‘ . . 4 ALL-U 7.": ‘ w‘p . v , ‘ ‘ ‘ ‘ . - . . ‘ . ~ \ . WWW[HIWW”WWWWHWUIWIHI 301535 2309 _. I LIBRARY Michigm State Uf‘iWQYSity PLACE ll RETURN BOX to roman this checkout from your record. TO AVOID FINES mum on or before data duo. DATE DUE DATE DUE DATE DUE MSU Is An Afflnnuivo Action/Equal Opportunity Inflation Wan-9.1 This is to certify that the thesis entitled Desorption Isotherms and Drying Rates of Shelled Corn in the Temperature Range of [too to lhOOF. . presented by J. Rodriguez-Arias has been accepted towards fulfillment of the requirements for Ph.D 'dqyeein Agricultural Engineering flwdee Major professor July 26, 1956 Date 0-169 DESORPTION ISOTHERMS AND DRYING RATES OF SHELLED CORN IN THE TEMPERATURE RANGE OF 40° T0 140°r. BY Jorge H. Rodriguez-Arias AN ABSTRACT Submitted to the School for Advanced Graduate Studies of Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering Year 1956 r, ‘ Approved by ( 9&4! d’ 5 Jig/€16 EélgiL..-.é;&E€%L_ig \_ \, .70 rg‘e El . 10 dri guez-lrin s 1 The investigation is primarily CUHCGVHVJ with an experimental inquiry into the theorvtical {rs-poets of grain drying with the broad objective of gaining fundamental informatian pertaining both to the equilibrium and to the rate relationships of the drying process, with particular reference to shelled corn. The experimental phase was directed toward obtaining hygrOSCOpie equilibrium data over a wide enough range of constant drying condi- tions to permit the accurate construction of desorption isotherms O O for temperatures of 40°, no , 86°, 100 , 132°, and 140°r. A static method was used whereby thin layer samples of grain were equilibrated above saturated aqueous solutions of chemically pure salts maintained in thermostatically controlled constant—temperature cabinets. Data obtained throughout the eguilibration period allowed accurate con- struction of drying curves correSponding to the testing conditions. When examined with the B.E.T. two-constant equation the iso- therms were found to yield very satisfactory linear plots in the prescribed region of validity as well as reasonable values for the equation constants. Further treatment with the U.E.T. three- constant equation and the Harkins-Jura equation led to the con- clusion that multimolecular adsorption is the predominant water- binding mechanism in shelled corn. The analysis strongly suggests that in the region of relative pressures from zero to 0.75 the ad- Sorbed water consists of a first unimolecular layer of firmly bound molecules plus four to five additional layers'of decreasingly bound molecules; that beyond a relative pressure between 0.30 and 0.45 enough lateral interaction between adsorbed molecules deveIOps Jo rge El . l'io dri gue z—lr i as 0 I H to cause the formation of a condensed film, with condensation in increasingly larger capillaries occurring beyond a relative pres- sure of about 0.75. The isotherms were found to obey Smith's equation in the range of relative pressures from 0.45 to 0.90. The average isosteric heats of desorption at various moisture levels from 8 to 22 percent, dry basis, over the temperature range from 600 to 122°F were calculated by three different methods, all based on the Clausius-Clapeyron equation. Henderson's equation successfully describes the isotherms in the relative pressure range between 0.10 and 0.60, but it tends to considerably understate the sorption beyond that range and to slightly overstate it at the lower pressures. Furthermore, with single—valued constants the equation fails to account correctly for the temperature dependence of the isotherm. The thin layer behavior of shelled corn was found to obey closely an exponential drying law analogous to Newton's law of cool- ing. However, the rate constant was found to decrease according to stepwise discrete changes in value at various intervals throughout the drying process, which seriously hinders the usefulness of the simple equation. The instantaneous vapor pressure potential appears not to be the most important single factor governing the instantan- eous drying rate; widely divergent drying rates occurred under identical vapor pressure potentials. Over restricted ranges of moisture content the drying rate could be characterized by an equa- tion analogous to 0hm's law with the vapor pressure potential as Jorge H. Rodriguez-Arias 3 the driving force and the reciprocal of a mass transfer coefficient as the resistance. Electromagnetic irradiation of shelled corn at a moisture level of 15 percent, dry basis, with doses of 106 and 107 reps applied on both sides of the corn kernels had no notice- able effect on the drying rate. DESORPTION ISOTHELLMS AND DRYING RATES OF SHELLED CORN IN THE TElHERATURE RANGE or 40° T0 140°: By Jorge H. RodriguezeArias A THESIS Submitted to the School for.Advanced Graduate Studies of Michigan.State University of Agricultural and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering Year 1956 fycrz/EV7 i ?,131957 ACKNOWLEDGMENTS It is with great pleasure that the author eXpresses his sincere gratitude to Dr. Carl W. Hall, under whose inSpiring guidance the investigation was undertaken and to whom the re- sults are herewith dedicated. His capable and friendly counsel, unfailing interest, and continuing encouragement throughout the course of the investigation and preparation of this thesis made the work particularly enjoyable. The author feels deeply indebted to Dr. Arthur W. Fhrrall, Head of the Department of Agricultural Engineering, for the grad- uate research assistantship that enabled him to undertake the in- vestigation. Thankful acknowledgment is also due to Professor Dennis E. Wiant and to Mr. Richard C. Nicholas for their valuable cooper- ation in connection with the irradiation tests, and to Mr.‘John S. Perry, of the United States Department of.Agriculture, who generously allowed the use of equipment and cheerfully gave of his time to take pictures with which to illustrate this thesis. The author wishes to express his grateful appreciation to Dr. Walter M. Carleton; Graduate Adviser, whose friendly interest in the author's graduate program was always a source of encour- agement. The author should also like to record his grateful acknowl- edgment to his wife whose sympathetic patience and understanding helped considerably to make possible the completion of this thesis. ii VITA Jorge H. RodriguezeArias candidate for the degree of Doctor of Philosophy Final examination, July 26, 1956, 10:00 A.M., Agricultural Engineering Conference Room Dissertation: Desorption Isotherms and Drying Rates of Shelled Corn in the Temperature Range of 40° to 140°F. Outline of Studies Major subject: Agricultural Engineering Minor subject: Food Technology (Horticulture) Biographical Items Born, April 24, 1915, Ponce, Puerto Rico Undergraduate Studies College of Agriculture and Mechanic Arts of the University of Puerto Rico, 1932-36, B.S.A. Texas Agricultural and Mechanical College, 1943-45, B.S.A.E. Graduate Studies Kansas State College, 1946-47, M.S.A.E. Michigan State University, 1954-56 Experience Instructor of Vocational Agriculture, 1936-37, Department of Education, Government of Puerto Rico; At the College of Agri— culture and Mechanic Arts of the University of Puerto Rico: Instructor of Horticulture, 1937—43; On leave, 1943-47; Assis- tant Professor of Agricultural Engineering, 1947-48; Associate Professor of Agricultural Engineering, 1948—49; Associate Pro- fessor and Head, Agricultural Engineering Department, 1949-53; Professor and Head, Agricultural Engineering Department, 1953- 54; On leave, 1954-56; Graduate Research Assistant, Agricultural iii Engineering Department, Michigan State University, 1955-56 Military Service: A.E.T.M. S l/c (Radar Program) U.S. Navy, 1945-46; U. S. Naval ReserVe, 1946-50 Professional and Scientific Societies American Society of Agricultural Engineering, Member, 1939 American Society for Engineering Education, Member, 1948 Institute of Food Technologists, Professional Member, 1956 American Society of Agricultural Sciences, Member, 1940 Colegio de Agronomos de Puerto Rico, 1937 American Association for the Advancement of Science, 1938 Honorary Societies Gamma Sigma Delta, Puerto Rico Chapter (Charter Member), 1938 Sigma Xi, Associate Member, 1956 Married to Carmen Teresa Quinones, May 9, 1948 Children: Jorge Humberto (1949); Jaime Osvaldo (1953); Nelson Rafael (1955) TABLE II. III. IIIA. IV. VI. VII. VIII. IX. X. III. XIII. XIV. XVI. iv LIST OF TABLES PAGE Equilibrium relative humidities above saturated salt solutions at various temperatures ................. 55 Experimental equilibrium moisture contents of shelled corn at various relative humiditdes and temperatures .... 71 Experimental data sheet ............................. 75 Analysis of data sheet ............................. 76 Computation of data for a/X versus X plots from desorption isotherms ................................ 81 Evaluation of a9 and as from plots of Figure 8 ..... 84 Point values for the graphical evaluation of isosteric heats of desorption ................................. 91 Calculations of isosteric heats of gesorption for shelled corn over the temperature range 86 to 122 F .......... 94 Differential heats of desorption for shelled corn from 0thmer plots of isotherm data ......................... 99 Desorption isotherm constants for shelled corn ......... 106 Computation of data for B. E. T. plot of the loo°r isotherm 103 Computation of data for Harkins-Jura and Smith plots .... 118 Comparison of data by Coleman and Fellows with corresponding values calculated according ts Henderson's equation and experimental constants OOOOOOOOOOOOOOO0.00IOOOOOOOOOOOO 135 Values of half-response periods for shelled corn under different drying conditions ........................... l4l Drying rate constants, k , from semilogarithmic plots .. 147 Drying rates of shelled corn at equal values of p under different conditions ............................ 155 Mass transfer coefficients, K. , for shelled corn under various drying conditions ............................ 161 LIST OF FIGURES F IGUILE PAGE 1. Diagram showing the structural arrangement of the starch malecule COOCCCOOOOOOOOOOO0.0.0.0000...OOOOOOOOOOOOOOOOO 8 2. Two main types of containers used as constant-humidity Chambers 00......00....OCOOOOCOOOOOOOOOOOOOOOOO000...... 61 3. Constant-temperature cabinet with regular load of constant- humidity Chambers OOOOOOOOOOOOOOO0.0000000000000.000.... 61 4. Constant-temperature cabinet with most jars removed to ShO' constTUCtiou features 00000000000000.0000...eooeoee 63 5. Weighing equipment and general set-up for the weighing operation .COCOOOOCOOIOOOOOOOOOOIOOOOOOOOOOOOOOOOOOOOOOO G3 6. Brunauer's classification of the five isotherm types in phy81031 adsorption ooooeeeeooeeeeooeeeeeoeeeeeeooeeeoee l7 7. Desorption isotherms for shelled corn ................... 79 8. Plots of a/X vs. I from desorption data, showing method of evaluating a2 and a8 ............................. 82 9. Desorption isosteres for shelled corn ................... 97 10. .Evaluation of the heats of desorption for shelled corn at Various UOiBture IOVQIB ooeoeeooeoo0.0000000000000000... 90 11. 0thmer plots of desorption data for shelled corn of various maistu" levels .0......COOOOCOCCOOOOOCOCOCCC0.0.0.0.... 97 12. Variation of the 0thmer ratio of latent heats with moisture content or Shelled corn ooeoeeoeeeeeeeoeeooeeeeeoeoeeeee 100 13. B. E. T. plots of desorption isotherms for shelled corn .. 105 14. 'Variation of constants c and v of the B. E. T. equation, m . Vith temperature 0.00.00.00.00...ooeeeeooeeeoeooeooeeeee 110 15. Desorption isotherm for lOOoF plotted according to the three- constant equation.of the B. E. T., as compared with experi- mental pOints .OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 115 16. H-J plots of desorption isotherms for shelled corn ...... 119 FIGURE 17. 18. 19. 20. 21. 25. 26. 27. 28. 29. 30. 