>m pan Awmv owmam>m 05mm may cw mommIm How moflfiwm :o uoam> gown: mo :oMuQAOmp< fi.w¢fl—=U H I‘lllléll omm oom omm oom omH cod om d 1 q o J q .58 omoo. u floeoHHUdev B .50 mm. H e $ ..___T_.__T_ A mv oEmm .A m>v 30H x N N pow memo Hmucoezomxo I‘ll XX x X wH.m .mfid 50.6 down - .efidflc 0:. edudfiu d>dsu mH.m .mfid scum x x Aumpv Ema; you dude .efldflm £552. edpufim d>usu I I x A .om.m duzwfld m.n ma m.NN m.Nm 001 x M-—- o0 m.nc mm 116 ponderomotive forces which cause the enhancement in the mass transfer rates, the internal relaxation fields in the fine pores ought to be con- sidered rather than any overall, macrosc0pic, applied fields. To carry the conclusions even further, this result seems to imply that it is not really essential that the applied fields be non-uniform for the field- induced effects to be observed. Indeed, the average s in non- uniform field configurations is quite high compared to the average s obtainable by applying uniform external fields. For example, in Figures 5.18 and 5.20 the average for the dry silica gel bed is estimated to be about 2.24x108 (Vz/cmz). If a uniform field between two parallel plates were to produce the same average , then one would require an average field strength of 14.97 KV/cm or a voltage drop of AV = 58.1 KV needs to be applied across an inch of interelectrode space (from equation 4.1, with e 2 1.53). Thus, it may well be the extremely high voltages that must be applied across electrodes in a uniform field geometry that preclude the possibility of observing any field-produced phenomenon, rather than the experimental constraint of an externally applied uniform field. 5.6(c) Desorption Experiments: Water Vapor-Silica Gel As explained in Section 3.1(a), the desorption process from narrow cylindrical pores filled with capillary-condensed liquid is supposed to take place by a very different mechanism than in the case of adsorption. The liquid meniscus contracts and becomes concave towards the vapor. It is hemispherical in shape with the radius of curvature given by (Ro-tc), where Ro is the capillary radius and tC is the thickness of the adsorbed film (see Figure 5.21). The pressures at the gas-liquid interface 117 (given by the Kelvin equation for curved surfaces of tension, equation 3.2) are extremely high, and ordinary applied electric fields may not be expected to alter them significantly. Also, the desorption mechanism is best visualized as brought about by vapor molecules diffusing to the mouth of the pore along the adsorbed mono- or di-layer film on the pore walls (see Figure 5.21). The pressure gradient driving force for this kind of surface diffusion is due to much higher surface pressures than in the case of multilayer adsorption. The magnitudes of theoretically derived electric field-induced diffusion fluxes do not compare favorably with the ordinary surface fluxes just described. Figure 5.22 represents the kinetics of desorption of water vapor in Silica Gel S—2509 (M.P.D. = 60 A0). The experiments were conducted both with and without an applied, cylindrical electric field (AV = 6.6 KV). Within experimental error, no appreciable changes in the desorption kinetics were noted. Of course, the literature abounds with results of enhanced evaporation rates from capillary porous bodies in the presence of corona discharge fields [P11,P12,K5]. The enhancement in the fine-pored bodies (diameters 20- 60 A0) has to be ascribed to the presence of ionic charges and the resultant reduction in the vapor pressure above the capillary mouths [P12] and not to any field-induced phenomenon. Adsorbed layer - .. - - - - - - .. —0 Ps .——‘—.‘— «__.—fl“ ‘1 ‘L‘\ ‘\.\. ‘u ‘dflsn.‘ux\‘u ‘uu‘\.“ Figure 5.21. Desorption from a cylindrical pore. 118 C 2 K B o.) 70. .‘O x ‘ . . '2'3. ...... No field 1 " 85 ‘ruanflAV=66KV f .8 W 60L . .eb ODE E d 3 50" . 'r—HIII- I 40- ' I II" | 30» . f . ,5. .37 cm. 20L ° ? 10» f O "o 4 A 1 4 J 0 40 80 120 160 200 ——-¢-—. t (mins .) Figure 5.22. Desorption kinetics, water vapor - Silica Gel S—2509, P/Ps 2 0, T = 25° C, AV 2 6.6 KV. 119 5.7 Preliminary Experiments with Treated Silica Gel S-2509 In this final section, the industrial Silica Gel S-2509 was subjec- ted to chemical treatment with the intention of obtaining some prelimin- ary information on the role of alkali ions in the adsorption process. Industrial specimens of silica gel always contain various ionic impuri- ties [AZ]. The Silica Gel S-2509 was found to contain significant amounts of sodium.+ The gel was placed in concentrated hydrochloric acid overnight to remove any foreign ions [D4] and then washed thoroughly with deionized water. The sample treated in this way (Sample I) had significantly lesser amounts of sodium and essentially no chlorine. The deionized silica gel was next placed in a saturated KCl solution for about 24 hours. The KCl-treated sample was then thoroughly washed with deionized water. The resulting chlorine-free sample contained small amounts of K+ ions (Sample II). In Figure 5.23 are shown the adsorption kinetics of water vapor in silica gel samples I and II, with and without an imposed, cylindrical electric field. As can be seen from the results, the two samples, I and II, behave rather identically. This might indicate that the potas- sium concentrations are much too small to show any specific differences. The 'no field' adsorption data are somewhat higher than that for the ’untreated' Silica Gel S—2509 used until now. The 'with field' data are, however, not correspondingly higher than that for the 'untreated' sample. Two reasons may be offered at this point to help explain this decrease +The relative concentrations of Na, K, Cl and other elements in the silica gel samples were estimated by the "Neutron Activation Analysis' technique in the M.S.U. nuclear laboratory. 120 .>¥ e I >< .H u mm\a .u 0mm n 2 pm mcoflu3H0m Hux was Ho: cue: poumopu How mowflflm cw :oHumHomvm uoam> gown: .mm.m mpsmflm A.m£..nEv u. I” é om; 0mm 0mm oMm owm omm o3 om oo i3 H2958 4444 a .Eofl :32. A : oHQEmmXXXXX I .233 00000 .3. .efieflm oz. a 3 395mm . o o o e % o>.So Lima 0:. .poumoppcz. o. . .mv o. e 2 up 9. .8 O O. . . o>h:o .pfiofim cuwz. .poumouuca. L mm. % 001 x (aIduIes Bul/‘spe 8m) M .- 121 of 'field—induced' adsorption rate due to the chemical treatment: (1) the Na+ ions which were originally in the sample also played a role in the 'enhancement' of field-induced adsorption kinetics;+(2) the removalny significant quantities of sodium from the gel matrix could have altered the gel surface characteristics considerably, thereby also affecting the polarizabilities of the adsorbed water and the resultant field forces. One is tempted to choose the first explanation over the second one. However, the removal of Na+ ions from the sample should have decreased the activity of the gel by providing fewer sorption centers at the inner surface of micropores in the gel [Pl]. Instead, the activity is actually slightly increased. Whatever the actual explanation, it seems clear that the enhancement of adsorption kinetics in the untreated silica gel sample is at least partially due to reasons other than the impact of ponderomotive forces on the adsorbed water. The authors in [P1] have observed definite improvements in the adsorption kinetics due to the introduction of significant amounts of Ca2+ and K+ ions. More work needs to be done to estimate the exact role of the alkali ions in the field- induced adsorption phenomena. +As mentioned earlier, the field-induced adsorption kinetics in the sys- tem Silica Gel S-2509-water vapor is predicted in a theoretical 'single- pore' model described in Chapter VI. Since only the effects on polar- ized adsorbate is considered in this model (the role of surface alkali ions, Na+ in this case, is excluded), the HCl treated silica gel 'no- field' kinetics of Figure 5.23 are used to predict the 'with field' adsorption rate curve. CHAPTER VI MATHEMATICAL MODELING: MASS TRANSPORT IN A SINGLE, OPEN CAPILLARY PORE IN THE PRESENCE OF AN ELECTRIC FIELD In this chapter the mathematical mass transport model for water vapor diffusion and adsorption in an open, cylindrical pore is presented. Boundary and initial conditions similar to those existing in the silica gel bed used in the experiments are imposed. The mass balance equation is solved numerically on the computer, using the implicit finite differ- ence scheme. Solutions for the concentration profiles in the pore are obtained for both the 'with field' and 'without field' cases. Finally, the relative adsorption rates obtained in the lsingle pore' model are applied to the actual experimental 'no field' data in order to predict the 'with field' adsorption kinetics. The predicted and experimentally obtained adsorption rate curves are then compared. 6.1 The Mathematical Problem Figure 6.1 depicts a single, cylindrical, open pore of radius R0 and length L. Diffusion of water vapor into this pore can be brought about by primarily two mechanisms (see discussion in Chapter III, Section 3.2a): first, by a combination of Knudsen and surface diffusion in the vapor phase, and second (simultaneously), by a bulk adsorbate volume flow. 122 123 b_,/ ////D//% -.h—rz—_Z_E0f 7777777///777//W7 IF L J Figure 6.1. Single, cylindrical, open pore: (a) Knudsen and sur- face diffusion; (b) bulk adsorbate volume flow. As briefly discussed in Chapter III, the bulk adsorbate volume flow is generally expected to be small, owing to the strong adsorbate- adsorbent interactions. For gaseous diffusion with surrounding relative pressure p/pS = 1/3, bulk volume flow in silica gel is non-existent, as only a monolayer is known to form. Estimates for the diffusion coeffi- cient for monolayer formation rate are obtained by fitting the mathemati— cal model (to be described) to the experimental data. Correcting this coefficient for the concentration dependence, as given by equation (3.16), and using the corrected estimate for the coefficient in the mathematical model when the surrounding p/ps = 1, gives a fairly good fit for the experimental data. This seems to suggest that surface diffusion is the predominant mode of transport in the fine—pored capillaries. Gaseous Knudsen diffusion combined with surface diffusion of adsorbed molecules during the residence time of adsorption will be considered here to repre- sent fully the mechanisms of mass transport. Further, in equation (3.10) it was seen that the contribution to the overall diffusion coefficient from the surface diffusion mechanism far exceeds that due to Knudsenian diffusion. Equation (3.21), then, represents the mass flux into this