31. vi LIST OF FIGURES (Cont.) Determination of the an constants for the 40°F desorption PAGE iBOtherm 0000.00.00.00.eeeeeeeeeoeeeoeeeeeoooone.eeooeeoo121 Smith plots of desorption isotherms for shelled corn .....124 Desorption isotherm of shelled corn at 100°? plotted according to the B. E. T. and Smith equations, illustrating a method of obtaining the intermediate linear region ....126 Comparison of curves plotted according to Henderson's equation With experimental isotherms eoeeeeoeoeoeoeoooeee 131 Temperature dependence of constants k and n of Henderson‘s Hendgraon.8 .quation for Shelled corn 00000000000000.0000 133 Variation with time of various parameters and mass transfer coefficients in thin layer drying of shelled corn .......139 Semilogarithmic plot of moisture ratio vs. time curve of Figure 22 showing behavior of rate constant k .......... 145 Method for computing mass transfer coefficient, K.g , from data of Figures 22 and 23 ............................... 159 Drying curves for shelled corn fully exposed to various dwing conditions 0....O...OOOOOOOOOOOOOOOOOOOOOO00......164 Semilogarithmic plots of drying curves of Figure 25 showing slope breaks with correSponding changes of rate constant k Drying curves for shelled corn fully exposed to various drying conditions OOOOOOOOOOOOOOOOOOOOI0.0.0.0....0000000 Semilogarithmic plots of drying curves of Figure 27 showing slope breaks with corresponding changes of rate constant k Drying curves for shelled corn fully exposed to various dTYing conditions OOOOoooooeeeooooeoeoooe ....... 0.0.0.... Semilogarithmic plots of drying curves of Figure 29 showing slope breaks with corresponding changes of rate constant k Drying curves for shelled corn fully exposed to various drying conditions ........................................ 165 166 167 168 169 170 vii LIST OF FIGURES (cont.) FIGURE 1: AGE 32. 33. 34. 35. Semilogarithmic plots of drying curves of Figure 31 showing s10pe breaks with corresponding changes of rate c0n8tant k 0000000000000...00.000.000.000000000000171 inng curves for Shelled corn .OOOOOOCOOOOOOOOO0.00.00.01.72 Semilogarithmic plots of drying curves of Figure 33 showing slepe breaks with corresponding changes of ratC CODStant k 0.0000000.0000000000000000.000000000000173 Drying curves of irradiated and control samples of shelled.7 1 4 corn COOOOOOOOOOCOOOCOOOOOOOOOOOOOOOOOOOCO0.00.00.00.00. 53'9")": LI viii LIST OF SYMBOLS Surface area of adsorbent; slope constant in Harkins-Jura linear equation. Angstrom, 10"8 Intercept constant in Harkins-Jura linear equation centimeter Abbreviation for Brunauer, Emmett, and Teller (also B.E.T.). Constant of integration; concentration in differential equations for diffusion Degrees Centigrade Energy of gas per gram in the adsorbed state Energy of gas per gram in the gas phase Heat of adsorption in the first unimolecular layer (B-E-T theory of multimolecular adsorption) Heat of liquefaction of adsorbate (B-E-T theory of multimolecular adsorption) Free energy of the system Change in free energy of the system Degrees Fahrenheit Enthalpy, heat of adsorption Abbreviations for Harkins-Jura Change in enthalpy Constant in Harkins-Jura equation for area of adsorbent Absolute temperature, degrees Kelvin Mass transfer coefficient, (lbs. H20) (100 lbs. dry grain)”1 (hr)"l(p-i)'l Adsorption coefficient (Langmuir equation) Molar heat of adsorption (desorption) of adsorbate (0thmer equation) Molar heat of vaporization of reference substance (water) in 0thmer equation Molecular weight; moisture content, percent (either wet or dry basis as specified); amount of adsorbate per gram of adsorbent 5"? 0H0 d.b. “z—F‘ ix LIST or summons (Cont.) Equilibrium moisture content, percent dry basis Initial moisture content, percent dry basis Avogadro's number (6.023 x 1023 molecules per mole); eXperi- mental constant ianage‘s equation 55 Holes of gas adsorbed per gram of adsorbent (Equation 6) Integral heat of adsorption Isothermal heat of adsorption (= isosteric heat of adsorption) Isosteric heat of adsorption 'Universal gas constant, 1.987 cal (0K)Dl(g-mole)-l .Absolute temperature, degrees Rankine Relative humidity, percent Entropy Change in entropy Temperature (either 0C, 0F, OK, or 0R) {Molar volume of liquid Change in volume Relative humidity Moisture content, percent dry basis Constant in B-E-T derivations Bull's designation of moisture content at saturation pressure Constant in B-E-T derivation Energy constant in BéE-T equations ; concentration (equation 52) Dry basis (referring to moisture content) Density of liquid Base of natural 10garithms, 2.7128+ Adsorption potential, (Equation 18) Number of layers in multimolecular adsorption Constant in Henderson's equation (43); specific drying rate constant, hr-l; constant in Page's equation 55 Constant in Henderson's equation; number of molecules striking a unit area of surface per unit time (equation 45); size con- stant in BéE-T three-constant equation d 2 LIST or SYMBOLS (Cont.) Partial aqueous vapor pressure Equilibrium vapor pressure of grain Saturation vapor pressure Vapor pressure difference or potential, psi Pounds per square inch Pounds per square inch, absolute Differential heat of adsorption (or desorption) Radius of capillary (equation 14) Bare surface area of adsorbent in B—E-‘l‘ derivations .5 Surface area that is covered by l, 2, ... i layers of zidzorbed molecules Volume of gas adsorbed Molar volume of gas SSize constant of BéE-T two-constant equation ‘Iater vapor adsorbed expressed in percent wet basis (Smith equation 42) (Zonstant in Smith equation 42, slope of linear plot (percent wet basis) (Zonstant in Smith equation 42, intercept of linear plot, percent ‘wet basis) ‘Wet basis (referring to moisture content) Time, hours Density of gas in bulk phase (equation 13) Density of gas in adsorbed state (equation 13) Surface tension Area of adsorbent (Harkins-Jura equation 41); summation sign xi TABLE OF CONTENTS Page IN TRO DUCTI 0N . O O O O O O O O O O O O O O O O O O O O O O O O O O O 0 O O O O O O O O O O O O O O O O O O O O l ONECTIWS O O O O O O O O O O O O O O C O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 6 {mL—‘TED LITEmeF FEE; . O C O O I O O O O O O O O O O O I O O O O O O O O O O I O O O O O O O I O O I O O O 7 ftygrOSCOpic Nature of Cereal Grains .................... 7 ltygroscopic Equilibrium Relationships .................. 10 lVature of Adsorption ................................... 13 llepresenting Adsorption Equilibrium Data ............... 14 {types of Isotherms ..................................... 16 Thermodynamic Functions of Adsorption .................. 18 Various Heats of Adsorption ............................ 20 Adsorption Theories and Equations ...................... 23 Lanb‘muir's Equation . C C C C O I O O O O O O O O O O O O O O C O O C O C O O C O C 23 Potential Theory . O O O C O O O O O C O C O O O O O O O O O O O O I I O O D O C C O 25 Capillary Condensation Theory ...................... 26 Polarization Theory ................................ 27 BAE-T Theory of Multimolecular Adsorption .......... 28 Hurkins-Jura Equation 0.000000000000000...000000.000 35 Smith's Equation ................................... 38 Henderson's Equilibrium Equation ................... 39 .Adsorption Rates and Equilibria ........................ 40 iDrying of Hygroscopic Solids ........................... 42 IPeriods of Drying ...................................... 43 IEquations for the Falling—Rate Period .................. 44 Differential Equations for Diffusion ............... 44 Lewis Exponential Equation ......................... 46 Law of Exponential Growth .......................... 47 Page's Equation .................................... 50 EXPERILENTAL 0.00000000000000000000000000000000000000000.0000. 52 Materials .............................................. 52 Apparatus and Procedure ................................ 58 Controlling Relative Humidity ...................... 54 Constant Humidity Chambers and Sample Containers ... 59 Temperature Control ................................ 62 Preparation of the Samples ......................... 64 Drying Rate Data ................................... 65 Determination of Moisture Contents ................. 67 Irradiation Tests .................................. 68 ‘cesults ...........OCOOOOOCOOOOOOOO.........OOOOOOOOOOOO 7O xii TABLE OF CONTENTS (Cont.) Page ‘LNMJYSII;$ AND DISCUSSIQ’N ....0.............O...........O0.00. 78 Desorption Equilibrium Data ..............,............ 78 Construction of Desorption Isotherms .............. 78 Construction of Isosteres ......................... 86 Calculation of Isosteric Heats of Desorption ...... 88 Clausius-Clapeyron Equation 88 0thmer Graphical Method 95 Brunauer, Emmett, and Teller Equations ............ 101 Harkins-Jura Equation ............................. 117 Smith's Equation ................................. 123 Henderson's Equilibrium Equation .................. 127 Drying Rate Data ...................................... 188 Drying Curves ................... ..... ...... ..... .. 138 Factors.Affecting the Half-teSponse Period ........ 140 Determination of Drying dates ..................... 144 Testing the Vapor Pressure Theory of Drying ....... 153 Mass Transfer Coefficients ........................ 158 SUIflLEIY MJD CONCLUSIONS 0000000000000...accessoocoosscooassoc 175 SUGGESTIONS FOR FURvTHE'. ITOIK ooccscooccoc00000000000000.0000 183 ii-EFBIIEIJCES ....ooooococooccccscoooccccccceases.cococoooccco 185 INTRODUCTION The problem of drying and storing cereal grains has long been of great importance to the American farmer and to the nation's in— terests as a whole. The same is undoubtedly true for any of the other grain-exporting or grain-importing areas of the world; in fact, the value of grain as a food.for mankind makes the problem line of worldwide concern. The request made to the Food and Agri- (nilturdl Organization - as a result of discussions at the Inter— xuitional Meeting on Infestation of Foodstuffs held in London in .Augmst 1947 -— to conduct a critical review of the methods of grain drying and storage in use in all parts of the world was only a re- flection of the present and potential importance of the problem and sure evidence of its worldwide scope. With the advent and subsequent development of mechanized har- vesting methods, artificial drying of grain has attained unprece- dented importance. In the United States alone it has been estimated that nearly ten percent of the grain produced on farms never gets towbe utilized because of losses during harvesting and farm storage. (22) Both harvesting and storage losses can be greatly minimized by adoption and proper management of sound drying practices. Recent studies have revealed that for a picker sheller minimum field losses of corn will occur when the moisture content is as high as twenty- four to thirty percent wet basis (22 ). On the other hand, the recommended maximum moisture content for safe storage as shelled corn is, under most conditions, around thirteen percent wet basis. Obviously, a method of removing the excess moisture is necessary in «order to realize the benefits of mechanized harvesting and still assure safe storage after harvesting at high moisture levels. It ‘was estimated in the above studies that approximately 55 percent «if the normal harvest loss of corn could be saved by making prOper use of artificial methods of drying. Similar results have been .Obtmined elsewhere for wheat where harvesting by combine at about 11% percent moisture resulted in a reduction of one to two percent (xf the normal expected losses. Regarding losses in storage the ‘possibilities of effecting savings by drying are even more impres- sive. Hall (22 ) has estimated that approximately 95 percent of the storage losses of both grain and hay could be prevented through proper storage and drying, and that possible savings of 75 percent of‘the total losses which occur during harvesting and storage could be realized by a combination of early harvest and subsequent drying. Itis clear from the foregoing that the importance of artificial drying of grain can hardly be overemphasized. Since the inception of artificial grain drying there has been a need for information concerning the drying characteristics of the Various kinds of grains as a basis for design. While considerable research effort and funds have been increasingly spent in agricul- huul drying, most of the