cylindrical pore in the presence of an electric field 124 dC e (e -1) dB2 J=-D M 05 —> z 5 dz ' RT 2 37 (3°21) where the surface diffusion coefficient DS is defined in equation (3.16) as D = KAV BI-C = K'C 3 16 s s N! g g ( ' ) Equation 3.21 may be rewritten as Meo(€S-1) dE2 dC = _ - ._-> J2 D5 1 RTx2x(ng/dz) xdz x dz (6'1) e' ng = '05 (17 where e Meo(€S-1) dE2 _ - .1 Ds ’ D5 1 RTx2x (ng/dz) x dz (6'2) is the enhanced diffusion coefficient in the presence of the electric field (note that in the pore the gradient of the field squared and ng/dz are always opposite in sign, thus always enhancing 05). Writing a mass balance for the water vapor adsorption in this single, cylindrical pore is made exceedingly complex due to two main reasons: 1) The cross-sectional area through which diffusion takes place varies all along the pore, as the adsorbate concentration profile is dependent on the gas-phase concentration profile in the pore. 2) The electric field is a function of the adsorbed amount which, in turn, is a function of Cg (thus introducing a second source of 125 non-linearity). In Figure 6.2 is shown an elemental volume in the pore. The mass balance over such a volume is given as z z+Az Figure 6.2. Elemental mass balance. so so _ = __E. 5 JzAlz .JzAl2+Az 31: Avg + at x ZnROAz (6.3) where Alz is the area of cross section for diffusion. For surface dif- fusion AIZ is given by Alz = 2n0ylz where o is the thickness of the surface layer through which the surface diffusion occurs (assumed to be a constant). R0 = radius of empty pore (RO-y) = thickness of adsorbed layer, y is defined in Figure 6.2 Cg = gas phase concentration (g/cma) CS = adsorbate surface concentration (g/cmz) Avg = (ny2|Z + nyzlz+Az) g;- = volume of gas in element In general, when adsorption is present '3? X ZTTROAZ >> at Avg 126 and one may neglect the latter term. mass flux may be written as 8C __S 8 N 01‘ where the prime refers to the presence from equation (6.3) -Ds fix 27fy0lz + Ds 3z x Dividing by A2 and taking the limit as 3 an 53' Rafi? yo or 3C 3 all) Inserting the expression for D;3 given Ds = K’Cg from equation (3.16) into eq 8 BCg M80 .__ v ___.- ___. e - 32 K Cg 32 2RT x ( 5 1) From equations (6.1) and (6.2) the of an electric field. Therefore, 3Cs 27fyolz+Az = F X ZfiROAZ Az+0, one gets 8C = R -—i (6 4) 0 8t ° 3C = R ——5 (6 5) 0 8t ' by equation (6.2) and the relation uation (6.5), one obtains 3C 5 0 3t dEZ 32' YO = R (6.6) At this point, the often used assumption that the adsorbate phase and the gas phase are at all times in dynamic equilibrium is invoked; i.e., CS = f(Cg), where the relationship between Cs and Cg is obtained from the adsorption isotherm. Once again, since CS is not a linear 127 function of C8 (see Figure 3.3), the adsorption isotherm is broken into several regions, each of which may be approximated as a linear variation of Cs with Cg. Thus, one may write C5 = k1Cg + k2 where k1 and R2 are constants varying with each region of Cg chosen. Inserting the above expression for CS and carrying out the required differentiations in equation (6.6), one obtains 32c 3(c y) ac (C Y) gg+ g g g 32 82 32 Me d2E2 dc dE2 d(C y) 6152 -> —> - O -> 2RT (CgY)(€s-1) dz2 +I(CgY)YE?.dzi+ (Es-1) d2 52- lo PD (klcg4-k2) (6.7) l 7< Q Q) t The boundary conditions for this problem are a) Initial condition: Cg==0 at t==0, for all 2. b) Boundary condition: Cg==Co at z==O,L, for all t>’0. Co = surrounding vapor concentration Equation (6.7) is a non-linear, second-order partial differential equation with the non-linearity arising from: (1) The concentration dependence of the diffusion coefficient, DS = K'Cg; (2) The surface con- centration (Cs) dependence of the radius of gas-phase cross-section area, y (see Figure 6.2); (3) The dependence of the electric fields on the adsorbate concentration profiles; and finally, (4) The adsorbate concen- tration dependence of the surface hopping molecules' dielectric constant, 6 . S To avoid having to solve non-linear PDEs, the following procedure 128 is adopted in solving equation (6.7) numerically. A first estimate based on the values available at the beginning of a time interval are used for all the terms arising from the above non- linearities, and the equation to be solved reduces to 32c acg a a1 TEFE + a2 TE? - a3 = a, §?-(klcg+-k2) (6.8) where a1, a2, a3 and a“ are constants. Having obtained a first approximation for the concentration profile, the coefficients a1, a and 33 are corrected for by using values corres- 2 ponding to 'average' concentrations over the same time interval. This 'iterative' procedure is repeated three times over each time interval before moving on to the next time interval. Using dimensionless variables 6 = Cg/CO , Y = (CgY)/(CmRO) , C = Z/L one obtains for equation (6.7) 826 36 BY L2 a ”50 dzfiz d8 d52 aY dEZ where 1 DC — K1Cm0 (constant) and Cm = gas-phase concentration Cg for monolayer coverage with the boundary conditions 129 a) G = O at t 0, for all Q. b) G = l at C 0,1, for all t>0. 6.2 Numerical Solution of the Second Order Partial Differential Equation (6.8) The Implicit Finite Difference scheme was used to solve equation (6.8) for the concentration profiles. Let G = G(I,N), where the index 1 refers to position in the pore and N refers to time. Also, let C = Cs/Cso ~< ll ‘03 ll be the dimensionless adsorbate concentration (C==C(I,N)). Y(I), k1 = k1(I,N), k2 = k2(I,N), a = Lz/DC Mao/(2RTCO) , E = E(1) , as = 55(1) In the Implicit Finite Difference scheme where AZ 326 _ G(I+1,N+l) - 2xG(I,N+1) + G(I-1,N+1) 3:2 ’ A22 = step size in C ( =.Ol in this work) 36 _ G(I+1,N+l) - G(I-1,N+l) a; 2xAZ EI.- Y(I+l) - Y(I-l) 3c - ZXAZ dZEZ 2 2 2 _: _ E (I+1)-2xE (I) + E (I-l) ch " A22 gg? = E2(I+l) -E2(I-1) d; 22(AZ dc 65(I+l) -es(I-l) dc 22, ravg==.0667 cm) of ==ll.89 KV/cm (see Appendix B.2). In the actual experiments certain non-idealities exist. Among them are: (1) the gas-phase concentration at the mouth of eagh_pore is not = C0 (the surrounding concentration), at time t==0; (2) A distribution of pore sizes exists resulting in the smaller pores being filled first and the larger pores filled last; (3) The overall dielectric constant is not uniform over the entire bed, especially at small times, owing to the 132 .fimo>p:o Hmowuopoozuv wfioflm ofipuuofio unocufiz vcm Law: .Hovoe whomuofiwcfim a“ camp :ofiumHOmp< .m.o opswfim x.mCMES 6 cow cmm 0cm 0mm com omH 9: cm c .1 d 1 4 ¢ 1 d d (O .m.NN i me 363 oz Emdm 6262c no“: . méo ()01 x (aIdmes 8m/°spa 8111) M .__7__ 133 particles closer to the bed boundaries being exposed to the humid envi- ronment earlier than the particles in the center of the bed. Nevertheless, the single-pore model can give valuable qualitative and quantitative estimates of the effects of the applied fields in the real laboratory situations, once the 'no field’ adsorption rate curve is known. For a given IV (i.e., for a given amount adsorbed in the single pore), the ratio of the rates of adsorption in the field and no field cases (dW'/dt)/(dW/dt) can be used to predict the rate of adsorption in the actual bed for the same W, given the (dW/dt) for the non—ideal bed.+ In this fashion, the adsorption kinetics in a bed of silica gel for a given applied field may be predicted, given the kinetics without the field. Figure 6.4 gives dW/dt vs. W for both 'with' and 'without' field for the single pore. Table 6.1 lists the ratio (dW'/dt)/(dW/dt) vs. W, obtained from Figure 6.4. Also listed is dW/dt for the actual experi- ments with Silica Gel S-2509, represented in Figure 5.23.+ Next, the predicted dW'/dt is obtained for the experiments in Figure 5.23 (dW'/dt = (dW'/dt)/(dW/dt)| x (dW/dt)bed). In Figure 6.5 is single pore plotted dt/dW' for the bed vs. W. The area under the curve gives ' Z %%3 dW'). Thus, W' is obtained as a function of t. Figure 6.6 t(=f shows the experimental and predicted adsorption kinetics for this sample. The electric field-induced surface diffusion enhancement of the polarized +The prime refers to the case with the field applied. +As mentioned earlier, this theoretical model is applied to the HCl treated Silica Gel S-2509 so as to exclude possible ion-related adsorp- tion rate effects. .mommnm How moflfiflm pom u .m> .3 wfioflx ou o>a:u Hmhmouch .m.o opsmflm .anfllidVllll. n. c. m. w. m. m. H. 1.1: (O m.H m m.v o \\\\\\\ m.m~ ma .Hopos ohomuofimcfim Mom connomwm .¢.6 mnswua pczoem .m> :ofiumuomwm mo ovum .3HOZAII.$IIIII n. o. m. w. m. N. H. ‘ ‘ ‘ ‘ ‘ I 6262c “sogufiz 6262c :62: o.~ up aMP zOI x 10 1P MP zor x Table 6.1. an Electric Field. 135 Estimation of Adsorption Rate Curve in the Presence of . {—1 [:4 R) .. . or . . . 3W“ W' (min) For Single Experimental Estimate for W' W' Pore for Bed for Bed 0 1.00 1.0526 1.0526 .950 0 0 10 1.000 .5556 .5556 1.800 S 5.9 15 1.117 .3704 .4137 2.417 10 13.7 20 1.340 .3226 .4323 2.313 20 36.2 25 1.362 .3077 .4191 2.386 30 61.3 30 1.3084 .2500 .3271 3.057 40 99.1 40 1.128 .1980 .2233 4.478 50 146.6 50 1.088 .1869 .1972 5.072 60 205.8 60 1.055 .1316 .1388 7.203 65 250.7 65 1.000 .1077 .1077 9.285 67.5 276.2 67.5 1.00 .0773 .0773 12.93 68.5 288.2 70.0 1.00 .00 0.0 w .o.H u 66\6 .>¥ o u >< .6 6mm u e um Eopmxm homm> poumzuaow mowfiflm a“ mo>pso mama :ofiumnomwm Hmucoefipomxo paw wouowvohm .c.o onzmfim oov cmm com omm cmH ooH om oo m.n ma m.mm 6 3 l om \ \\ m.nm .\\ mv o>asu .vfioflw 0:. amazoEwpomxo wouuflm o>psu m.mm o>hso oo 53: nouoflvohml II ..I. I. I. :. m.no o>pso Hmucoefinomxo .vfioflm :uflz. wouufim o>pzu 1;? 001 X M“' 137 adsorbate molecules seems to represent fairly well the observed experi- mental enhancements in the case of silica gel free of any surface ions. That the field-induced effects in the untreated Silica Gel S-2509 in Figure 5.18 is larger may indicate the additional role played by the ions in the ion-assisted field—induced effects. CHAPTER VII FLY ASH RESISTIVITY, CONDITIONING AND THE EFFECTS OF APPLIED ELECTRIC FIELDS Both from widespread experience and theoretical investigations, the electrical resistivity of fly ash (and other highly resistive dusts) is reckoned to be one of the most common causes of poor precipitator per- formance [W2]. In an Electrostatic Precipitator (ESP) gas ions are formed in the high field regions near the wires and flow to the grounded plate. The ions attach onto particles in the gas to be cleaned, and the particles, in turn, are precipitated on the grounded collecting plate. However, as the ion densities produced in the corona wire vicinity are much larger than those used in charging the particles [W4], the bulk of the ions have to pass through the particle deposits which form on the ground electrode, thus constituting the D.C. corona current. When the bed of fly ash or dust has a high electrical resistivity, a significant voltage drop develops across the bed causing dielectric breakdown by ion- ization of the gas within the interstices of the particle layer [D2]. This phenomenon, known as sparking or back corona, can severely limit the effective voltages used in the precipitation process, and conse- quently bring down the collection efficiencies [W2]. The mode of conduction through a bed of fly ash particles may be either due to volume conduction or surface conduction. The former involves the motion of electrical charges through the interior of the particles and is dependent on the composition and temperature of the 138 139 particle. In surface conduction, electrical charges are carried in the surface moisture and chemical films adsorbed on the particles. Below about 3000 to 4000 F (the temperature at which most ESPs operate), sur- face conduction becomes the predominant mechanism due to the increased adsorption of moisture and chemical films which occur at these lower tem- peratures [W2]. In an effort to lower the bed resistivity, various 'conditioning' agents have been introduced into the gas stream, so as to increase either directly or indirectly the amount of moisture adsorbed on the particles. Often, much success has been achieved due to such con- ditioning. However, all attempts to explain the significant lowering of bed resistivity have thus far omitted the possible effects that high, non—uniform electric fields existing in the bed may have on the adsorp- tion process, and also on the equilibrium distribution of the adsorbate in the bed. Ditl and Coughlin [D1,D2] have proposed a model composed of neat, spherical fly ash particles stacked on each other, with the interparticle contact resistances accounting for the entire layer resistance (see Fig- ure 7.1). While conducting equilibrium experiments with fly ash as adsorbent and argon and water as adsorbates (at T = 200 C), they observe hysterisis and conclude this to be proof of capillary condensation (see Figure 7.2). By introducing a ring-like liquid condensate at the points of contact between the spherical particles (see Figure 7.3), they then go on to explain how the ash layer resistivity is significantly lowered due to this condensation phenomenon. 140 [IV y - direction of current flow Figure 7.1. Idealized array of uniform, spherical fly ash particles packed in a layer. 2.0 1 l 1.8 ;T 5 I I 1.6 If T 4 53 7:3 1' >< 4 " oadsorp.‘ i 1.2 0.: (b) odesorp. & N W _ E... 1.0 3: C63 [- 5:0 .2052 0.8 h—I 2 I- .’a" d m . 1’ > 0.6 +2 _,’ .. 0.4 o adsorp. E l ’ Bdesorp. ' n 0.2 U) 0 A J A 1 n l T "g 0 0.01 0.02 0.03 0_ l 41 .1 1 I l L, - K H O O 0.2 (3J1 0.6 0.8 1.0 adsorbate conc. [—g—§;—] m p/po Figures 7.2(a) and (b). Equilibrium curves for fly ash-argon (a); and fly ash-HzO-air (b) [D1,DZ]. 141 line of contact between two particles 42] x . . . K liqu1d meniscus Figure 7.3. Geometrical properties of capil— lary condensed liquid at a point of contact between spherical particles. However, certain discrepancies seem to exist in this model. First, in expressing the dimension YK in Figure 7.3, the authors have taken recourse to the Kelvin equation (with certain simplifying assumptions) yK ‘ 1n(; 2p.)RT (7'1) 5 k where vg = molar volume of condensate Y = surface tension of condensate p5 = vapor pressure at saturation of condensate pK = partial pressure of vapor in gas phase T = temperature 0K and R = gas constant For typical conditions in an ESP with water being the adsorbate, v£= 18 cc/gmole, Y = 46.73 dynes/cm at T = 430.90 K [82], (pK/ps) 2 .09, R = 8.3x10 (dyne cm)/(gmole OK) and one obtains from equation (7.1) _ o yK - .98 A 142 Thus, yK, the radius of curvature of the wedge-shaped interparticle pore, is of submolecular dimensions, and as such, the Kelvin equation is inapplicable.+ Also, the argument they put forward to explain the pres- ence of capillary condensate even at low, relative, partial pressures (p/ps) is quite ambiguous. As the relative pressure p/pS is increased beyond a reasonably high value (say, 0.6 = 0.7) capillary condensation may become possible and is indeed observed experimentally by the authors. In the desorption process the liquid-like adsorbate begins to evaporate and as the desorption mechanism is often quite different from the adsorp- tion one, especially when capillary condensation is involved, hysterisis is observed in the isotherms. The fact that hysterisis persists even at low relative pressures is due to the decreasing radii of curvature of the condensed liquid and does not, by itself, prove the possibility of con- densation at such low relative pressures. The moisture contents of conductive fly ash have been reported by White to be typically 0.1 to 0.3% by weight [W4]. The specific surfaces of these ashes were about .5 to l mZ/g. For these values an elementary calculation leads to the presence of five to ten molecular layers on the fly ash particles [W4], assuming that all the moisture is present in the adsorbed form. As the adsorptive force fields for water adsorbed on fly ash are known to be rather weakft this would tend to imply that much of +Actually, the application of the Kelvin equation is strictly impermis- sible for radii of curvature less than about 10 to 15 Ao [F1]. ++It is as a result of this that a 'conditioning' agent is used, so as to bind the water molecules more strongly onto the fly ash surface indirectly [W2]. 143 the adsorbed moisture is in the capillary-condensed liquid state, pri- marily at the interparticle contacts. Thus, though it is hard to explain capillary condensation in fly ash based on a Kelvin mechanism, the phenomenon, nevertheless, would seem to occur, especially for conductive fly ash. 0n the other hand, even when less than a monolayer of water has been adsorbed by a bed of fly ash, Ditl and Coughlin [D2] have reported a significant decrease in the fly ash resistivity. These observations would lead one to seek an explanation for the presence of capillary condensation in a fly ash bed (that has been exposed to an applied electric field either in the ESP, or in the course of a resistivity experiment when a voltage drop has to be imposed across the ash bed) in the phenomena attendant with the extremely high inter- particle contact electric fields that are known to exist. In addition, the charged nature of the ash particulates prior to precipitation may play some role in the equilibrium moisture content of these particles. In the following section, a possible mechanism leading to the enhance- ment of surface adsorbate concentrations at the interparticle contact regions, due to the field characteristics, is postulated. 7.1 Interparticle Field and Concentration Gradients Equation (2.22) of Section 2.4(a) gives the Kelvin pressure distri- bution in the presence of external electric fields and realized charges . E:0 2 grad P _ EOE d1v(€E) + 7(6- 1) grad E (2.22) The first term on the right-hand side is due to an average realized charge 2, and the second is due to the local electric field E. 144 Neglecting any real charges in the bed, one gets grad p = jf-(e-l) grad E (7.2) This equation implies that the Kelvin pressure distribution (and, there- fore, the concentration distribution) will be such that in regions of high field strengths, higher pressures (or concentrations) will result in the limit of thermodynamic and mechanical equilibrium. The fields estimated at the interparticle contact briefly mentioned in Section 4.1(f) are reconsidered here. contact radius a plane of contact Figure 7.4. Interparticle contact dimensions. In particular, the equation for the field 55(6) along the particle sur- face went as 55(9) = Ea/(-(ln —2:—O)Sin20) (4.8) 145 Along the surface E 2 2 _ d 2 _ +8 1 -4Cot0 VsEs (e) ‘ d(Roe)[Es (9)] ” 1%) x (In a/2Ro)2 X Sin“0 For typical ash bed values quoted in Section 4.1(f) _ 2x103V’ _ -6 ~ +3 - .32 cm , RO - 10x10 m , RO/a - 100 one has VSESZ(6) = 3.44x1018 Vz/cm3 for 0 = l0 = 1.10x1015 Vz/cm3 for e = 5° = 3.47x1013 VZ/cm3 for e = 10° The equations for the fields estimated in Section 4.1(f) were for a dry particle-particle contact with the presupposed assumption that the interparticle air gap does not break down electrically. Actual fields should take into account the existence of adsorbate and also some dielec- tric breakdown in the contact vicinity. These factors would reduce the field magnitudes somewhat, but nevertheless, the above numbers may be used as an upper limit. Using a crude estimate for the dielectric con- stant of water vapor adsorbed on fly ash (e) to be about 30, one obtains from equation (7.2) II ._a grad p 4.36x109 atm/m at 0 and II U1 grad p 1.39x106 atm/m at 0 where p is the hydrostatic pressure in the adsorbate. Thus, in the equilibrium limit, extremely high pressure gradients (and, therefore, adsorbate concentration gradients) need to exist at the interparticle contact points, so as to overcome the ponderomotive forces created by 146 the high fields. The above analysis may be used to explain why the resistivity of a bed of fly ash is reduced significantly, even for adsorbed amounts of less than a monolayer of water vapor. However, it does not necessarily predict an enhancement in the total amount of adsorbate in the bed, due to the imposed fields, as the redistribution of matter, due to the extremely high and non—uniform interparticle contact fields, is a very 'local' phenomenon affecting a rather small percentage of the available surface area (specifically, at the interparticle contacts). In Section 4.1(e), the field characteristics around a charged spherical particle were estimated. Estimates for typical charged fly ash particulates yielded very strong field gradients at the particle sur— face. It is to be remembered that the fly ash particulates prior to being collected on the grounded plate are charged. The adsorption kin- etics and equilibria of moisture adsorbed from the surrounding flue gas could well be affected by these charges. From the knowledge gathered thus far, it seems improbable that the rate of gaseous adsorption onto the particles will be affected, as the rate controlling mechanism is gas phase diffusion. However, it is probable that the presence of ionic charges on the particle surfaces could affect the equilibrium amount of water vapor adsorbed, possibly, by altering the adsorbate-adsorbent bond characteristics (for example, by more strongly binding the adsorbate, much like 'conditioning' agents such as NH3, 803, etc.). If this hypoth- esis were indeed proven to be true, then, as the particles give up their charges on precipitation, this would lead to further redistribution of the adsorbate on the particle surface, due to altered surface properties. In this way, one could visualize a significant amount of interparticle 147 capillary condensate brought about by a combination of particle charges and local non-uniform fields in the ash layer. 