investigations to date have been concerned With finding immediate solution to practical problems without much regard to theoretical analysis. As a result, present design [practice concerning grain drying equipment and processes have reumined largely dependent on experience and empirical knowledge rather than on precise scientific principles. Despite a few note— *worthy contributions in recent years there still exists a pressing need for more extensive fundamental research which may yield addi- 'tional engineering data and at the same time lead to the develop- xnent of more exact relationships for grain drying. This need has been materially accentuated by the recent trend toward increased ties of heated air in drying, and the consequent use of elevated temmeratures in the drying process. Most of the present available data concerning hygroscopic equilibria of grains has been the re- sult of pioneering work performed at a time when heated-air drying had not come into being. Consequently there is a great dearth of basic information pertaining both to the equilibrium and to the rate relationships of the drying process in the range of tempera- tures usually employed in drying with heated air. It is a well—recognized fact that in any bulk drying process the decrease in moisture content of the grain is controlled by the drying characteristics of the individual kernels. For any given grain these characteristics are known to depend mainly on the mois- ture content, and on the temperature and humidity conditions of the drying air. A knowledge of the characteristic drying rates of fully exposed grain under a wide diversity of drying conditions is of unquestionable value in solving design problems and in the prOper management of drying equipment and processes. The energy relation— ships involved in any process are always of interest from the stand- point of economy and efficiency. It is well known that the heat re- tpiired to remove one pound of water from grain is substantially larger than that required for the vaporization of one pound of free water. However, little is known as to the exact amounts of heat meedbd for drying the various kinds of grain at various moisture levels. In spite of recent contributions along that line, there is grea1.need for additional data on the heats of drying of agricul- tural crops. The far-reaching deve10pments in the field of adsorption theory which have taken place over the past fifteen or twenty years have ‘provided important tools with which to probe deeper into the myster- ies of the water relations of cereal grains. It is felt that nothing can.contribute more to pave the way toward the development of exact Imathematical equations for grain drying than to elucidate the mechan— isnm by which water is bound in the grain. A most fruitful approach t0 the study of the fundamental water—grain relationships has been found in the theoretical analysis of desorption isotherms on the basis of existing adsorption theories. Obtaining accurate hygroscopic equil- ibrium data over a wide range of temperatures afforded a valuable op- POrtunity for contributing to that end. The investigation is primarily concerned with an eXperimental inquiry into the theoretical aspects of grain drying with the broad objective of gaining fundamental information pertaining both to the equiliJarium and to the rate relationships of the drying process, with rumrticular reference to corn. There were several reasons for selectxing shelled corn as the eXperimontal material. In the first place hit was considered that corn is by far the most important cereal grain :in the United States where the annual crop of well over 3,000 millixrn bushels is fed mostly to livestock and therefore must be safelyr stored until it is consumed. Secondly, while at present corn does ruat hold such an outstanding position in Puerto Rico as it does on the mainland, it is even now the only cereal crop grown to any consiJlerable extent in the island. Furthermore, it occupies a high- ranking position among the potential cr0ps which are being considered for (EXpansion in the present efforts toward improving the balance in the (axisting agricultural pattern of the island. Mechanization of ”"3 Corn crOp is now being intently explored and most assuredly will s°0Hbe widely adOpted; there is little doubt that artificial drying will-have to go hand in hand with the mechanization effort. It was felt”, therefore, that by working with corn the results of the inves- tiga-‘l’aion could make a more immediate contribution to Puerto Rican agriculture. In the third place it was considered that most of the recerrt work on grain drying theory has been done in Canada and the United Kingdom on wheat grain, the re being perhaps more information available pertaining to wheat than to any other of the cereal grains. In'Viewof the foregoing, it appeared logical that corn be selected 0-S the material for this investigation. OBJECTIVES {The investigation was undertaken with the following specific objectives in mind: 1. To obtain hygroscopic equilibrium data for shelled corn ovez“a wide enough range of constant drying conditions to enable the construction of desorption isotherms at temperatures of 40°, 60°, 86°, 100°; 122°, and 140°r. 2. To obtain information on the characteristic drying rates of shelled corn under the various test conditions. 3. To test the validity of the vapor pressure theory of drying as applied to agricultural products, and in particular to grain. 4. To obtain information concerning the magnitudes of the '“Nits of desorption for shelled corn at different moisture levels. 5. To investigate the applicability to the desorption iso— theruns of various isotherm equations and theories in an attempt to €31ucidate the exact nature of the water-binding mechanism in 8l'lelled corn. 6. To obtain experimental evidence of the validity of Hen- denSon's equation in correctly accounting for the shape charac- telY’I’lstics and temperature dependence of the desorption isotherms. 7. To explore in a preliminary way the possibilities of in- fluencing the drying characteristics of shelled corn by means of electromagnetic irradiation. l’l‘lLATED LI TEXLATURE Hygroscopic Nature of Cereal Grains Most problems related to cereal grains, whether they are con- cerwued with harvesting operations, conditioning, storing, marketing, or even processing are dominated to a greater or lesser degree by considerations of water content. Depending on the vapor pressure that; it is capable of exerting, the water associated with the grain Imus been conveniently divided into two general types: free water axui bound water. According to this criterion, the water in the grain that exerts its full vapor pressure at any given temperature 18 called free water, while that which exerts less than its normal ‘Varuor pressure is classified as bound or hygroscOpic water. The ex1nent to which the latter type exhibits a lower than normal vapor Pressure will depend on the particular type of binding involved. E11011 type of binding in turn is characterized by a particular erkergy of reaction, and for any given grain it has been found that both are related to the level of moisture content. In general, the loWer the moisture content the greater is the binding energy in— volved and consequently the lower will be the vapor pressure exerted “15 any given temperature. The water-binding prOperty of solids is termed hygroscopicity, and it is perhaps the most important single characteristic of grains from the standpoint of conditioning and storing problems. ’7.) While: conceivably cereal grains may at times contain appreciable amounts of free water, it is generally recognized that it is the hygroscOpic type of water that plays by far the most important role in the practically important range of moisture contents. This practical range of water content has generally been def‘ined between 10 and 35 percent wet basis. (2 5) .A deeper insight into the hygroscopic nature of cereal grains may be gained by a brief consideration of the structural character— istics of two of the predominant constituent substances occurring in g;rain, namely, starch and protein. Both of these are classified among the group of compounds generally known as high polymers, or macromolecules, so-called because their individual molecules are 3- Pesult of the linking together by actual chemical bonds of a ilarwge number of ordinary chemical molecules to form a large mole— ‘NIle which then exhibits associative effects. Starch, on the one hand, is a natural high polymer built up by repetition of the basic glucose unit into a long branched chain 0-3 represented by the formula shown in Figure 1. This natural high polymer is characterized by hydroxyl groups on the ring, . \p / 0112011 H o a s OH H __,. o _4__ u bn \ J ‘1 Figur'e 1. Diagram showing‘the structural arrangement of the starch molecule. ring oxygen, and bridge oxygen, all of which are points of polarity in the molecule and therefore suitable Ioci for in- teraction with water molecules. Proteins, on the other hand, are derived essentially from the combination of amino acids and charac- terized by the presence of the polypeptide chain made up of repeti- tions of the peptide unit: where each different R represents a side chain characteristic Of particular amino acids to be found in various parts of the chain. According to the reSults obtained independently by several investigators, summarized recently by {ilynka and Robinson (25), the re are two hydrOphilic groups in the structure of the proteins which are capable of binding water probably through the formation of hydrogen bonds. These are, 'in the first place, the amino acid Side chains which usually carry a wide variety of polar and ionic groups; and secondly, the oxygen and nitrogen associated with the DeDtide bonds in the peptide chain. It has been suggested that the amount of water held by a protein is thus primarily determined by the number and availability of these two polar groups. The finding by Benson and his co—workers (5) that water adsorption 10 by proteins was independent of the surface an-a in the range below one—fourth the saturation vapor pressure led them to suggest that water adsorption takes place at Specific sites on the protein mole- cules. In line with these views,i3now gt_gl have also found a defin- ite correlation between the relative amounts of protein and carbo- .hydrate content and the general pattern of water sorption by various itaedstuffs. There can be little doubt therefore as to the vital role; that both proteins and starch play in the water relations of co real grains . Hygros00pic Equilibrium Relationships The relationship between the vapor pressure of water over a lu13r0500pic solid and the moisture content of the solid can be deteérndned by experiment, and is usually given in the form of a curve wherein the rmisture content of the material is plotted against t'herelative humidity of the air in equilibrium with the material. The lisual arrangement is for the moisture content values to be plodrted.as ordinates and the relative humidities as abscissae. Be- cause! the equilibrium relationship is uSually obtained at a constant Specified temperature, the curve is designated an isotherm. Fur— thernu>re, depending on whether water is taken up or given off by the ‘SOIid in approaching equilibrium, the curve is referred to as a SOFption or a desorption isotherm, respectively. More often the SO'TYtion isotherm is called an adsorption isotherm, since in most cusesthe sorption mechanism involved is specifically one of ad- s . °°Ppt10n, 11 Since the isotherm represents an equilibrium relationship, the same curve should, theoretically, represent the end points of both water sorption and desorption processes applied to the mater— ial. In practice, however, when sorption and desorption isotherms have been obtained experimentally, the curves frequently do not coincide over their full length but the desorption curves give lowex'equilibrium relative presSures for a giVen moisture content thari do the sorption curves. This phenomenon is generally known as lrysteresis, and though it is not as yet fully understood, sevwaral hypotheses have been advanced to account for its occur- rernce. (25) The most satisfactory eXplanations are still based on.