7.2 Preliminary Experiments with Fly Ash The results of experiments dealing with the adsorption of water vapor on fly ash (conducted in the M.S.U. laboratory) are represented in Figures 7.5 and 7.6. Owing to the limited sensitivity of the electro- balance used, the necessity of keeping the entire sample weight to the minimum possible and the extremely small water vapor adsorption capacity of fly ash (relative to silica gel, porous alumina, etc.), there is understandably some scatter in the data corresponding to p/pS = 2/3 (no condensation). Figure 7.5 represents the adsorption of water vapor on fly ash at a relative saturation of 2/3. In case (2) the cylindrical sample pan was of much smaller diameter than the one used in case (1), and consequently, the sample experienced a higher average field. In both the cases the application of the cylindrical field seems to result in a net reduction in the maximum amount of moisture adsorbed. A small corona current was recorded when the field was on. The current flow reduced significantly when the fly ash particles were removed from the sample pan, indicating that the presence of the fly ash led to inter- particle air gap breakdown and the resultant ionic current. 0n shutting off the voltage, the bed seemed to gradually adsorb more moisture until the water content reached almost the same capacity as with no field on. °C. This phenomenon occurred repeatedly, both at T = 250 C and at T = 37 Three possible causes may be given to explain this behavior: (1) As observed by Panchenko et a1. [P10], the application of strong electric fields led to a significant reduction in the water vapor adsorption cap- acity of cellulose and potato starch, possibly due to a rearrangement of m (mg.) m (mg.) 148 2.4' 1 6 90.91} No field . O h," AV=3KV(T=37 C) 1"" Av=6KV(T=250 C) a; c; a: 0.8 ' 2 V v ' ' 0.0 4' ‘ l i 4 t (mins.) Figure 7.5. Fly ash-H20 vapor, p/pS 2 2/3: (1) 1.6 cm dia. pan; (2) .7 cm dia. pan. 9.6- "°"'}No field 1 8.05 000000 _ X xx lira: AWL—5 KV IJ|JI|Iw. AV==6 KV Figure 7.6. Fly ash-water vapor, p/ps = l. 149 the particles in the regions of smaller available surface area. The fact that the fly ash bed seems to regain its original capacity fairly soon once the field is turned off, seems, however, to eliminate this hypothesis. (2) The ionic current could be sufficient to heat up the bed, and thereby reduce its adsorption capacity. Rough calculations made in Appendix A.5 offer some credibility to this explanation. (3) The presence of positive ions (negative corona) may itself be responsible for a net reduction of adsorption capacity (how, it is unclear). Changing the central filament electrode from the negative terminal (negative corona) to the positive terminal (positive corona) essentially eliminates the current flow (at AV==3 KV) and, surprisingly, even the observed reduction in adsorption capacity. In Figure 7.6 is represented the adsorption kinetics of water vapor on fly ash at p/ps 2 l and T=25° C. Within experimental error, ng_effects were observed, even with sufficiently high fields and significant adsorption. The adsorption kinetics remained unaffected, even though a corona current (for a nega- tive corona) was still observed. This may be due to the fact that though the corona current was essentially of the same magnitude as in Figure 7.5 (3 to 4 uA), the net voltage drop across the bed is much smaller in this case, owing to significant decrease in resistivity (or increase in diel— ectric constant) of the bed. To summarize the experiments conducted with fly ash, one might say: (1) When no ionic current is present, the adsorption kinetics and equi- libria of water vapor on fly ash are essentially unaffected by the applied fields for 2/35_p/p55;1. (2) The ionic current seems to affect the maximum amount of adsorbate adsorbed when the relative pressure of surrounding vapor is less than 1. 150 Based on these observations and the conclusions derived from the experiments in Chapter V, appropriate recommendations for future work with fly ash, especially in relation to its resistivity, are made in Chapter VIII. CHAPTER VIII CONCLUSIONS AND RECOMMENDATIONS FOR CONTINUED RESEARCH 8.1 Conclusions The various conclusions arrived at from the theoretical and experi- mental investigations conducted in this work are listed below: a) The_gas-phase electro-convective flux is negligible. Various experiments described in Chapter V, wherein the gas-phase diffusion fluxes determine the rate of adsorption, have shown that the field- induced enhancements are negligible. Considering that the polarizabil- ities of even polar gases are extremely small (when compared with adsor- bate or liquid-phase polarizabilities), this result is only to be expec- ted. The theoretical analysis conducted in the available literature thus far [P2,P12] has proposed the electro-convective gas-phase flux described by equation (1.4) as the predominant field-induced transport flux. This is certainly not true. b) Field-induced surface diffusion fluxes are negligible for dif- fusion over monolayer covered adsorbents. For adsorbents with micropores in which surface diffusion and simultaneous Knudsen diffusion is pre- dominant, the effect of applied fields is minimal when only a few layers of adsorbate are present in the sample. The polarizabilities of mole— cules adsorbed in the monolayer are comparable to those in the gas phase and, as such, the ponderomotive forces are weak. Interactions with the 151 152 adsorbent surface tend to further weaken the field-induced phenomena. c) Field-induced surface diffusion fluxes are appreciable for dif- fusion over multilayers of adsorbed vapor. The polarizabilities of multilayer adsorbed vapor are generally large and could even exceed that corresponding to the bulk liquid state. Surface interactions are weaker, and strong internal field gradients could exist in the pores of the adsorbent. Adsorption kinetics in moist capillary porous adsorbents of a polar vapor like H20 is definitely enhanced by applied electric fields. d) Internal relaxation field gradients are responsible for the enhanced fluxes and not the nature of the overall, externally applied fields. Theoretical calculations of field gradients in a moist silica gel bed have led to the conclusion that the gradients resulting from local fields in a pore (relaxing with the progress of adsorption) are much larger in magnitude than the gradients existing in the macroscopic adsorbent bed. Experiments conducted in Section 5.6(b) seem to confirm this hypothesis. Uniform externally applied fields of the same average field squared () as those existing in a bed subjected to a non- uniform external field should produce similar adsorption rate enhance- ments. Observations to the contrary have been made in references [P1, P2,P3], but for much lower s in the uniform field case. e) Surface ions in adsorbents definitely alter the adsorption kinetics. Silica Gel S-2509 containing significant Na+ ions showed definite reduction in the field-induced effects when treated with con- centrated HCl to remove all surface ions (Figure 5.23). The surface ions play a significant role in the field-induced mass transport phen- omena. f) The 'single-pore' theoretical model represents the field-enhanced 153 adsorption kinetics in ion-freepporous adsorbents with cylindrical pores fairly well. Given the adsorption characteristics (including the surface diffusion coefficient) for diffusion in porous adsorbents like silica gel in the absence of an external field, the field-induced enhancements due to the action of the ponderomotive forces on polarized adsorbate mole— cules is satisfactorily predicted by the application of this mathematical model. The procedure of translating the enhanced mass flux ratios obtained in the 'single-pore' model to the actual adsorbent-adsorbate system works fairly well, as long as the pore characteristics and the adsorbate characteristics in the pore are known quite adequately. g) The adsorption kinetics of nonjpolar adsorbates in porous media is unaffected by applied fields. The observation that non-polar, low dielectric constant vapors do not experience additional field-assisted mass fluxes [P2,P3] is confirmed in this work. CZCI“ was used as adsor- 0 bate at p/ps = I and T = 25 C. h) Desorption or evaporation phenomena from moist capillaries in electrostatic fields are essentially unaffected. Enhancements in evapo- ration rates from fine capillaries observed in [P11,P12] are due pri- marily to the ionic corona discharge and not the applied fields. Experi- ments conducted in Section 5.6(c) to observe the field-related effects on the desorption process of water vapor from silica gel yielded no dis- cernible changes when electrostatic fields were used. Theoretical investigations of the desorption phenomena seem to consolidate this observation. i) Field-induced adsorption phenomena are significantly influenced by a flow of ionic current through the bed. Various experiments con- ducted when small but steady ionic currents were registered through the 154 adsorbent sample seemed to affect the adsorption kinetics significantly. In the case of silica gel the kinetics were enhanced. For fly ash the maximum adsorbed vapor was lowered in a partially saturated surrounding. The reasons behind these phenomena arising from electrodynamic effects or possible Lentz-Joulean heat production are, at present, unclear. j) Adsorption characteristics of water vapor on fly ash are unaf- fected for a humid environment (p/ps==l) but noticeably affected for a partially saturated environment (p/p§}=2/3). The flow of ionic current through a bed of fly ash (the current resulting from interparticle air— gap breakdown) seems to affect the adsorption equilibria of water vapor .4 for p/ps==2/3. In the presence of capillary condensation observed at p/ps==1 the equilibria seems to be unaffected. The rate of gas-phase diffusion into a bed of fly ash is expected to remain unaffected (from (a) above). However, theoretical calculations for the equilibrium bet- ween ponderomotive and mass flux driven forces at the interparticle contact region seem to indicate a possible enhancement of local, adsor- bate concentrations. 8.2 Recommendations for Continued Research The number of experiments that could be conducted to further probe into the effects of applied electric fields and electric discharges on gas-solid adsorption characteristics is endless. A few ideas that strike the author's mind, and that fall along the lines over which this work has developed thus far, are mentioned below. In Section 8.2(a) various experiments that could be conducted on capillary porous dielectrics, in order to further consolidate one's understanding of field-induced 155 phenomena in these well defined systems, are listed. In Section 8.2(b) experiments that could have a more direct bearing on the consequences of fly ash conditioning in the presence of particle charges, ESP fields and interparticle contact fields are suggested. In all these experiments it is to be noted that the experimenter would do very well to come up with some indirect means of measuring the adsorbed quantities, rather than use the existing direct gravimetric techniques. This would significantly reduce the problems associated with shutting off the field when making measurements, and of having to account for the repulsion—attraction effects due to accidental or unavoidable charging of the adsorption sample and pan. This would also help in constructing a heavier adsor- bent pan, sturdier electrode assembly and provide the facility of making current and voltage drop measurements exclusively across the sample. 8.2(a) Further Experiments with Capillary Porous Materials l) A method to significantly enhance the alkali ion concentrations in silica gel has to be found. Experiments of water vapor adsorption in gel samples with predetermined concentrations of surface ions will yield important information on the relative magnitudes of the pondero— motive forces acting on the polarized adsorbate and on the hydrated ion complexes. 2) Experiments conducted in Section 5.6(b) seemed to suggest that the field-induced adsorption rate phenomena were on account of internal relaxation fields and did not depend (explicitly) on the nature of the applied overall field. To confirm this observation, one needs to create uniform fields (between two parallel plate electrodes) of intensities at least five times larger than those used in this work (=12 KV/cm). In 156 such high fields the adsorption behavior of water vapor in porous silica gel at p/p$==l should be studied. 3) A.C. fields of low frequencies were found to have no discernible effects on the water vapor adsorption characteristics in silica gel [P3, P5]. A.C. fields of high frequencies (several KHz) should be applied across the adsorbents and the resulting phenomena arising from oscillat- ing ponderomotive forces and decreased dielectric constants (E a l/fre- quency) investigated. The effect of alternating fields on the maximum amount of adsorbed material should be noted, especially for those instances where the adsorbate-adsorbent bond strengths are known to be relatively weak. 4) Just as for Silica Gel S-2509, water vapor adsorption studies should be investigated in the presence of non—uniform fields for other adsorbents like porous glass, zeolite beads, etc., at a relative pres- sure of = l. The relative magnitudes of the electrical effects on the multilayer adsorbate formation in these adsorbents should provide infor- mation on the relative polarizabilities of water vapor adsorbed on these surfaces. 5) Adsorption experiments in point—plane electrode configurations should be further investigated to estimate the role of a discharge of ions in both the kinetics and equilbrium characteristics of gas-solid adsorption. If possible, the adsorbent temperature should be monitored so as to estimate the role played by the production of Lentz-Joulean heat. The adsorbent sample pan should be constructed in such a way that the adsorbent geometry lends itself to easy field analysis around a point electrode. 157 8.2(b) Experiments with Fly Ash As mentioned in Chapter VII, a bed of fly ash particulates may be assumed to consist of ideal spheres arranged one on t0p of another (see Figure 8.1). The diffusion of water vapor into this bed is through the macropores formed in between the particles. Diffusion through the gas phase is expected to be far greater than surface diffusion. As such, the rate of adsorption on the fly ash particles is not expected to be enhanced due to any field-induced effects. However, besides the effects of electric fields on gas-phase diffusion phenomena, two other effects need to be considered. First, What is the role of the ionic current passing through the ash bed in influencing the adsorption characteris- tics?, and second, What is the influence of the strong, non-uniform interparticle fields on the equilibrium distribution of adsorbate in the interparticle contact region? Figure 8.1. Bed of ideal spheres. The ionic current in a bed of fly ash subjected to an electric field can be due to two sources: 1) breakdown of the gas in the interparticle contact vicinities, resulting from extremely high fields; and 2) a cur- rent, due to a corona discharge from a fine wire, point, etc., placed away from the bed, as in Figure 8.2. For the experiments conducted in Chapter VII, it was confirmed that the current registered was due to the first of the two sources mentioned above. At p/ps = 0.67, the adsorption capacity of water vapor on fly ash was found to be reduced when the 158 electrode Figure 8.2. Corona discharge through bed (neg- ative corona). current passed through the bed. It was hypothesized that this could be due to a heating effect, though this hypothesis is open to question. To more nearly simulate the ash bed in a precipitator and to study the effect of an ionic current through the bed, the following experiment is proposed. Fly ash is packed into an annular sample container and placed con- centric with a central high voltage electrode (shown in Figure 8.3 below). fly ash .t__3 ..... __. - _.L__.J. Figure 8.3. Annular pan with fly ash. [Il‘llllllllc Iv 159 If the central electrode is a fine filament, then, by applying a high enough voltage, a corona discharge could be maintained (negative and/or positive). By replacing the central filament with a rod, similar fields could be applied across the ash bed without any current flow. In the case of the experiments in Chapter VII, positive ions passed through the bed to the negative filament electrode. In this experiment both positive ions and electrons (the latter would simulate the ESP) could be made to pass through the bed. It remains to be seen whether the passage of electrons through the bed would have an opposite effect from the one observed in Chapter VII. As for the influence of strong, non-uniform interparticle contact fields, one needs to conduct the following experiments: a) Obtain capacitance measurements of fly ash as a function of moisture content in a dielectric cell. From these measurements, as shown in Chapter IV, the adsorbed water vapor dielectric constants may be esti- mated. b) Knowing the dielectric constants of water adsorbed on fly ash, one needs to estimate precise field distributions on the particle sur- face in the contact regions, taking into account the simultaneous effects of adsorbate concentrations on the field strengths themselves. c) The equilibrium surface adsorbate concentration distribution should then be estimated based on equations referred to in Chapter VII. The results should help verify (theoretically) whether sufficient adsor- bate exists in the contact vicinities to justify condensation. Other experiments on fly ash that would help throw considerable light on the problem of fly ash conditioning include: 1) determining the maximum moisture content of charged versus uncharged particles in a 160 humid environment, and 2) determining the effects of applied electric fields on the diffusion of water vapor through fly ash impregnated with significant concentrations of alkali ions. The motivation for the former lies in the possible role that surface electronic charges may play in the adsorbate-adsorbent bond formation, and also in the influence that highly non-uniform radial fields may have on the adsorption phenomena. As for the latter, the role of alkali ions in the transport phenomena over fly ash particulates has been investigated [Bl,B2], but their role in the rate of adsorption of water vapor in a fly ash bed in the presence of an imposed field (and ionic leakage current) is not well understood. The ion-related surface transfer of water molecules is especially sig- nificant when only a monolayer or so of water vapor has been adsorbed. APPENDICES APPENDIX A ESTIMATION OF OVERALL ELECTRIC FIELDS APPENDIX A ESTIMATION OF OVERALL ELECTRIC FIELDS A.1 Dielectric Sphere in a Uniform Electric Field ” fl _ : #_,_——- fl * 'Ih' —- 1 _- l"- q ----n ‘ q _- tz:.:::. —- q ---- g fl # _____ f * fl a Figure 4.2. Dielectric sphere in uniform field. The potential distribution around a dielectric sphere subjected to a uniform external field is given by [R5, p. 93] R3 _ _ (8-1) _9 ¢1(r,0) - EorCose + (€+2) r2 EOCOSO (A.1) whereeziesthe dielectric constant of the sphere, R its radius and E0 0 the applied external field intensity. The field intensity in medium 1 is given by +n1 u I <1 6- u l thi (A.2) R3 = E [(5'1) 0 Sine - Sin0]e 0 +6 (8+2) 53' R 3 (€-__1)_9 + Eo[2(e+2) r3 Cose + C050 E 161 162 The force on a dipole molecule in a non—uniform field is given by E = peff'VE (A.3) 2 — u 0 D I where “eff - EFT-E is the effective dipole moment. 2 _ Ll , 2 5" 371., E V5 6_k—T VIE I (AA) From (A.2) then, 6-1 2R06 1 2 Rot5 |E|2 = E 2[[———]Z ——- Sin2 0 + 4[: 1 —g- C0520 0 6+2 r6 +2} r (A.5) R3 1R3 _ €1_0.2 6" O 2 +1 2[e+2]r 3 Sin 0 + 4[€+2);3-Cos 0] and 2 _ l_jL_ 2 jL_ 2 VIE I r 80 IE l :0 + 8r IE I Er (A'6) The radial component of the force f = frEr 2 u fr 6kT Bar IE2 I 2 2 6 6 11 E 2 R0 2 R : ——-(-)—— [-6[€ 1]O —7- SinzO - 24[:1] '—3 C0526 w —%— C0526] f—fi I NH ;_1 850 R 3 +6[€‘1] Fif- Sin20 - 12 2+ At the particle surface e-l 3Sin20 e-l 36 2 {6[—] KW - 12[m] X (8+2) C08 6} 01‘ 163 _ -3(e-1) (50“)2 _____ 2 _ . 2 fR0 - RokT x (€+2)2 x (2€Cos 0 Sin 0) (A.7) A.1(a) Average Field Gradient at Particle Surface Let f(0) = 26C0520 - Sinze then 2 n/2 f(0) = —- (ZECOSZO - Sin20)d0 avg n 0 = €-—1/2 . avg 3 (8—1) “E0 2 . f(6) = --§— k1. 