‘the capillary theory of adsorption which will be briefly dis- cussed in a later section. It may suffice to caution at this poiJit that in the experimental determination of isotherm data it is important to adhere to the same direction of approach to equili- brixnn in order to avoid the adverse influence of hysteresis ef— feats; on the comparability of the data and on their suitability for «constructing isotherm curves. It is likewise important to desi4gnate the data according to the particular process involved. It Busy be added that when problems concerning drying processes are lander consideration it is preferable to refer to desorption isotherms, while adsorption data are more generally applicable to Problems in storage. The moisture content of the material that corresponds to the relative humidity of the surrounding air after equilibrium has been established is a point in the isotherm curve. This is usually called the equilibrium moisture content or quite frequently, the hygroscopic equilibrium of the material. Conversely, the cor- responding relative humidity is referred to as the equilibrium relative humidity for the particular moisture content, or as the Efiuilibrium relative pressure when it is expressed in decimal form. Actually, at equilibrium the vapor pressure of the water associated With the grain is equal to the partial aqueous vapor pressure of the surrounding atmOSphc-re so that the ratio of either one to the saturation vapor pressure of water at the specified isotherm tem- Pe Future gives the equilibrium relative pressure. It follows from the above considerations and from the defini— tions of free and bound waters that the moisture content corres- Ponding to a relative humidity of 100 percent is the moisture that divides the free and bound types of water in the material. Beyond this moisture content the material contains some free water and'a maximum amount of bound water, while below it the material contains "‘1? bound water. It is well to caution at this time that the term "free water" as herein defined, must not be confused with the simi- 1&1" term "free moisture content" to be introduced later in connection With the discussion on drying relationships. The latter term refers t° the difference between the moisture content at any instant and the equilibrium moisture content for the material in question, under a given set of drying conditions. This amount of moisture is actually the maximum that can possibly be removed from the l3 material under the specified drying conditions, and may obviously include both bound and free water depending on the particular moisture content under consideration. While there are undoubtedly other ways in which water may be bound.by cereal grains, such as in solution or in chemical combin- ation, it is now generally agreed among investigators of the subject that.the predominant binding mechanism involved is that of adsorp- tion” Because of its tremendous importance in connection with the problem under investigation, it is deemed appropriate to review ath‘this moment a few pertinent facts concerning the phenomenon of adsorption. Nature of Adsorption Whenever a gas or vapor is brought in contact with a solid, its Inolecules distribute themselves so that there will be a higher cOncentration of the gas at the surface of the solid than in the bull; of the gas. This is the phenomenon called adsorption; the Solid that takes up the gas or vapor is called the adsorbent, Whiflle'the adsorbed substance is called the adsorbate. The phenomenon of zidmorption is not by any means confined to solid-gas interfaces; itvmaybe expected to occur at any contact between a gas and a liquid, a liquid and a solid, between two liquids, and even, in certain circumstances, when two solids come into contact (9). In Water-grain relationships, the dry grain may be considered as an adsorbent, and water-dwhether in the liquid or in the vapor Pha80-as the adsorbate. 14 There are two general types of adsorption depending on the relative strength of interaction between adsorbent and adsorbate. When there is a relatively weak interaction between adsorbent and adsorbate, involving only forces of the order of magnitude of those active in condensation phenomena, the adsorption is called physical or van der Waals adsorption. On the other hand, when strong interaction takes place, involving forces similar to those active in chemical reactions, the adsorption is called chemical adsorption or chemisorption. The fact that chemisorption can not take place without an energy of activation being supplied to the Sywstem led Taylor (9) to introduce the term "activated adsorption" by"which name it is often cited in the literature. While the Probability of chemisorption playing at least some minor role has beeTl considered by several investigators, it is now generally agreed that; it is the van der Waals type of adsorption that is almost Who} ly concerned in grain-water relationships. Representing Adsorption Equilibrium Data In any adsorption equilibrium the number of molecules falling 0“ idle surface and being adsorbed must be equal to the number of mOlecules which are set free from the surface to re-evapornte. For it given adsorbate and a unit weight of adsorbent, the amount °f a-dsorbate adsorbed at equilibrium is a function of the final Pressure and temperature only. This general relationship may be Stated thus M = f ( P9 T) (I) 15 where M is the amount of adsorbate adsorbed per gram of adsorbent, p is the equilibrium pressure, and T is the absolute temperature. By keeping one of the three variables constant while the others are vafiying, the above relationship may be obtained in any one of three different ways. When the pressure of the gas or vapor is varied while the tem- perature is held constant the plot of the amount adsorbed against 'Une pressure is called the adsorption isotherm, and the general 180 the rm e 'plation is M = f ( p ) T = constant (2) This is by far the most frequently determined and indeed the most ifiquartant eXperimental relation in the field of adsorption. It car; be readily identified with the equilibrium moisture content— Ieljrtive humidity curve of cereal grains and similar hygroscopic mate rials which has been previously mentioned, since i“ describing SOPption of vapors it is customary to plot relative preSsureS or relatxive humidities rather than absolute pressures. It may be POintmed out at this point that except for the hysteresis effects c0mm0nlyencountered, the general characteristics and energy rela- tionships invOlved are the same for the equilibrium curve regard- 1938 ()f whether the isotherm is obtained by an adsorption or a desOl'Ttion process. 'Phe other two methods of representing adsorption equilibrium data are by means of the adsorption isobar and the adsorption lsoSteI‘e. The isobar is obtained by plotting the amount of 16 adsorbate adsorbed against the temperature at which the adsorption takes place while the pressure is kept constant. The relationship the n be come 8 M = f ( T ) p = constant (3) The adsorption isostere is the curve obtained from a plot of the variation of the equilibrium pressure with temperature correSponding to a constant amount of adsorbate adsorbed. The equation 'of the isos te re is thus P = f ( T ) M = constant (4) The isosteres resemble the vapor pressure curves of a psychrometric chart, increasing at first slowly then rapidly with temperature. JUSt as every point on the vapor pressure curve represents a pres- sure and a temperature at which water and its vapor are in equili- brium with each other, on the isostere every point represents a Pressure and a temperature at which grain of a given moisture con- tent is in equilibrium with the water vapor of the surrounding atmo s phe re . Types of Isotherms There are various types of isotherms which can be found in the literature. In 19le llrunauer and his co—\‘.'orl.:ers (9) prOposed a Classification of isotherm types which has since been widely adepted by other investigators and authorities in the field. Their classification includes five principal type-q, according; to shape Characteristics, which they designated by Roman numer'nls from I l7 ,/ «n m 3 s > > Type I Type II 0 p/ LO 0 p/ 1.0 ps ps Type II m Type III ‘3 '8 > > O p/ LO 0 p/ ps p3 In $3 Type 1 O {3/ LG ps 9 Figure 6 Brunauer's classification of the five isotherm types in physical adsorption. 18 to V as shown in Figure 6. The curves are imaginary iso- therms which illustrate the general shape characteristics of each type. Brunauer 3.39.}... also gave the names Langmuir isotherm and the S-shaped or sigmoid isotherm to Types I and II respectively, but none to the other three types. Type II isotherm has been generally attributed to multimolecular adsorption, and is of great importance in relation with cereal grains and related materials. Thermodynamic Functions of Adsorption When a. gas or vapor is adsorbed by a solid, the adsorbed par— ticles are either held rigidly to the surface, or they are free to move over the surface in two dimensions. Since prior to adsorption the gas molecules moved freely in hree dimensions, it follows that the adsorption process must always be accompaz'zied by a decrease in entropy. The atoms or molecules constituting a given solid are held together by different forces. Whatever the nature of these forces an 8"to"! located inside the body of the solid is subjected to equal forces in all directiozls, whereas an atom in the plane of the sur- face is subjected to unbalanced forces, the inward pull being greater than the outward forces. This results in the solid ex— hibiting a surface tension, similar to that of liquids even though of much greater magnitudes (9). Upon adsorption of a substance by the Solid, the atoms or molecules of the former tend to saturate s . ome of the unbalanced forces of the surface, thereby decreas1ng 19 tho surface tension and hence also the free surface energy, this: being the product- of the surface tensioi; and the surface area. Since any process that tends to decrease he free surface energy occurs Spontaneously, it is seen that all adsorption ' phenomena, whether physical or chemical, are spontaneous in char- acter and always result in a decrease of the free surface encrg of the system. Thermodynamically the state of adsorption equili— briunlis attained when the change in the free surface energy of ‘Uuz system is zero. The change in heat content of the adsorbent—adsorbate system is given by An = AF + TAS (5) where (\F is the change in the free energy of the system, T is the absolute temperature, and AS is the entropy change. Since, as was seen before, both AF and A3 are always negative it folltnvs that [3” must also be negative. This means that the ad— Sc31‘1Ybion.process results in the evolution of heat, and is there— fore (hascribed as exothermic in character. The decrease in the heat (mantent of the system is generally called the heat of adsorp‘ tion. The general magnitude of the h\ut of adsorption serves as {inmasnire of the nature of the forces involved in the process and “my assrist in distinguishing between physical and chemical adsorp- tion. Iln van der Waals adsorption it is of the same order of mag» rutude {18 the heats of condensation of gases, whereas in chemi— f‘OI“) ' . . . . ‘tlQIl it compares With the heats of chemical reactions. mffl until-d. Various Heats of Adsorption It is: deemed necessary at this point to differentiate be- tween the various heats of adsorption that can be found in the literature. Let it be assmaied for the sake of illustration that a definite amount N£1 moles of an ideal gas is adsorbed by the clear surface of 1 gram of adsorbent. The amount of heat liber- _ .:' annu- ated in. this: process is; called the integral heat of ad:.~;orption. A If the energy of the was per gram in the {gas phase is denoted by ID ‘ L" (”l-’1 the energr of the gas per gram in the adsorbed state by L.) 153 a and assuming that no external work is done in the process, this loss of heat from the system is given by .