5+2 (e-1/2) (A.8) r=R0 o For H20, U = 6.183(10-28 Cle and k = Boltzmann's constant = 1.38x10.23 CV/OK, T = 2980 K, e 5 and R0 = .175 cm (for alumina beads). If 10KV O 2.5” - 1.575 KV/cm , then f avg = - 3 X (5—1) r=R .175 cm (1.38x10‘23it298)CV O 6.18x10-28C _ fl(.752_.302) J 2nr1.dr 1.776 (KV/cm) avg .30 2 _ _ 2 :12 2 3 VEa - ( 932.23) x r3(V /cm ) and .2 ~_ 7 2 3 VEavg 1.471x10 (V /Cm ) 166 A.3 Cylindrical Bed of Dielectric Particles in Cylindrical Electrical Field HIIIIF—IIII- —————o-—- Figure 4.4. Cylindrical sample bed coaxial with cylindrical field. Once again, the Laplace equation in cylindrical coordinates, com- bined with the two boundary conditions mentioned in Section A.2, lead to the relations -dva - (vi_vR,) I +a dr 1n R'/Ri ?'Er [Tl II I V : (EaViln Ro/Ri + EOVR lnR /Ri) I I (colnR /R1 + ealn Ro/R ) and therefore, (Vi'VRO) _ 1 _ E _ a - (lnR'/Ri+€aln RO/R') ? - r (B-HED Bzx-4 1 1 . 2 = __ -._ ’ (R'+Ri) ’ (R'z-Rii) [Ri R'] For Figures 5.8, 5.9 and 5.10: (V.-VR ) = AV = 3000 V, R = 1.25 cm, R' = 0.5 cm, Ri = .0089 cm 1 0 O and ea 2 360 (approximate value for A1203 particles, CaC03 powder and porous glass). 167 = 1.739 (KV/cm) = 3.46x10° (VZ/cma) For Figure 5.11: Same as above, with AV = 4000 V, R' = .35 cm = 2.975 (KV/cm) = 10.2x10° (VZ/cm3) For Figure 5.12: AV = 4000 V, R' = .175 cm, 6 = 46 a o = 4.01 (KV/cm) = 1.90x109 (Vz/cma) For Figure 5.13(a): AV = 6500 V, R' = .35 cm, 6 = 28 a o = 5.82 (KV/cm) = 3.913x109 (v2/6m3) For Figure 5.13(b): AV = 6500 V, R' = .175 cm, 6 = 26 a O = 10.23 (KV/cm) = 1.24x10‘° (VZ/cm3) For Figure 5.14: AV = 4000 V, R' = .35 cm, 8 = 3s a o = 2.975 (KV/cm) = 1.02x109 (v2/6m3) For Figure 5.15: AV = 6000 V, R' = .175 cm, Ea = 1.580 168 = 11.01 (KV/cm) = 1.43x1010 (Vz/cm3) For Figure 5.16: AV = 6000 V, R' = .175 cm, 6 2 48 a O = 6.02 (KV/cm) = 4.28x109 (Vz/cm3) For Figure 5.18: AV = 6000 V, R' = .16 cm, s = 1.58 a o = 11.893 (KV/cm) = 1.680x101° (v2/6m3) A.4 Calculations for Section 5.6(b); Keeping Average E2 Constant but Decreasingpthe Average VE2 For the pan-electrode geometries used in Figures 5.18 and 5.20, the overall electric field is given by (see Section A.3) _ (AV) _1 e + - lnR/Ri+elnRo/R r +T For the grounded filament electrode geometry used in Figure 5.18, Ri = .00889 cm, R' = .16 cm, R0 = 1.25 cm; and for the thick grounded electrode geometry in Figure 5.20, Ri = .0348 cm, R' = .18 cm and R = 1.25 cm. 0 The average field squared is given by RI 2 _ 1 2 _ n(R'2-Riz) x 2n JR r(E )dr 1 01‘ AV2 2 R' (1r1R'/Ri+€lnRo/R')2 X (11124212) 1n fil- (A.9) 169 For Figure 5.18 2 = , 2) = 6000 AV 6000 V, aDd .. (E (2.89+€X2o056) 2 x 226.5 E, the dielectric constant of the bed, varies as adsorption proceeds towards saturation. The variation of amount adsorbed, W vs. a, may be taken from Table 4.1. For Figure 5.20, one has (AV) 2 <2): E (1.674-Ex1.911) x 101.21 (A.10) Table A.1 lists W, e and the AV obtained from equation (A.10), so as to keep the same as in equation (A.9) (for the same W). Also listed in Table A.1 are the average field gradient squared for the two cases where is given by sz I I (lnR /Ri+elnRO/R ) —1—} : R' 2 x 4{§f- 1 Note that while the average are maintained the same, the average in Figure 5.20 is only 38% of the same quantity in Figure 5.18. A.5 Approximate Calculations for Temperature Rise of Bed Due to Ionic Current For Silica Gel: mass of dry sample 2 60 mg Q (1x10'5 A)(1000 V);(14,33 cals/min (AV) .0143 cals/min P‘ H At equilibrium Q = hAATeq 170 Table A.1. Comparison of Fields for Figures 5.18 and 5.20. (VEZ>' 2 W 5 AV (KV) . . §%%;§f for Figure for Figure 5.18 5.20 0 1.53 6.83 1.646x101° 6.25x109 0.38 .10 2.08 7.07 1.167x101° 4.44x109 0.38 .20 4.18 7.55 4.55 x109 1.73x109 0.38 .30 7.39 7.84 1.83 x109 6.96x108 0.38 .40 10.98 7.99 9.24 x10° 3.51x108 0.38 .50 14.63 8.07 5.52 x108 2.1 x108 0.38 .60 18.48 8.12 3.59 x10° 1.36x10° 0.38 .70 22.30 8.16 2.52 x10° 9.59x107 0.38 1m“ - RT — 171 where h = heat transfer coefficient of N2 - gel interface A = area of heat transfer ATeq = temperature difference at equilibrium between bed and surroundings for constant Q For heat transfer by natural convection, h may be obtained from Figure 13.5-1 of reference [88]. For air, Pr 2 .73, pair 2 7.36x10'“ gm/cc at T = 298° K, p 2 1.754x10'“ g/cm sec, k z 6.27x10‘5 cal/ f sec cm OK; and for d = .32 cm 3 2 Cr = é—Qréél 2 1.897 AT U Tf For AT 2 0.50 K (estimate), Gr 2 .95; and from Figure 13.5-1 of [58] h 2 2.05x10'ucal/cm2 sec OK . AT 2 Q/hA 2 .0143 cals/min x 1 min/60 secs ' eq 2.05x10‘“ cal/cm2 sec °Kxnx.32 cmx2.5 cm 2 .46° c For Fly Ash: ? mass of dry sample = 150 mg Q 2 (3x10-6 A)(2000 V) x 14.33 cals/min (AV) .0858 cals/min Gr 19.86 AT Q r‘——-4 I U I? I2 172 For AT II o . 5 C (estlmate), Gr 2 99.3; and from Figure 13.5-1 of [88] :T I? 1.79x10-“ cal/cm2 sec OK AT : Q/hA : .0858 cals/min x 1 min/60 secs eq 1-79X10-“ cal/cm2 sec PKxnxJ cmx 1 cm I? 3.64° (3 NOTE: The unsteady state temperature rise of protions of the bed away from the heat transfer surface could be higher than the equilib- rium temperature rises estimated here. A.6 Chargpd Spherical Dielectric Particle in Uniform Electric Field Figure 4.5. Charged particle in uni- form external field. (e-l) Ro3 e Roon E = EOCose [2(e+2) ;g-+ 1] + 3[€+2] r2 (A-ll) The first term is due to the dielectric sphere existing in the external uniform field, while the second term is due to the charges on the sphere. At saturation the force on an approaching ion F = qionE = 0, i.e., no + 173 more ions are caught (for n/2<:0< .1986, then 62 = .0927 x 1.05 + (.1986-.0927) x 43.3 + (Ci-.1986) x 104 177 Rewriting equation (4.13), one has 6 +2 36 6 o (6 -€O)(€ +2) L]- 3 ILL-.9. + +J 2 [ 3 (2€p+1) + 3(61-1) (£1 2) 3(82-1) (8.3) where 6p = dielectric constant of particle Thus, knowing W (gms adsorbate overall/gm dry adsorbent) and assum- ing a uniform adsorbate layer (as in 4.3(b), Part 1(1)), one can obtain C. ( 1 W/Wmax) and then 63 and 62 as described above. Finally, from the above equation (B.3), the dielectric constant for the particle 6p may be estimated as -b - /b2-4ac E = p 2a where o o b = 5 _ 96 _ 6(6 -1) + (66 -3) 3 41Tc1 411C2 o o - 6 - 215$) _36_ a 2 - 47rc2 and C - 2 41rc1 + 411C2 B.l(d) Overall Bed Dielectric Constant, 6 Treating the bed as spherical solid particles of dielectric con- stant 6p interspersed with air, one has 41m2 4nc1 3 (€p-1)/(€p+2) 0 (only two phases, particle and air) From (4.9) and (4.10), then, 178 E(6+2)/3 = Ep'6l + [2ETTIE63 (8.4) and E(6-l)/4n = 3(6p-l)6lEp'/{4n(6p+2)} (8.5) which can be solved for 6, knowing 6p = particle dielectric constant 63 = volume fraction of macropore (or interparticle) void volume (==.4715) (see B.l(c)) 61 = volume fraction of particle space in bed = (1-63) 5 = -b 4’2ng where 6 +2 a = 2(ep+2)/(ep-1)-2 and c = - -B——--2 B.l(e) Overall Electric Field Estimate AV Er = (lnR'/Ri-+6lnR'/RO) %- (see Figure 4.10) In this work with Silica Gel S-2509, AV = 6000 V, R' = .16 cm, Ri = .00889 cm, and R0 = 1.25 cm. The value of r to be used is that corresponding to the average of the field squared in the bed, and has been estimated in Section B.2 as r 2 .0667 cm avg 179 B.l(f) Obtaining the Local Particle Field Having obtained the macroscopic overall field E, equation (8.5) may be used to estimate Ep' = Ep(6p+2)/3, where Ep is the average particle particle field. However, due to the long, narrow pores in silica gel and the extended diffusion time periods, the adsorbate concentration in the pore will be non-uniform, decreasing as the pore center is reached. Con- sequently, the local particle dielectric constant 6pi may be very differ- ent from the average particle dielectric constant 6p. In Section 4.3(b), Part II, it was shown that the local particle fields Epi may be obtained from the relation Epi 2 Ep(€p+2)/(Epi+2) (B.6) Knowing the local adsorbate concentration Ci’ the analysis under- gone in B.l(c) may be reapplied to the small, local segment whose adsor- bate concentration is Ci’ and thus the local dielectric constant 6 may pi be obtained. Knowing Epi’ Epi is easily obtained from equation (B.6). Finally, equations (4.9) and (4.10) may be rewritten as (Epi+2) €1+2 €2+2 6 38pi E 5 B Epi 3 = 3 5151 + 3 52 2 + 26pi+1 pi a ( '7) (E i-l) 6 +2 6 +2 where 62 = local adsorbate dielectric constant (obtained from knowing Ci and applying equations as in Section B.l(c)) 61 = local gel solid volume fraction 62 = local adsorbate volume fraction 6 = local gas phase volume fraction 180 From (8.7) and (B.8), the fields E1 and E2 can be estimated, and E3 (gas phase field) is next obtained as E3 = 36piEpi/(26pi+l). Thus, E and E the required adsorbate and gas phase average, internal fields 2 3’ respectively, are obtained as functions of the local Ci' B.2 Estimation of ravg: Radial Position of Average For the internal fields, the gradients of the internal field squared VEgi are dependent on the magnitudes of the overall field squared E2, and not the overall gradient of the field squared VEZ. Hence, one needs to estimate the magnitude of the average field squared . In Figure 5.18 and the model described in Chapter VI, the bed has dimensions Ri = .0089 cm, R' = .16 cm, R0 = 1.25 cm, and consequently, E2 _ AVZ l “ (lnR'/Ri+6lnRO/R')2 r2 82 T2 , where B = f(6) The average E2 is given by R' 2 2 _ 2 x2n l _ 28 R' (E > ‘ B Trc'R'Z-RiZ) IR ‘77“ ‘ (R' -R )1“[Ri or 2-1n.l6/.0089 2 _ 2 = 2 - B x(.16?-.00892) 226.5 B Also, r may be defined as avg 2 = 2 avg which then gives r = .0667 cm avg APPENDIX C EXPERIMENTAL DATA 8 DATA ANALYSIS C.1 BLANK DATA: (Field data same as No Field data) DATA FOR ADSORPTION OF WATER VAPOR ON BEADS: _t_: 111%: O 0 EXPERIMENTAL DATA 6 DATA ANALYSIS APPENDIX C Spherical, Porous, Alundum Beads in Uniform Field (averaged) 4 .30 12 .55 20 .70 (for Figure 5.3) 28 .80 36 .90 (Corrected for blank readings) No Field data With E 4 12 20 28 36 44 52 60 mg _— £0me 11 .12 .11 .7 .69 10. 10. 