« = E ... " ‘4?th Na. ( 3; ha) (6) The integral heat of adsorption Qint usually expressed in kilo- calories rer gram, is: therefore proportional to the amount 0f gas which is adsorbed. Now if the amount of gas adsoroed .is increased by (”1 incremental amount (we. , an additional amount 0f heat, dfif, ’ Will be liberated. Keeping the tern:.‘t‘t'i'~tul“‘- constant, the differ- ential coefficient 11" . ((“1nt/ (1 Na )T (7) 1| 0 C O I S culled the differential heat of adsorption, sometimes also refe 1"Fed to as the instan aneous heat of adsorption, which will b _ e “Quoted by qd . “ given above is now differentiated If the expression for Lint nth r'eSpect to Na , one obtains ( (“Err - Ea) ) ____ 3‘, L = ; _ .2 J L L, ‘0‘ qd ( d"’int/ (ua)T Eg 1a + \a ( (Wu )T () Since for an ideal gas 13" is a function of the temperature only, L) the above equation simplifies to For the case in which the adsorption is performed under isother- ma] conditions and without change in the total number of molecules, then work is done in the process, since a volume dv of gas at a Pressure p , correSponding to the number of molecules which are M180 rbed, has disappeared. Applying the perfect gas law, this amount of work is pav =dNaRT (10) W118 re '1 is the universal gas constant. Therefore, the work done per mole of gas adsorbed is given by the product =1 T. Be-i ““139 of the isothermal conditions of the process, Huckel (9) has called the quantity Qisothz qd 4" RT (11) the isothermal heat of adsorption. Since, however, q(1 4» RT ~ always refers to a definite quantity of gas adsorbed at different temperatures a:::‘ pressures, Brunauer preferred to call it the 18°17"teric heat of adsorption, which term has been more widely adontea and which will therefore be adhered to throughout this C1188tartation. The fact that this amount of heat of adsorption can also be derived by thermodynamic arguments from the explicit equation of the adsorption isostere (6) lends additional support to the adoption of the latter term. The heat of adsorption may be measured directly by calori- metric determinations, in which case it is usually termed the calorimetric heat of adsorption. When it is thus determined, the value obtained usually lies somewhere between (1d and Qisoth 9 l. depending on the conditions of the eXperiment. It is fortunate, however, that in most cases the fraction of heat HT is small as and Q. qd isoth , usually not amounting to Compared with both more than about 53-10 percent of the total heat of adsorption. (9) From thermodynamic considerations it may be safely assumed that the same amount of energy involved in the process of adsorp- tion will have to be supplier! in order for desorption to take place. Exactly the same terms defined above and conveying essentially the same meaning may therefore be applied to the quantities of heat inVolved in desorption processes. - when the heats of adsorption are larger for a given adsorbent- “dSorbate system than the corresponding heats of liquefaction of the adsorbate, as is usually the case for cereal grains and water, it is sometimes convenient to refer to the difference between the “'0 by the general term of net heats of adsorption. Thus Becker and Sallans (4) have recently reported values on the differential net, heats of desorption of water from wheat at 25°C as calculated from desorption isotherms. They also defined the heat of dehydra— uOn as the additional heat above the normal heat of vaporization which is required to reduce the moisture content from saturation to a designated level, usually expressed in calories per gram of grain, dry basis. This actually corresponds to the net integral heat.of desorption for the moisture level under consideration. Besides the foregoing, the term latent heat of vaporization has also been frequently applied to the amount of heat necessary to evaporate water from agricultural cr0ps. (17, 30) It should rurt be confused, however, with the same term as applied to free wateru In the sense in which it is most frequently used with reikarence to grains, the term is intended to mean the differential he a ts of adsorption. Adsorption Theories and Equations It is beyond the sc0pe of this dissertation to delve into fidscxrption theory in too much detail. Two very thorough discusSionS on iflie subject have been given by Brunauer and by de Boer in their Vellneknown books on adsorption. However, it is considered neces- saryr to review briefly some of the salient features of the most important theories of adsorption as a background to an understanding 0f litter discussions pertaining to the analysis of the eXperimental data, _ LUmgmuir' s Equation Although as early as 1814 T. de Saussure (9) had already outdained many of the points featured by the later adsorption the— Oriens, until 1914 no satisfactory treatment of these phenomena had 24 as yet been formulated. In 15:15.: Langmuir (33) Preposed a theory based on his belief that adsorption was essentially a chemical process leading to a unimolecular layer of the adsorbate. In arriving at his isotherm equation Langmuir made two simplifying assumptions. He first assumed that the heat of adsorption was the same for every molecule striking the bare surface of the ab- sorbent and furthermore that this heat of adsorption was independent of the other molecules already adsorbed. Secondly, he assumed that every molecule striking another one already adsorbed was elastically reflected, and only those molecules condensed that made contact with the clean surface of the adsorbent. The Langmuir equation is 1% p — l 4» IR p Where v is the volume of gas adsorbed, p is the pressure, and V (If?) KL is the adsorption coefficient which in turn is a function of the temperature only. DCSI‘)itG the two simplifying assumptions involved in its derivation, which considerably limit its scope, the Langmuir iso- therm equation is now regarded as perhaps the most important single equuftion in the field of adsorption, serving in many cases as the StavI‘tdng point in the derivation of other equations. Type I ad- sorPtion isotherms are best interpreted in terms of Langmuir's equation and accordingly, are sometimes referred to as Langmuir Isotherms. ‘m f C! Potential Theory AJ)out the same time that Langmuir postulated his theory, Polang'i (0) proposed another theory following an altogether dif- ferent, approach. He assumed that adsorption was a physical process due tol long range attractive forces extending out from the surface of the {adsorbent and leading to multimolecular adsorption. The Polanyi. theory has also been known as the potential theory. Polanyi define(l the adsorption potential at a point near the adsorbent sur- face as 'the work done by the adsorption forces in bringing a mole- cule frxnn the gas phase to that point. This work is conceived as a work <>f compression, and mathematically its value is given by the so-cnlled hydrostatic equation ei ... v dp (13) where e. is the adsorption potential at a point where the density 0f the adsorbed substance is /Oi , /Ox is the density in the gas phase, and v = M//o where l: is the molecular weight of the ab— SOPbate. V is the molar volume of the adsorbate. It is funda— mental to Polanyi's theory that the adsorption potential at any given point is characteristic. of the adsorbent alone and is not affected by either the temperature or the presence of other mole- cules. Hence it is peasible to map out the entire adsorption SP&Ce into a number of equipotential surfaces, the diSposition of which would be characteristic of the adsorbent. The potential theory applies to both unimolecular and multimolecular adsorption and has been credited by Drunauer as being the only theory that can handle quantitatively adsorption on strongly heterogeneous surfaces. Another noteworthy feature of the theory is its success in predicting the temperature dependence of physical adsorption. However, since the theory does not attempt to formulate an iso- therm equation, the scape of information: obtainable is limited. ,— Capillary Condensation Theory It has long been known that if a capillary is immersed in a liquid that wets its walls, the liquid rises in the capillary and forms a meniscus which is concave toward the vapor phase. The vapor pressure over the meniscus is lower than the normal vapor pressure of the liquid by an amount equal to the pressure exerted by the column of liquid in the capillary. The vapor pressure lower- ing over the cylindrical capillary is given by Kelvin equation 20"! rRT (l4) 1n ps - 1n p = Where D is the equilibrium vapor pressure over the meniscus in the capillary, ps is the normal vapor pressure, O/is the surface tension and V is the molar volume of the liquid at temperature ’r: “Jul r is the radius of the capillary. It will be seen that the Smaller the radius, the greater will be the vapor pressure “wring according to equation (14). It was Zsigmondy in 1911 who first correlated the adsorption of water with the capillary preperties of the adsorbent (55). llis °°n°1usicn that in capillaries of sufficiently small diameters 27 (such as those occurring in silica gel) liquid would condense at pressures far below the normal vapor pressure, may be regarded as the first formulation of the capillary condensation theory. In terms of the theory every value of relative pressure correSponds to a capillary radius that can be calculated from the Kelvin equa- tion. As the vapor pressure is increased always larger capillaries fill until finally at the saturation pressure all the pores of tle adsorbent fill with liquid. Today most investigators agree that capillary condensation plays some role in physical adsorption. It is generally believed, however, that it becomes important only when adsorbents have capil- laries at least several molecular diameters in width, and then only at the higher relative vapor pressures. Polarization Theory The polarization theory was first proposed by de Boer and ZWikker in 1929 (9) and again in a somewhat different form by Bradley in 1936 (7). It explains the adsorption of non-polar m°19°ules on ionic adsorbents by assuming that the uppermost layer of the adsorbent induces dipoles in the first layer of ad- Sor'bed molecules, which in turn induce dipoles in the next layer, and 80 on until several layers are built up. Dipoles are mole- cules which though neutral, have both positive and negative Charges. If the center of gravity of the negative charges does “0t cOincide with the center of gravity of the positive charges ‘ "‘vca. \‘R - \ \ I ‘- =‘~.;Ac*.r ‘.‘.L. r‘ 11. N- 28 the molecules are said to possess :1 permanent vipole moment. Their electrical nature enables them to induce an electric field in their neighboring molecules; they are also f‘ree to turn and align them— selves in order to satisfy the charges. Water constitutes a. good typical example of a dipole molecule. The B—E—T Theory of Multimolecnlar Adsorption This theory, first postulated by Brunauer, Emmett and Teller in 1938 (10) and two years later by Brunauer, Deming, Deming, and Teller (11) is based on the assumption that the same forces that produce condensation are also responsible for the binding energy of multimolecular adsorption. In contrast with he polarization theory which attributes (adsorption to the action of induced di- POIE‘S, the B-E-T theory of multimolecular adsorption ascribes the course for adsorption to the totality of the van der ‘.‘.'e.als forces. According to Brunauer, the B-E-T theory constitutes the first at— tempt to give a unified theory of physical adsorption. Its most general epmtion includes all five isotherm types as Special cases and (leg cribes the shape of each isotherm type through the entire range of adsorption, from zero pressure to saturation pressure. 