10. .01 10 52 79 Field data I. 4 12 20 28 36 44 52 60 E3 .18 .39 .08 .84 .27 .68 .11 .15 |r+ 12 20 28 36 44 52 60 Id 12 20 28 36 44 52 6O HHH OOO‘DkDmV 44 .90 .26 .77 .51 .95 .29 .63 .96 In? .27 .27 .80 .72 .10 .51 .68 .95 52 .90 6O .90 |r+ 12 20 28 36 44 52 6O |r+ 12 20 28 37 44 52 60 10 10. .03 11 H OOWO‘M .93 .68 .54 .29 .47 78 182 C.2 Drying Grade Silica Gel— Water Vapor in Uniform Field (for Figure 5.4) (Blank readings negligible) No Field data E E E E E E E E E E 4 .0095 4 .0067 4 .0067 4 .0071 105 .1435 20 .0378 12 .0244 20 .0373 20 .0395 135 .1689 36 .0622 28 .0520 36 .0614 36 .0658 165 .1910 52 .0830 44 .0756 52 .0823 52 .0865 195 .2100 68 .1025 60 .0956 68 .1004 68 .1056 225 .2253 84 .1181 76 .1138 84 .1174 84 .1230 250 .2237 90 .1240 90 .1283 90 .1226 With Field data E E E E E E E E E E 4 .0066 4 .0068 4 .0064 4 .0070 105 .1443 12 .0255 20 .0393 12 .024 20 .0396 135 .1691 28 .0530 36 .0653 28 .053 36 .0657 165 .1907 44 .0770 52 .0871 44 .0778 52 .0847 195 .2068 60 .0979 68 .1076 60 .097 68 .1039 210 .2147 76 .1157 84 .1241 76 .1152 84 .1238 225 .2212 90 .1296 90 .1304 90 .1293 C.3 Water Vapor Adsorption on Bed of Alumina Beads in Uniform Field (for Figure 5.5) (Blank readings small) Without Field data With Field data E 9.8 E E8. E E8 E E8 5 1.45 5 1.45 5 1.61 5 1.50 10 2.88 15 4.01 15 4.27 15 3.72 25 5.74 25 5.67 25 5.89 25 5.15 35 6.76 35 6.78 35 6.76 35 6.46 45 7.63 45 7.57 45 7.55 45 7.51 60 8.43 60 8.49 62 8.87 60 8.18 70 8.89 70 8.93 70 9.10 75 9.08 80 9.28 80 9.25 80 9.57 90 9.46 90 9.53 95 9.71 90 9.43 105 10.02 100 9.78 110 10.00 100 9.87 120 10.21 110 9.95 120 10.17 110 10.17 120 10.12 120 10.21 183 C.4 Water Vapor Adsorption in Crushed A1203 Particles in Uniform Field (for Figure 5.6) (Trouble during weighing with field on for approximately first 15 mins. Reading at t = 15 mins. taken as start of adsorption.) Without Field data E E8. E 15 O 15 25 2.54 25 35 4.47 82 45 6.21 90 60 8.39 105 75 10.16 123 90 11.64 With Field data E E E 15 0.00 15 25 2.46 25 35 4.62 35 45 6.18 45 60 8.63 60 75 11.18 75 90 12.59 90 C.5 Adsorption of Water Vapor in Crushed 2.78 11.01 11.89 13.08 14.38 .00 .30 .66 .71 .62 .17 .68 Hooooxbmo Hp Alumina in Cylindrical Field and Annular Screen Sample Container (for Figures 5.7a, b, c, and d) BLANK DATA: (averaged) No With Field Field E_fl__fl&_ 6 .80 .80 14 1.46 1.24 24 1.78 1.43 34 1.94 1.50 45 2.06 1.51 60 2.18 1.52 75 2.27 1.54 E 90 105 120 135 150 165 180 NNNNNNN No .37 .39 .44 .47 .50 .51 .52 t 140 160 180 200 220 240 105 120 140 160 180 200 220 240 With Field Field _fl__m8_ b-ID—OI—II—II-‘HI—I .56 .58 .58 .58 .58 .58 .58 E8 15 16. 17. 18. 18. 19. 12. .00 15. 16. 17. 18. 18. 19. 14 .46 47 35 09 82 30 86 31 36 09 11 72 34 184 (All the following data obtained after subtracting blank.) For Figure 5.7(a) Without Field data E E8 E E8 E E8 E E8 6 2.61 90 22.33 6 2.53 75 20.53 9 7.13 105 23.23 14 6.74 90 21.85 24 11.13 120 23.86 24 10.96 105 22.72 34 14.21 137 24.50 34 13.96 120 23.32 45 16.70 151 24.93 48 16.93 135 24.19 60 19.19 166 25.28 60 18.64 150 24.63 75 21.13 180 25.86 With Field data E E8 E E8 E E8 E E8 0 0 90 22.33 0 0 75 20.53 6 2.61 105 23.23 6 2.54 90 21.85 19 7.13 120 23.86 14 6.74 105 22.72 24 11.13 137 24.50 24 10.96 120 23.32 34 14.21 151 24.93 34 13.96 135 24.19 45 16.70 166 25.28 48 16.93 150 24.63 60 19.19 180 25.86 60 18.44 75 21.13 For Figure 5.7(b) Without Field data E E8 E E8 E E8 E E8 8 4.18 105 21.57 6 3.0 105 22.31 14 7.49 120 22.10 14 8.49 120 23.18 24 11.84 130 22.45 25 13.25 135 23.39 34 14.64 190 24.44 35 15.84 150 23.60 45 16.68 200 24.37 45 18.22 165 24.09 60 18.54 210 24.61 60 20.15 180 24.08 75 19.64 220 24.65 76 20.96 200 24.33 90 21.18 90 21.71 E E8 E E8 6 2.69 92 21.71 14 6.97 105 22.29 24 11.35 124 22.84 34 14.76 140 23.43 45 17.10 160 23.87 60 19.03 306 26.15 75 20.55 317 25.82 With Field data For Figure 5.7(c) 14 24 34 45 6O 75 185 2. .60 .84 14. 16. .02 19. 11 18 98 29 26 19 For Figure 5.7(d) E E8 E E8 0 0 90 21.48 20 9.98 105 22.29 27 12.47 120 22.61 34 14.74 130 23.19 45 16.52 140 22.79 60 18.67 150 23.49 75 19.89 212 24.02 220 24.22 E E8 E E8 6 3.2 105 21.95 14 7.94 120 22.79 24 10.96 140 23.55 34 13.71 160 23.72 45 16.47 180 24.16 60 18.13 288 24.36 75 19.95 298 24.21 90 21.16 Without Field data E E8 E E8 8 9.43 91 24.92 14 13.99 100 25.12 24 17.82 110 22.34 34 20.31 120 25.69 45 21.67 242 27.03 60 23.33 250 27.03 75 24.21 Without Field data E E8 E E8 6 7.5 60 23.63 14 13.84 76 24.61 24 17.86 195 27.62 35 20.59 205 27.62 45 21.92 215 27.62 90 115 144 154 165 180 210 220 16 24 34 45 6O lfl 15 24 34 45 19.90 21.68 21.96 22.28 22.93 23.18 24.26 24.41 With Field data E8 E E8 9.95 75 23.62 14.45 90 24.46 17.52 105 24.80 19.98 120 25.18 21.51 220 26.39 22.98 228 26.52 With Field data E E E8 6.91 60 23.24 13.87 77 24.57 17.05 90 25.27 20.01 105 26.36 22.17 120 26.36 143 26.78 221 27.60 C.6 Water Vapor Adsorption in Crushed 186 Alumina in leindrical Field (for Figure 5.8) BLANK DATA FOR C.6, C.7, C.8: Without Field data E8 0 .51 .87 H .11 .27 .39 E 40 50 60 70 80 90 100 28 HHD—‘t—‘D—‘h—‘b—l .46 .50 .54 .55 .55 .55 .55 (Blank data subtracted) Without Field data With 14 24 34 46 60 Field data mg 5. 10. 15. 17. 20. 22. 27 82 13 99 51 17 t 6 15 24 34 45 60 75 fl 4 10. 14 17. 19 21 23. .91 62 .64 63 .96 .76 19 77 90 105 120 135 150 324 90 105 120 135 150 202 24 25. 26. 27. 27. 27. 30 24 25 .09 07 19 08 72 95 .47 .51 .64 26.48 26.88 27 30 .49 .4 (averaged) 14 24 34 45 60 76 92 11 15. 18. 20. 22. .08 .07 24 25 .34 .18 18 36 33 21 With Field data (3KV) t 120 135 150 170 190 210 230 m_g 0 .42 .69 .90 1.02 1.15 E8 26. 27. 27. 27. 28. 28. 29 81 23 47 82 44 90 .03 E 40 50 60 75 90 100 HHHD—ID—IH £8 .20 .26 .28 .30 .30 .30 187 C.7 Water Vapor Adsorption on CaC03 Powder in Cylindrical Electric Field (for Figure 5.9) (Same blank data as in C.6, with blank subtracted) Without Field data With Field data E E8 E E8 E E8 E E8 E E8 6 1.76 55 3.80 6 2.09 6 1.97 50 3.98 12 2.46 70 3.90 11 2.49 12 2.50 60 3.78 18 2.77 80 4.09 18 3.15 18 2.78 76 4.05 24 3.13 90 4.19 24 3.29 24 3.21 90 3.99 32 3.41 100 4.29 32 3.44 32 3.44 100 4.05 40 3.57 110 4.19 40 3.42 40 3.62 50 3.67 60 3.75 75 3.85 C.8 Water Vapor Adsorption in Porous Glass in Cylindrical Electric Field (for Figure 5.10) (Same blank data as in C.6, with blank subtracted) Without Field data E E8 E E8 E E8 6 3.77 6 3.77 6 3.79 12 6.26 12 5.62 12 5.93 18 7.46 19 7.12 18 6.90 24 8.54 24 7.58 24 7.71 32 9.05 32 8.49 32 8.68 40 9.57 40 8.84 40 9.14 51 10.33 50 9.43 40 9.68 60 10.34 60 9.80 60 10.18 75 10.70 77 10.77 70 10.48 90 11.11 91 10.33 80 10.77 106 11.28 105 10.43 90 10.77 120 11.28 128 10.79 99 10.77 With Field data E E8 E E8 E E8 E E8 6 3.86 40 9.68 6 3.29 32 8.94 12 6.22 50 10.41 12 5.99 40 9.19 18 7.41 62 10.33 18 7.22 50 9.38 24 8.46 75 10.67 24 7.83 65 10.04 32 9.02 90 11.01 100 11.03 110 11.16 188 C.9 Water Vapor Adsorption in Linde Zeolite Beads in Cylindrical Electrical Field (for Figure 5.11) (Blank data negligible) Without Field data E E E E E E E E 6 .0085 60 .0797 6 .0073 80 .0977 14 .0219 80 .0986 14 .0200 105 .1183 22 .0346 100 .1137 22 .0332 120 .1283 30 .0447 120 .1256 30 .0432 150 .1419 40 .0575 140 .1351 40 .0559 182 .1501 50 .0687 160 .1415 50 .0671 210 .1544 60 .0784 240 .1577 With Field data E E E E E E E E 6 .0072 80 .0923 6 .009 80 .0999 14 .0188 100 .1090 14 .0213 105 .1197 22 .0303 120 .1222 22 .0344 120 .1306 30 .0400 140 .1315 30 .0456 150 .1443 40 .0525 160 .1387 40 .057 180 .1522 52 .0657 170 .1413 50 .070 210 .1585 60 .0736 60 .0813 225 .1594 C.10 Water Vapor Adsorption in A1203 Beads Strung on Ground Electrode Filament in Cylindrical Field (for Figure 5.12) BLANK READINGS: (averaged) No With Field Field 3_ mg mgpi 6 .01 - .30 14 .03 - .40 22 .07 - .46 30 .07 - .50 4O .07 - .50 50 .07 - .50 6O .07 - .50 189 11.86 12.11 12.30 12.41 12.55 12.55 Without Field data With Field data (with blank subtracted) E E8 E E8 E E8 E 6 3.06 60 11.81 6 2.96 70 14 6.08 70 12.17 14 5.94 80 22 8.11 80 12.51 22 7.98 90 30 9.47 90 12.65 30 9.36 100 40 10.60 110 12.75 40 10.50 110 50 11.51 120 12.68 50 11.17 120 60 11.63 C.11 Water Vapor Adsorption in Drying Grade Silica Gel in Cylindrical Non-Uniform Field (for Figures 5.13a, b) BLANK DATA: 3; O 10 40 60 80 No field mg: 0 .28 1.02 1.10 1.10 With field mg: 0 .24 .90 .98 1.00 Without Field data E E 90 .2384 110 .2714 130 .2873 155 .2934 170 .2950 With Field data E E 10 .025 25 .0758 40 .120 60 .1719 80 .2156 100 .2536 For Figure 5.13(a) (AV = 4 KV) t 10 25 40 60 80 E 120 140 160 180 200 W .0282 .0796 .1253 .1796 .2253 W .2811 .2918 .2960 .2986 .2995 t 100 120 140 160 90 111 131 151 W .2622 .2862 .2942 .2974 .2333 .2688 .2893 .2962 With Field data E. .E 10 .0175 25 .0746 40 .1296 60 .1850 80 .2380 Without Field data (AV = t 100 120 140 160 E. E. 10 .048 25 .1215 42 .1895 60 .2463 76 .2813 90 .2920 105 .2972 120 .3000 With Field data E. E. 10 .0502 25 .1222 40 .1826 60 .2622 75 .2922 90 .2945 105 .300 120 .300 t 10 25 40 62 75 90 105 120 t 10 25 40 60 75 90 105 120 190 6.5 KV) E. .E E. .E .2729 10 .0229 100 .2885 25 .0750 120 .2935 40 .1257 140 .2961 60 .1844 160 80 .2371 For Figure 5.13(b) W .2723 .2886 .2923 .2936 W .9479 .1235 .1822 .2449 .2791 .2912 .2958 .2994 .3000 .0539 .1233 .1894 .2951 .2896 .2962 .3000 .3000 (All values standardized to W+ ==.30) max E. E. E. .E .0425 10 .0474 10 .1161 25 .1251 25 .1754 40 .1862 40 .2445 60 .2499 60 .2447 75 .2813 75 .2926 90 .2913 90 .2980 105 .2952 105 .3000 120 .2980 125 135 .3000 135 E E E E .0541 10 .0541 10 .1284 25 .1388 25 .1953 41 .2154 41 .2731 60 .2861 60 .2939 75 .2966 75 .2969 90 .2983 90 .2991 105 .300 105 .3000 120 .300 120 t 0 90 110 154 10 25 40 60 75 90 105 120 W 0 .2486 .2780 .2912 .0484 .1255 .187 .251 .284 .295 .2994 .3000 +Each experiment involves a different geometry and size distribution of silica gel particles. To bring about some uniformity in the comparison, an average maximum value of W==.30 is taken for the samples and the cor- responding Wmax are corrected for this maximum. With Field data E. E. 10 .0505 25 .1259 40 .1889 60 .2618 75 .2914 90 .2957 105 .2998 120 .3000 (cont'd) t 10 25 40 60 75 90 105 120 135 W .0546 .1305 .1902 .2544 .2848 .2930 .2961 .2988 .3000 191 t 10 25 4O 60 75 90 105 120 W .0505 .1291 .1982 .2659 .2925 .2974 .2976 .3000 t 10 25 40 60 75 90 105 120 W .0474 .1220 .1845 .2483 .2815 .2900 .2957 .3000 t 10 25 40 61 75 90 105 120 CHECK FOR POLARIZATION-DEPOLARIZATION EFFECT IN SECTION 5.4(d): No Fieldgpoint IZIIH 150 .2230 IZII" 132 .2735 With Fieldgpoint E W; 150 .2220 C.12 Water Vapor Adsorption in Silica Gel 5-4133 (25 A0, M.P.D.) in Cylindrical Field (for Figure 5.14) (Blank data negligible) Without Field data E. E. 1.5 .0112 11 .0818 25 .1446 40 .1956 60 .2478 With Field data E. E. 1.5 .012 10 .080 25 .1554 40 .2145 t 80 100 121 140 160 60 82 100 120 140 W .2874 .3171 .3319 .3359 .3384 .2767 .3211 .3370 .3417 .3429 t 16 25 40 60 Id 1.5 15 26 40 60 W .0071 .1136 .1516 .2023 .2558 .0100 .0997 .1522 .1987 .2678 t 80 100 120 157 160 80 100 120 140 W .2956 .3274 .3418 .3493 .3496 .3210 .3435 .3467 .3477 E W; W .0562 .1278 .1890 .2525 .2814 .2927 .2957 .3000 132 .2698 192 C.13 Monolayer Water Vapor Adsorption in Silica Gel S-2509 (60 A0, M.P.D.) in Cylindrical Field (for Figure 5.15) (Blank data negligible) Without Field data t 0 10 25 43 61 E. .E E. E. 1! LE .E 0 0 0 32 .0665 6 .0291 .0316 l .0052 45 .0721 15 .0482 .0547 5 .026 66 .0776 30 .0617 .0648 15 .0493 85 .0787 45 .069 .0733 71 .0729 With Field data t 0 ll 25 40 60 80 CDIfl 5.5 15 30 45 60 E. E. E. .E 0 0 0 0 .0354 l .0035 15 .0560 11 .0383 30 .0676 26 .0577 ' 45 .0768 41 .0669 65 .0821 109 .0768 80 C.14 Water Vapor Adsorption on Alundum Beads Strung on Ground Filament Electrode in Cylindrical Field (for Figure 5.16) E8 E. E8. E. .E8 .E 0 90 15.44 0 0 60 1.46 143 18.23 5 1.22 94 4.64 180 19.81 15 4.66 120 8.30 210 20.72 30 8.15 185 10.84 45 10.45 224 12.59 W .0245 .0528 .0687 .0728 .0743 .0743 12.30 15.40 17.00 19.78 21.15 Without Field data 193 S—2509 (M.P.D. : 60 A0) in Cylindrical Field (for Figure 5.18) (Blank data negligible) (All values of W corrected for Wm E E 15 .1016 25 .1404 40 .1924 60 .2489 90 .3197 112 .3666 130 .4035 205 .5317 240 .5820 275 .6270 302 .6577 332 .6852 370 .700 E E 5 .0478 16 .1075 30 .1619 61 .2554 101 .3558 139 .4365 With Field data E E 10 .0672 25 .1384 40 .1891 61 .2511 90 .3471 140 .4802 160 .5239 180 .5582 210 .6035 250 .6584 271 .6816 300 .6960 330 .7000 t 10 25 4O 60 90 120 175 215 242 275 364 183 230 278 312 346 366 91 156 210 255 289 306 330 W .0817 .1477 .1967 .2548 .3266 .3864 .4830 .5447 .5851 .6275 .7000 .5185 .5915 .6539 .6844 .6963 .7000 .3667 .5230 .5978 .6658 .6892 .6943 .7000 t 10 25 40 60 90 120 165 294 330 363 IH 15 30 61 90 121 10 25 41 61 80 158 180 216 300 423 = .70 ax W .0736 .1329 .1802 .2320 .3023 .3632 .4466 .6324 .6716 .7000 .0481 .1061 .1668 .2661 .3309 .3992 .0788 .1547 .2199 .2910 .3488 .5359 .5797 .6397 .6912 .7000 gm adsorbed gm adsorbent 12 10 31 60 141 204 240 278 306 421 157 188 228 265 304 341 Id 15 31 60 95 133 177 333 W .0798 .1661 .2496 .4190 .5234 .5765 .6268 .6562 .7000 .4706 .5262 .5876 .6352 .6717 .6853 .0506 .1107 .1846 .2775 .4008 .4970 .5628 .7000 ) C.15 Multilayer Water Vapor Adsorption in Silica Gel 5 15 31 60 93 124 137 201 263 310 343 362 385 Ifl 15 30 60 90 133 142 193 230 261 280 .0482 .1039 .1684 .2570 .3408 .4089 .4356 .5477 .6329 .6800 .6934 .6968 .7000 .0512 .1110 .1757 .2803 .3842 .4747 .4981 .5963 .6512 .6881 .7000 With Field data IEIIH 5 .0542 (cont'd) 45 75 .2391 .3305 194 110 .4177 160 .5221 190 .5751 235 .6460 280 .685 C.16 Adsorption of Non-Polar CzClu in Porous Silica Gel S-2509 in Cylindrical Electric Field (for Figure 5.19) (Blank data negligible) (All values of W corrected for W max t 10 21 30 45 60 Without Field data W .0396 .3964 .6996 .8845 1.046 1.05 t 1 10 22 35 51 69 W .0398 .3933 .7215 .9658 1.048 1.050 1.05) t 1 10 28 40 55 65 3 300 .7000 With Field data W .0406 .4061 .8646 1.032 .05 1.05 p...- C.17 Adsorption of Water Vapor on Silica Gel S-2509 t 1 10 25 40 55 65 in the Same Average but Smaller Average (for Figure 5.20) (No Field data same as in C.15) (All values of W corrected for W max With Field data 15 30 61 95 121 157 208 257 W .0495 .1037 .1705 .2952 .3977 .4589 .5421 .6383 .7000 7: <: \l\l\l\l\l\l\l\lo\ U'IMMEOU‘l-bNNED 15 31 60 91 116 343 .052 .12 .179 .270 .354 .409 .700 \l\l\l\l\l\l\l MMU'IU'ICNNO .70) 16 32 63. 88. 139. 166. 200 227 316 U1U1U!U‘I .06 .123 .195 .304 .377 .506 .563 .626 .665 .700 H 7': < \l\l\l\l\l\l\l\l\10‘ U1U1UIUIU‘IU'IU1U'NO .0399 .3996 .7955 .0304 .05 .05 195 C.18 Desorption Kinetics: Water Vapor- Silica Gel S-2509 (M.P.D. = 60 A0) (for Figure 5.22) Without Field data With Field data E. E. E. E. E. E. E. .E 16 .0293 10 .0085 10 .0127 11 .0177 31 .1117 21 .0627 20 .0599 20 .0655 46 .2111 35 .147 30 .1254 30 .1255 62 .3221 51 .2528 47 .2352 45 .2265 125 .6617 66 .3551 63 .3475 60 .3410 142 .6922 88 .4945 89 .5040 90 .5087 171 .7062 115 .6230 113 .6184 120 .6344 239 .7109 149 .6979 130 .6614 147 .6906 177 .7112 155 .6921 169 .7043 170 .6991 C.19 Data for Adsorption Isotherm (for Figure 3.3) (All data corrected for blank experimental data) Without Field data W p/ps W p/ps W p/ps W p/ps .0467 .140 .0447 .1368 .1000 .451 .675 .898 .0711 .280 .0738 .3090 .2214 .701 .689 .960 .1148 .457 .1650 .6170 .5980 .893 .690 1.000 .2681 .697 W: .664 W: .3758 W; .5369 W; .697 p/ps: .889 p/pS: .7922 p/ps: .833 p/ps: 1.0 With Field data w p/ps w p/ps w p/ps w WPS .0494 .1413 .0507 .195 .651 .882 .104 .456 .0824 .3187 .0931 .427 .684 .960 .2854 .753 .2709 .7233 .686 1.000 .709 1.000 g; .6839 g; .4561 w; .2347 .4835 g; .7024 p/ps: .923 p/ps: .8235 p/ps: .705 .825 p/ps: 1.0 w; .701 p/ps: 1.0 196 C.20 Procedure for Obtaining Initial Dry Silica Gel Sample Weight Example Maximum 'calibrated' weight==100 mg. Weight of sample pan (without adsorbent) brought to equilibrium with surrounding moist atmosphere (p/ps==1) = WS-+50 mg. (reading = 41293) say); 50 mg. acts as counterweight. Sample pan removed from chamber, filled with dry R.T. sample and immediately inserted back in chamber (t==0). After 1 min. reading taken (50 mg. wt. removed), reading = L1449_ After 5 min. reading = 41963_ (.1663- .1449) _ 2 initial reading = .1663 - 0 8 - .1396 (4 min/5 min= 0.8) '. sample weight (when dry) (.l396-.1293)x:100+-50 (counter wt.) 51.03 mg. sample C.21 Fly Ash-Water Vapor Data (for Figures 7.5 8 7.6) FOR FIGURE 7.5, CURVES 1 (Same blank data as in C.6; corrected for blank data) Without Field data With Field data E E8 E E8 E E8 E E8 E E8 6 1.09 6 1.18 6 1.3 6 1.45 10 1.42 13 1.73 12 1.81 12 1.81 12 1.61 20 1.67 19 1.94 20 2.26 19 1.83 19 1.98 31 1.80 24 1.93 37 2.36 26 1.92 26 1.89 41 1.92 32 2.05 47 2.36 35 1.82 35 1.84 40 2.24 60 2.59 45 2.02 50 2.48 70 2.60 60 1.84 60 2.42 70 2.44 197 FOR FIGURE 7.5, CURVES 2: Without Field data With Field data E E8 1E. E E8 E E8 0 0 5 .26 5 .39 5 .35 15 .56 15 .74 15 .86 3.1 31 .57 30 .43 31 .98 3.4 42 .47 40 .65 52 .97 51 .39 69 .97 FOR FIGURE 7.6, CURVES 1: Without Field data With Field data E E8 E E8 E E E8 HE E E8 5 .93 105 6.54 .6 5 .96 81 5.66 15 1.92 120 7.18 17 2.52 102 6.29 30 3.44 229 9.33 2.5 30 3.91 132 7.93 45 4.18 249 9.74 47 4.61 3.7 157 8.29 60 4.94 271 10.10 3.3 60 5.09 346 10.85 75 5.44 90 5.93 FOR FIGURE 7.6, CURVES 2: Without Field data With Field data E E8 .IE E E8 5 .32 5 .37 16 .94 5.4 15 .54 30 1.43 5.2 30 1.52 45 1.7 45 1.95 61 2.11 60 2.3 80 2.41 81 2.43 100 2.70 101 2.71 131 3.05 198 C.22 Water Vapor Adsorption in Crushed Alundum Beads in Point-Plane Electrode System (for Figure 5.17) Without Field data E E8 E E8 5 2.29 5 2.45 15 5.88 15 5.88 28 7.62 28 7.88 35 8.74 36 8.66 45 9.41 45 9.11 60 10.12 60 9.89 75 10.54 75 10.40 90 10.72 90 10.47 113 10.96 105 10.61 120 11.03 120 10.65 With Field data (Push on Pan (final) = 0 mg) E E8 E E8 E E8 5 2.4 5 2.44 5 2.31 15 6.23 15 6.06 15 5.26 25 7.98 25 8.14 25 7.83 35 8.98 35 9.49 35 9.10 45 9.62 45 10.15 45 9.77 60 10.28 60 10.76 60 10.56 75 10.71 75 11.00 75 10.69 90 11.04 90 11.18 90 11.00 105 11.33 105 11.26 105 11.08 120 11.33 120 11.33 120 11.26 Push on Pan (initial) 199 C.23 Water Vapor Adsorption in HCl Treated Silica Gel S-2509 (Blank data negligible) gm adsorbed (All values of W corrected for W = .70 ) max gm adsorbent SAMPLE I Without Field data With Field data E E E E 5 .0540 6 .0638 15 .1119 26 .1669 31 .1771 53 .2601 60 .2673 80 .3398 95 .3590 113 .4250 131 .4375 173 .5480 178 .5172 247 .6682 222 .5974 287 .6940 278 .6708 312 .6971 326 .6938 345 .7000 359 .6999 375 .7000 SAMPLE 11 Without Field data With Field data .t. E E E E E E E 5 .0526 5 .0533 5 .0506 5 .0575 16 .1163 17 .1249 15 .1122 15 .121 31 .1743 33 .1896 32 .1833 30 .1852 60 .2636 97 .3697 60 .2763 61 .2907 98 .3645 138 .4593 92 .3651 90 .3683 146 .4612 170 .5186 127 .4500 124 .4548 181 .5241 213 .5910 176 .5499 151 .5062 224 .5967 237 .6262 226 .6342 200 .5982 279 .6703 334 .6979 255 .6713 334 .7000 420 .7000 364 .7000 440 .7000 APPENDIX D EQUIPMENT DESCRIPTIONS APPENDIX D EQUIPMENT DESCRIPTIONS (l) 'SPELLMAN' High Voltage D.C. Supply Range: 0-20 KV (see Figure D.1) (2) 'CAHN' Gram Electrobalance (Adapted for remoted weighing) Precision = 0.1 microgram Accuracy = 0.05% of range Maximum Load on Loop B (used in this work ) = 1 g Sensitivity = .001 mg 6 V Calibration battery replaced by filtered and stabilized D.C. power supply. (see Figure D.2) (3) Blue M 'Magni Whirl' Constant Temperature Water Bath (4) 'Simpson' Ultra High Sensitivity Volt Ohm Micro-Ammeter (see Figure 0.1) (5) Model D-612T ELECTRO Filtered D.C. Power Supply (see Figure D.1) (6) 'RAYTHEON' Voltage Stabilizer 200 ”Dz; - o RHPEELAN '.... _C Figure D.1. l) H.V. Supply; 2) Multimeter; 3) D.C. Power Supply; 4) Variacs. Detachable Weighing Chamber Figure D.2. CAHN Gram Electrobalance 202 Figure D.3. Polystyren Foam Figure D. 4. Adsorption Chamber with Electrode Assembly. Adsorbent Pans used in this work. 203 Figure D.5. Adsorption Chamber in Water Bath with Weighing Chamber. Figure 0.6. Overall view of all equipment. APPENDIX E COMPUTER PROGRAM FOR SINGLE-PORE MODEL APPENDIX E COMPUTER PROGRAM FOR SINGLE-PORE MODEL As mentioned in Chapter VI, the mathematical model for surface dif- fusion and adsorption in a single, open, cylindrical pore was solved on the computer by the 'Implicit Finite Difference' scheme. The following page represents the 'flow chart' for the various operations. Some of the terms used in the G(I,N) = G(I,N) = DZO = 02(loc.) = DP(1oc.) = EP(loc.) = ES(Ioc.) = EG(loc.) = w = 02(avg) = DP(avg) = D = E = EP(avg) = ALPHA, BETA = DC = XA, XB, xc, x0 flow chart are described below: Surface adsorbate concentration (dimensionless) Gas phase concentration (dimensionless) Surface diffusion coefficient (for monolayer) Local, adsorbate dielectric constant Local, particle dielectric constant Local, particle field strength x r Local, adsorbate phase field strength x r Local, gas phase field strength x r gms. adsorbed/gm. dry adsorbent Average adsorbate dielectric constant in bed Average particle dielectric constant in bed Dielectric constant of overall bed Average field strength in bed x r Average particle field strength in bed x r (defined in program) Dielectric constant of surface hopping molecules Matrix elements 204 eta I 205 FLOW CHART FOR COMPUTER PROGRAM <¢e~ DZO=4.6E-11 DC=f(C(I,N)) I ‘EP(1oc.) 02(loc) DP(loc.)*--< ES(loc.) EG(loc.) DZ(avg)i xr Alpha 1 [Y(1)l * A L_____. _ XA(I),XB(I). XC(I),XD(I) C(I,N+l) DP(avg)‘ D,E .I’ EP(avg)‘ W=O W<.0649 Solve Matrix Yes DP(avg)=0 ,EP(avg)=0 L___._.. .L______. V L———————an Print W,T,G(1,N+1),C(I,N+l) 206 In Section E.l is given a sample output for the variation of W with respect to time T when no external field is applied. Section E.2 repre- sents the corresponding output when the field is imposed. Sections E.3 and E.4 give the dimensionless gas phase and adsorbate phase concentra- tion profiles in a single, model pore for the 'no field' and 'with field' case, respectively. PAGE .17 00.43 12/14/82 207 FTN 4.80552 74/175 OPT-1 Computer Program for 'Single Pore' Model PROGRAM PONOER O'- I ) Dv 0 w m A XN d o O t . . a - N M w ' " D 'o- > . v 00 o h m o w 0 w ‘9 ‘— U> a o m 0 \ x . U z n . 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