1 ' . T1118 Includes the rec-ion of ummolecular adsorption, multimole- culnr adsorption and c;:«.]r-illa.ry cox‘ulensatien, in contrast to the Separate treatments accorded to these regions by the pl‘eViOHSl)’ ‘ . O dlentlolled theories. Because of the great importance which the theory of Brunnuox, Emmett and Teller have obtained during the last years, and also because of its heaving on tee analysis of the experimental data of this investigation, the arguments followed by its origiwuiors in the derivation of their most useful equations will be new pre- senter] in some detail. lLet s , s , s ....... s. ,... represent the surface area lrflt- is covered by 0, 1, 2, ..... i, ... layers of adsorbed role— culess. :aince at equililufilni s0 must xmnmiiu Canstant, the ‘ate of coridensation on the bare surface must be equal to the rate of evapoxwltion from the first layer, or a p s = b s e 1 (15) I“ whel(* p is the pressure, is the beat of adsorption in the .LJ 1 first layer; and a1 and [)1 are constants. .At equilibrium 5 also must rennin constant. Fr m the l Principle of microscopic rQersibility it follows therefore that —eQ/Rm La aO p 51 = 130 sn e (16) (.4 Lu ‘. . . . or tne rate of condensation on top of the first layer 1s equal ‘ O 0 t0 tde rate of evaporation from the second layer. In equation (16) £2 13 the heat of adsorption in the second layer, and a0 and b” (.4 C- a‘” Constants. Extending the same argument to an , 83 , etc. -E3/RT as p 32 = b8 83 e 2 : (17) ‘ ° -Ei/RT a. s. = b. s. e 1 p 1-1 1 1 30 The tot-:Ll surface of the oulsorUent is given by and the total volume adsorbed is i=oo 1 i=0 where V0 is the volume adsorbed on one squxe cent imetcr of the adsorbent surface when it is covered with a. complete unimole- cular layer. It follows that i=~oo is. 1 V 'V i=0 0 A v " v = i=oo (60) o 1" $1 ———4i~=0 u’ie re v is the Volume of gas arl-mrbcd when tin- entirc- azlsoz‘be‘wt m Surffice is covered with e complete unimoleculer layer. The summation indicated in eouution (30) can be carried out, If the simplifying assumptions are made that E = E = 00... E. = E (21) vmere BL is the heat of liquefaction, and b b3 hi -_4;_ = .... = .... z H2 “2 a3 “1 g ( ) w . . here g 13 an appropriate constant. This is equivalent to assuming that the evaporation-condensation preperties of the molecules in the second and higher layers are the same as those of the liquid state. The assumptiwl is deemed reason- able ()n the grounds that the effect of the adsorbent is probably quite small alreidy in he second layer, since the van der heals forces; Have a very short range of action. Now s1 , s2 , s3 , ..... si ... can he eXpressed in terms of 50 thus ‘ I. m :23 S] = y So , where y .. (al/bl) I) e 1/ ( ) v /u s“ = x sl , where x = (p/g) GLL/ T (34) 2 S3 = x 82 = x 81 (20) s - - i—l s - ti—1 5 - c xi 8 (96) i'xgi-l‘x '1‘)“ o“ o’ “‘ where « _.‘ 31 2 c=flx=aly%)ew1%VT (n Substituting into equation (12) co V/vm = 0 Sn! i=1 1 x (28) [I + 0° xi] 80 c i=1 I The summation represented in the denominator is merely the sum of an infinite geometric progression (“’1 .x=X 29 1:_1=1 ( ) l—x About the summation in the numerator it is noted that co ‘\ w 1 32 Substituting (29) and (30) into (530) v/Vm = (l -Ax)£(31( - x + c f) (31) If the adsorption takes place on a free surface, then at pq , the saturation pressure of the gas, an infinite number of layers can build up. on the adsorbent. To make v =00 when p = p , x must S Ina equal to unity in equation (31). From equation (94) it follows that ILL/RT (pg/g) e '(32) I H and 3: ll p/p (33) 3 Substituting into equation (31) the B-E—T isotherm equation is obtained: v c p V = (p3 - p) (1 + (c-l)(p/ps)7 ‘34) For the purpose of testing, equation (34) may he put in the form p l c - l = -——- + -———————— a 35 V (ps _‘5) vmc vmc (P/IS) ( ) Equation (35) is the isotherm equation of the multimolecular adsorption theory for adsorption taking place on a free surface. It is a linear equation so that the plot of function p/v(ps-p) against p/p8 gives a. straight line, if the theory is obeyed. The intercept of the straight line is l/vmc , and the slow: is (c-1 )/vmc , The constants vm and c can be obtained from the expo rimental data . Hz- 33 The constant c is given by equations (10) and (14). (El—EL)/RT c = (allow/Illa”) e (36) From the nature of the constants a1 , bl , a2 , and b2 it follow: that alb2/bla:2 will not differ much from unity. As a. first ap- proximation it may therefore be written that 6(E1’EL)/”T c = (37) Thus from constant c the value of E the average heat of ad— 1 1 SOl’ption in the first layer, can be calculated. If the adsorption does not take place on a free surface but in ’1 limited Space, then at satul‘ation not an infinite but only 3- finite number of layers can build up on the surface of the adsorbent. FOP instance, if the maximum number of layers that can be adsorbed 0“ each wall of a capillary is denoted by n , then the summation 0f the two series in equation (20) is to be carried to n terms only and instead of equation (35) the following is obtained. v = vInc x l - (n+l)_xn + n Qua} (3g) l-x 14-(c-l)x--¢,[n+1 It will be seen that this is identical to Langmuir's isotherm e‘iu’ition with the constant h having t‘ze value c/p8 . The other limit is when n =00 , which is equivalent to the a‘15"‘01‘1ation taking)r place on a free surface. In this case equation (38) reduces to equation (35). It should also be noted that when x is small and n at least as large as 4 or 5, equation (35) be— Comes a very good approximation to (33). To use equation (39’) the 34 experimental data should therefore be plotted in the low pressure region according to the linear equation (35), in order to evaluate the constants vm and c from the s10pe and intercept of the straight line. These values of vm and c should then be used in equation (38) in order to solve for the value of n that gives the best agreement with the eXperimental data. Equation (30) in— cludes as Special cases the isotherm types designated as I, II, and III, in Figure 6. If n=l , it reduces to (31) and the Type I isotherm is obtained. If n is larger than 1, either Type II or TYPE III isotherms are obtained depending on the value of the con- Stunt, c. If the attractive forces between adsorbent and adsorbate are greater than the attractive forces between the molecules of the a“13(101'bate in the liquid state, Type II isotherms are obtained. If, on the other hand, the forces between adsorbent and adsorbate are Small so that E is smaller than B 1 L , then Type III isotherms are obtained. While equation (30) includes the first three isotherm types as Special cases it does not account for Types IV and V. The 31131183 of these isotherms suggest that capillary condensation sets in at. the higher relative pressures. To take care of this situa- tion’ Brunauer, Deming, Deming, and Teller (11) have derived other eCl‘La‘tions involving two additional constants. These need not be gone into here since aside from their theoretical significance in Successfully accounting for the shape of Types IV and V isotherms they are of little practical usefulness. 35 In general, the two-constant B—E—T equation has been found to be obeyed very closely for many adsorbents over the range of rela- tive pressures between 0.05 or 0.10 to at least 0.35, and sometimes 0.50. Outside of this range the equation usually breaks down. In recent years several investigators have applied the equation suc- cessfully to hygrosc0pic equilibrium data on grains and other bio- logical materials. For instance, Bull (12) measured the adsorption 0f water vapor by a large number of proteins and found that the BAR-T simple equation fitted the isotherms over the full range of Validity specified for the equation, namely, from a relative pres- EHJFQ of 0.05 up to 0.50. guite recently, Becker and Sallans (4) otrtained perfectly linear plots of desorption equilibrium data for o C . t1u3at.at 25 C up to a relative vapor pressure of about 0.85, which is 'the usual upper limit of applicability of the equation. Hogan amui Karen (26) also applied the equation to their data on hygro- scozric equilibria of rough rice and obtained fairly good linear plot»; over a range of relative pressures between 0.10 and 0.40. All (if these results tend to favor the view that the water-binding '“Nfiulnism predominating in cereal grains involves multimolecular ad‘mrz‘tion as. postulated by the B-E—T theory. I , . ° lax klng ..Jum Equation Wfiae accurate determination of the surface area of adsorbents h . . . . as lolig posed a difficult problem of great practical as well as t h 0 O heore tical importance. One of the most useful applications of t“; . . . ”e B‘Jf-T two—constant equation relates to this particular problem. "J 36 It Will. l3!) rs,-CL.11’-‘(l 1.51:5. t'u‘l (:Q)L:‘:‘.f"‘{ v!’? Of 1““ B—E—T equation represents the a-onunt of &(.l.’;“0rl\;!t'* now-«led fur the completion of a unimoleculor layer over the surface of the alsorbent. It follows that hnvi 13 leiua‘r‘innd v. (11:10 for VP. according to the procedure previously outlined, u knowledge of the area occupied by ore holo- cule of the arlcorhnto would readily allow t'oe calculation of the effective surface urea of the adsorbent. The method, thong‘x simple, Still involves; the. ussm'lpti'nl of a ‘TI()3-"‘C1!l;11' area for the :Lrlssorl'mte, a. regain-mint that is somofirw’e «lifficult to r"rlf‘ill. f' or C'zicuao (:73 In l0-3-.’, Yqu"‘iI=r= (1";«1‘11111. or f‘n- I‘niversi 3 pro-50:30:} a sixvl‘ln unit'lgd 0a" cletr)7‘lll‘"§l ‘3 Um. mtr'fizce area from t’m adsorptim‘ is‘..-Jt?m.~m, yithont the need of ussmning n. xm_)l(~CI_11m' area f0? t‘m t-Llsorhate. Their rvot'tod consists; first, 5.1: plotting Use IOgaritlm of the relative vapor I‘I‘L'QSHFQ against t'm- reciprocal of the square of the volume adsorbed. According to their theory, Straight lines are thereby obtained over the range of relative Pres-Sun‘s more a condensed film of the adsorbate is involved. Their equation for the above—mentioned linear plot is 2 Log (9/98) = D - M" (‘10) “'he re V represents the amount of adsorbate correSponqling to a. given equilibrium relative pressure. The area of the {u‘waorhent is then given by the equation = K A" (41) whe re L, is the surface area of the adsorbent, A is the 31099 or the linear plot referred to above, and K is v. constant which 37 has to be determined for a given adsorbed vapor at a given tem- perature. By means of an absolute method llarlcins and Jura have standardized values of K for a few gases and vapors at various temperatures. The areas obtained by application of their method have been found to be in very good agreement with those calculated by means of the B-B-T procedure. However, the usefulness of the H-J method has been greatly limited by a lack of knowledge con— cerning the behavior of the constant K in the above equation. Linus (34) has correlated the results of both the ilarkinsJura and the B-—E-—T equations and found that the square root of the slope A Of the H-J equation corresponds closely with the value of the con- stant vm of the B-E-T equation. Dunford and Morrison (15) have applied the ‘larkins-Jura equation to Bull's water-protein adsorption isotherms and obtained 300d linear plots in most cases over the relative vapor pressure range from 0.5 or 0.6 to 0.95. They also used Liang's method for correlating the l-I-J and the B—E-T equations and found good agree- Rent, between the calculated values of Vm and Afi. - It should be note d that whereas the value of vm relates to the lowermost por— 1- t‘ion of the isotherm, that of A2 corresponds to the higher pres- sure region. The general observation that the same value is ob- tained for these two Opposite regions of the isotherm led Dunford and Morrison to suggest that the same number of adsorption sites and hence the same surface area are probably involved in the for- mation of both the first monolayer at the lower pressures and the cOlidensed film at the higher relative pressures. 38 Smith's Equation Searching for an explanation of the mechanism involved ir he sorption of water by high polymch, Smith (44) derived the linevr e qua t i o n “' Vb — n" In (1 - p/p ) (42) fi 0) ‘v'iim‘e W is t‘.e amount of water vapor adsorbed expressed in percent wet basis. It will be seen that in the Flot of values of w a ‘3 o 0Fd1n0.trs against those, of the function ln(l - p/pfi) as abscissae, .' , . "' and Vb corresyond respectively to the 31099 and 1nte~cept of " I ‘ 0 O . . to. St-I‘J'lgdt 11mg obtained. In general, Smith found the equation to 3'1eld good str'r‘ight lines: between relative. pressure values of P . o '- o .. O 0.0 and 0.9.). According to omlth's treatment, w' represents at an _‘ _ . 7 o 0 _ , ’ “Ch -:> tage of the sorpth the weight Fraction of rater requl red to COT-‘Iplote the first layer of normally condensed water molecules “dd In that sense is roughly comlxarable to the constant v” of the “ ”‘E‘T equ tion. The intercept, "b , on the other hand is to be rhrr J‘T‘ded as the measure of a tightly bounrl substratum of water 1'; . . . 101C cules which paves the sorbir‘g surface of the polymer arrl ef— f0Ct'iVely reduces: the intensities of the. surf‘occ- forces of attrac— 11021 to the leVel of the forces in :1 liquid unto;- surface. "with O L v mm.) o. ~+ .cing,‘ agreement between the values of the BeE-T con— sari stfiult V” and those obtained by ave aging the values of W' and “b , which led him to suggest that the surface area given by the B”EMT procedure really correSponds to an average between that cOVered by the tightly bound water molecules and that covered by the first normally condensed layer. 39 Becker and S‘Jallans (4) also applied Smith's equation to their desorption isotlwrms of wheat and obtained curves which were essen— tial 1y linear in the range of relative preexures from 0.50 to 0.94"», which is the prescribed range of validity for t'1e equation. Beyond a relative pressure of 0.95 the function -ln (1 - p/ps) becomes highly sensitive to small absolute errors in the measurement of Pressure. Noting that the B-E-T and the Smith isotherm en‘vuntions tend to complement each other as to their respective regions 0f validity, Becker and Sellans suggested an interesting method of defining the int-@- l‘mediate linear region clmract+.~ristic of Type II isotherm by Plotting the data according to both eqllfl-tio"s On the same graph and “Va-"Ting a line tangential to the Smith curve and intersecting the B'Jg‘T curve at its point of inflection. They found that this pro- cedure resulted in an excellent fit of the exocrimental data and {5qu a smooth unbroken transition into the curved regions described by both equations. llende rson'fi Equilibrium Equation In an attempt to formulate an isotherm equation which could fleeount, for the temperature dependence of the eXperimental curve "ende rson (24) derived by thermodynamic reasoning the following equation: / —l£ T n: 1 _ P PS = e (43) where T is the absolute temperature, and k and n are exxueri- mental constants characteristic of any given hygroscolnic material. 40 The starting point for Henderson's derivation was Gibbs' adsorp— tion equation which relates the surface tension of the adsorbed liquid, 0 , the wetted surface of the adsorbent, s , the volume of the liquid adsorbed, v , and the osmotic pressure, P ,' as follows: :3 = - (dP/dS)T (44) llis complete derivation need not be included here; it may suffice to Say hat his derived equation turned out to be identical to an empirical relationship previously established, except for the ad- dition of the temperature factor in the course of his derivation. He found remarkable agreez-n;~nt beta-reen observed and calculated Values when the equation was applied to limited data available in the literature. Accordingly, he calculated and published the values or Constants k and n for a large number of agricultural mater- ials. While the equation appeared generally acceptable in des- cribing the shape of the isotherm and fitting limited experimental (18.1.0 ~, Henderson himself cautioned against its general use pending further experimental confirmation of its validity. Adsorption Rates and Equilibria Theoretically, adsorption phenomena on a free surface take Place with enormous rapidity, almost instantaneously. A brief look at the kinetic picture of the process will assist in realizing the order of magnitude of adsorption rates. Consider as an illus— tration that the clean surface of a hygrosc0pic substance such as 41 starch, or protein is suddenly exposed to an atmOSphere with a relative humidity of 10 percent at a temperature of 20°C. This is a. relatively dry atmosrzhere in which the pressure of the water vapor is 1.75 mm of mercury. From the kinetic theory of gases the number, n , of molecules of water striking each square centimeter of the surface per second is given by J- n = N p / (2 77M n '1')" (4.5) 22 ‘1). n - 3.52 x 10 x p / (M T)“ (45a) where p is the vapor pressure in millimeters of mercury, ’l‘ is the absolute temperature in degrees Kelvin, and M is the molecular "Eight of water. Equation (45a) then states that 8.5 x 1029 water molecules will strike each square centimeter of the surface each second. Such enormously large number of molecules striking the surface every second should cause adsorption phenomena to take place “early instantaneously. It must be emphasized, however, that such Ema-t speeds of adsorption as suggested by the number n can only "cm-1P immediately after the surface is exposed to the atmOSphere, at ‘Vhich moment there are sufficient water molecules in the direct proIii-mity of the surface. As the inmediate neighborhood of the surface is exhausted, a further supply of water molecules has to come from more remote parts. The Speed with which this takes place is determined by the rate of diffusion of water molecules in the intervening air. After the adsorption equilibrium is established, n O C O Wtlter molecules will strike each square centimeter of surface per second and the same number n will evaporate, this being the condition of the dynamic equilibrium. It will be clear from the above considerations that when an adsorption equilibrium requires considerable time to establish it- self, the cause of the delay is to be found in diffusion problems. These may involve principally the transport of the gas molecules from the bulk phase to the surface of the adsorbent, as in the case of the above example, or may also involve diffusion of the adsorbed gas from the outer surface of the adsorbent to the more interior parts 0f the porous structure. he latter would undoubtedly be the case with such materials as cereal grains, which often require equilibration periods in the order of weeks and even months. Drying of Hygroscopic Solids The drying of hygroscopic materials such as cereal grains Involves the removal or desorption of water, which may include bOth free and bound wntes depending on the initial moisture con- tent of the material and on the extent of the drying process. In any “Ting process, the equilibrium moisture content of the material as determined by the temperature and humidity conditions of the drying air, represents the limit to which the material can be dried, It is the free moisture content that is susceptible of being removed by drying rather than the total moisture content. Pe rio ds 0 f Drying Among the most fundamental investigations on drying theory are those of Sherwood (43) and Lewis (33). Sherwood has deve10ped a theory, now generally accepted, that postulates three possible dis— tinct periods in the drying process. These drying stages, classi- fied according to the rate of drying under constant drying condi- tions, are: (l) a constant—drying rate period, during which the surface remains completely wet, the rate of evaporation being the same as that from a free liquid surface of constant area; (2) a first falling-rate period, during which there is a falling off of vetted surface, the drying rate being directly proportional to the fraction of the surface that is wet; and (3) a second falling- rate period during which the rate of transfer of water from the interior of the material to the surface becomes the controlling factor, The moisture content of the material which marks the end of the constant—rate period and the beginning of the first falling— rate Period is designated as the critical moisture content. If the Critical moisture content is less than the required moisture content, the constant-rate period will constitute the whole drying process. On the other hand, if the initial moisture content is 1"“ thanthe critical moisture content, the whole drying process will take place in the falling-rate period. It has now been pretty “11 established that practically all agricultural drying process“ take Plnce in the falling rate period. In recent studies on the drying of wheat grain, Simmonds and his co-workers (44) found ‘that the critical moisture for wheat varied between 69 and 85 per- cent dry basis. They also found the critical moisture contents to show the same tendency to increase at lower air temperatures as was observed.with the equilibrium moisture contents. It may safely be assumed that in the practically important range of mois- ture content for cereal grains in general, the drying process takes place entirely in the second falling-rate period, which henceforth will be referred to simply as the falling-rate period. Equations for the Falling—Rate Period It has been pointed out that during the falling-rate period of drying the rate of internal moisture transfer controls the drying rate. Ihile several controlling mechanisms have been postulated to account for the internal flow of moisture-—including capillary flow, shrinkage and pressure gradients, and diffusion-—it is now generally agreed that in the practically important range of moisture content the most likely mechanism is one of diffusion (l, 3, 43). Differential Equations for Diffusion Numerous investigators have attempted to correlate drying rates with standard diffusion equations. (43,33 ) The limita- tions of the diffusion equations in drying have been summarized, and their restrictions to various materials and certain times of the drying cycle noted (27}. The classical hypothesis of Sherwood and.Newman (37,43 ) is worth mentioning. According to this theory, the potential producing movement of moisture within the solid is identified with a concentration difference. The differential equation expressing the change in concentration C at any point with respect to time is as follows for one-dimensional diffusion (infinite slab) 60/ 6e - n (age/6:2) (46) where D is the diffusivity of moisture in the material. Equation (46} is analogous to the temperature-time—distance equation for heat flow. In the case of diffusion in three dimensions the equa— tion is 60/69- . k(a2c/ax2 +52c/ar2 + 620/822) (47) where the diffusivity coefficient is now denoted by k . The equa- tion involves no implication that the flow at time 0- at a point (X, Y, I) is not in some definite direction. It merely resolves the direction of flow into components along the previously selected rectangular coordinates I, Y, and Z. The above differential equations merely express the general law for diffusional flow and are of no practical use as they stand. Fbllowing the approach of finding an equation which could be proved consistent with the differential equation and with the specific conditions of the problem, Newman (37) preposed solutions for solids of various shapes. Recently, Becker and Sallans (3) applied the standard solution of the non—stationary state diffusion equation out of spheres to the drying of wheat. 0n the basis of their 46 findings they postulated that the diffusion coefficient was inde— pmndent of moisture content in the range from 12 to 30 percent dry basis, and reported values for the coefficient as lying between 0.069 x 10"-6 and 2.77 x 10.6 square centimeters per second in the temperature range 20° to 80°C. Lewis Exponential Equation Based on the diffusion differential equation and assuming certain approximations, Lewis (33) derived the following expres- sion for drying under constant drying conditions, M- In M -u = -ke (48) 0 e Where M is the moisture content at any time, no is the initial moisture content, “e is the equilibrium moisture content (all mDisture contents expressed on a dry basis), 0- is the time in hOUrs, and k a proportionality constant which he called the drying ”“?fficient. Equation (48) is analogous to Newton's law of cooling and has come to be regarded as a fairly good approximation for fullyexposed drying rates. Hukill (29) employed this relation- ship in his analysis of bulk drying of grains. In their recent inVt-‘estigation on the drying of wheat grain, Simonds _e_t gl found 800d.agreement between their experimental data and equation (48). They used a dynamic method with air velocities in the range of so ‘0 160 feet per minute, and employed drying temperatures in the muse 70° to 110%. 47 Law of Exponential Growth Because of its importance in the analysis of drying phenomena, equation (48) merits closer examination. As stated earlier, it is analogous to Newton's law of cooling; or more generally, it is an application of the compound interest law, often referred to as tin law of exponential growth (or decay). Both of these names empha- size the fact that the increase (or decrease) is proportional to the Size of the thing that is increasing (or decreasing). In other words, if c is the concentration at time 0 then the rate of de- crease in concentration is given by dc -- d9 . k C (49) where k is a proportionality constant. The minus sign indicates that the concentration is decreasing with an increase in time. Equation (49) can be transposed giving -29. c - has (so) Integrating between the limits c at the time 02 and c 2 l at 01 , where 02 is greater than 01 , "‘9 Obtains ln (cl/c2) - 1402 - e1) (51) 48 If co is taken as the concentration at zero time and c the concentration at any time 0 , equation (51) simplifies to In (co/c) - he (52) or in (c/co) - - k e (53) It is evident that equation (53) is analogous to equation (48), the moisture ratio (1: - lie)/(llo - no) of the latter taking the place of the concentration ratio c/co of the former. The same relationship expressed by the foregoing logarithmic equations can be 01pressed in exponential form as follows 4:0 c .. coo ' l (54) E(Nation (54) can be readily converted to the logarithmic form by taking logarithms of both sides. The law of exponential growth finds wide application in des- cribing natural phenomena. It is applicable whenever it is found that the value of a quantity or property is changing with respect ‘0 “me variable at a rate which is proportional to the magnitude 0' the property. It can be deduced from the above equations that the fl“action of the preperty or quantity which is undergoing. change- “79 Ilolecules in a unimolecular reaction; atoms in radio-active disintegration; temperature decrease in a cooling process (Newton‘s 1“ or cooling); or molecules desorbed in a drying process under “aunt-drying conditions—in a given period of time is inde- pendent of the amount that is present. The constant k is known 49 as the specific reaction rate and may be expressed in any unit of time, such as reciprocal minutes, hours, or seconds. It should be noted that equation (48) is a linear equation so that if the func- tion in ((n - lad/(no - 113)) is plotted against the drying time a straight line will be obtained if the experimental data obeys the law of exponential growth. The slope of the straight line will give the value of the rate constant k directly. These features coupled with the fact that it has been found to fit experimental data surprisingly well in many cases have enhanced the usefulness of this equation in grain drying studies. In applying the law of exponential growth to any specific problem it is customary to refer to the time period corresponding to one half of unaccomplished change as the term period of half— response. In the case under consideration it is obvious that the change involved is moisture desorption or removal, that the total amount amenable to change is the initial free moisture content, Ho --Ie , and that the amount of change yet to be accomplished is the free moisture content at any given time, M - Me . Sometimes the free moisture ratio (M — He)/(M° — lie) is called the unac- complished.moisture change. In drying processes, as in other similar phenomena, the half-response period has attained some im— portance as a parameter in the formulation of approximation equa- tions with which to characterize the drying process. 'hen used in this connection, it is usually employed as a unit with which to measure the drying time. Hukill (28) employed it thus in develop— ing a method for predicting approximately bulk drying rates. It is also of general value in drawing drying curves of different samples on a more comparable basis, and in permitting constructing the curves over a longer span of drying time. It is clear from the foregoing that a knowledge of the mag— nitude of the half-response period for different drying conditions would constitute a fund of valuable engineering data for use in. practical drying problems. The value of the half-reSpouse period for any given drying process under constant drying conditions may be determined experimentally from the drying curve obtained by plotting the moisture ratio as ordinates against the drying time as abscissae. 0r, provided the rate constant k is known for the drying conditions under consideration, it may be calculated by equating the right—hand side of equation (48) to 0.50, and solving for the corresponding value of time '0 . Page's Modified Equation In an investigation of basic drying rates of shelled corn, Page (40) analyzed his results by using a modification of equation (48) as follows N -k'9 (M - lag/(no - Me) - e (55) Where the value of constant R was determined on the basis of time exPressed in half—response units, and N is an experimental con- Stant, He found that constant N was a function of relative hlullidityand obtained values of 0.60, 0.65, and 0.83 for relative 51 humidities of 35, 50, and 70 percent respectively; for the constant k be obtained a value of 0.68. 52 EXPERIMENTAL Materials The corn used in all tests for determination of hygroscopic equilibria and drying data was obtained from a lot purchased at a local elevator during the fall of 1954 and subsequently stored at 40°F. The corn was of the yellow dent type and of hybrid origin. About ten pounds of this lot were set aside for use in the inves- tigation and sealed in two glass jars which were kept in the same 40°F storage box. A representative sample of this corn taken at this time was tested for moisture content and found to be of 25.43 percent, dry basis. The samples used for the irradiation tests were obtained from a stock of five pounds of air—dried seed corn, variety Mayorbela, which was flown directly from Puerto Rico. Imediately upon ar- rival in August 1955, the seed was placed in tightly closed jars and stored at 40°F. Its moisture content was found to be 15.35 Percent, dry basis. The salts for preparing the saturated salt solutions used 58 controllers of relative humidity were all of chemically pure grade, and were obtained from the stock rooms of the Chemistry D'-’Nrt-nent of the University. The material used for making the sample containers consisted Of a Screen mesh sixteen-to-the-inch made of saran plastic. This mate r‘ial proved to be particularly suitable for this purpose owing 53 in part to the ease with which it could be worked, but mainly be- cause of its resistance to corrosion. Apparatus and Procedure Since it was considered essential for the purposes of the in— vestigation to obtain the drying data in the greatest possible de- tail, particularly over the initial stages of the desorption pro- cess, it was decided to employ a static method for obtaining the exPerimental data. The most serious objection which is generally alleged against static methods lies on the long periods of time necessary for attainment of equilibrium. Yet, this very circum- St”Nice made it feasible to obtain drying data to a degree of detail and precision not ordi'fi rily attainable with dynamic methods. .The method consisted essentially of exposing the samples of grain to atmOSplieres of constant temperature and relative humidity maintained in mo isture-tight glass chambers by saturated aqueous solutions of selected chemically pure salts. The glass chambers were kept in the nnostatically-controlled storage cabinets maintained at constant temperature within plus or minus one degree Fahrenheit. Periodic “eighing of the samples at appropriate intervals provided the neces- sary data for determining the drying rates. When essentially con- stant. 'Qight was maintained over a period of at least two weeks, it “as generally decided that equilibrium had been virtually at- mi“ed. Longer times were allowed for the sadlples held at the lower tempe ratures. As soon as possible thereafter the samples were 0‘} tested for moisture content by the air-oven method. A more detailed description of the apparatus and procedure employed shall presently be given . Contro l 1 ing ne lative Humidity The fact that a saturated aqueous solution of a salt at a given temperature will maintain a constant humidity within any en- closed Space has long been recognized as a valuable instrumentation technique for controlling relative humidity in small chambers, par- ticularly under static conditions. Numerous investigators (13, 50, 51: 52) have undertaken to determine the equilibrium relative humid- ities maintained by various salts at various temperatures, and pub- lished values are now available from various sources. The salts used in the present investigation were selected after a thorough sea-Feb of the literature and are given in Table I together with their corresponding values of relative humidity at the various “We ratures. In the preparation of the various saturated salt solutions two different procedures were followed. The first method con- 8iE‘t'ecl of weighing a predetermined amount of the salt on an ordin- ary Platform balance and thoroughly mixing it in a beaker with approximately 250 milliliters of distilled water. The mixture "‘8 then heated to a temperature of 212°? and held at this tem- perature long enough to make sure that the salt necessary to “turate the solution at the lower temperature had entirely dissolved. The solution was then transferred to the glass chambers TABLE I EQUILIBRIUM RELATIVE HUMIDITIES ABOVE SATURATISD SALT SOLUTIONS AT VARIOUS TEMPERATURES .-m‘ o n o “-n‘ ---‘ "Sfiflt "m° “—1 . ‘ “‘*--—O ...—h‘--~ - . -..-- o “—«v ....—H-.. -..-- o w 0“- -.-‘-o- up- — .-.‘g— ‘ ‘vo-Fo- Formula RH... ‘ - ”Kumt}. ~ 40°F Lithium chloride LiCl.fl20 14.0 Wexler and Hasegawa flagnesium chloride ‘IgCl2.6H20 34.6 " " Sodium dichromate Na20r207.2H20 59.3 " " Sodium chloride NaCl 75.1 N n Potassium nitrate KNO3 96.6 N n Potassium sulphate K2804 98.4 " " 60° F Lithium chloride LiCl.H20 12.8 Carr and Harris Magnesium chloride Mg012.6320 33.9 Wexler and Hasegnwa Ctummic oxide Cr03 37.5 Wink and Sears " " ” 45.4 Carr and Harris Sodium dichromate No.2cr207 .2820 56.6 lexler and Hasegawa Sodium chloride NaCl 75.9 Carr and Harris Potassium nitrate “03 94.3 Iexler and Hasegawa Potassium sulphate K2804 97.5 " " 86°F Lithium chloride LiCl.H20 11.2 'ink and Sears Potassium fluoride KF.2H20 27.4 Carr and Harris Magnesium chloride IgClz.6320 32.4 ‘Iink and Sears Chronic oxide Cr03 40.0 ' ” Potassium carbonate K2003 43.5 " " Sodium dichromate Na20r207.2H20 54.2 Carr and Harris “ " 52.0 Wink and Sears Sodium bromide NaBr.2820 56.3 " " Sodium nitrite NaNO2 63.3 ” " " " " 64.8 " " Oupric chloride Ou012.2820 68.3 Sodium nitrate NaNO3 72.8 Carr and Harris Sodium chloride NaCl 75.2 [ink and Sears Ammonium monOphosphate NB4H2P04 92.0 ” " 56 TABLE 1 (Cont.) Salt Formula R.H. Authority 100°? Lithium chloride LiCl.I120 11.1 link and Sears Magnesium chloride IlgCl2.61120 32.4 " " Chromic oxide CrO3 40.2 " " Potassium carbonate K2003 43.4 " " Sodium dichromate Na20r207.2320 50.0 " " Sodium bromide NaBr.2320 53.7 " " Sodium nitrite NaN02 61.8 " " Sodium chloride NaCl 75.1 " " Amonium sulphate (N34)2804 79.1 " " Potassium chromate K20r04 86.3 " " Ammonium monophosphate N8482P04 92.0 " " Potassium nitrate 10103 96.2 Wexler and Hasegawa 122°? Lithium chloride . LiCl.I120 11.4 Wexler and Hasegawa Potassium fluoride “.2320 20.4 Carr and Harris Sodium iodide NaI.2H20 28.4 " " Wignesium chloride IgClz.61120 31.4 Iexler and Hasegawa Chronic oxide CrO3 45.4 Carr and Harris Sodium dichromate Na20r207.2H20 47.1 'exler and Hasegawa Sodium nitrite NaNO2 59.8 " " Sodium nitrate NaNO3 68.7 Carr and Harris Sodium chloride NaCl 74.7 Vexler and Hasegawa Potassium chloride K01 81.2 Carr and Harris I"it-assium nitrate KN03 85.0 Iexler and Hasegava l’Otassium sulphate [(2804 95.8 " " TABLE I (Cont.) Salt Formula R..H. Authority 14o°r Potassium fluoride [CF 21.0 Carr and Harris Sodium iodide NaI.2H20 25.3 " " Chronic oxide CrO3 45.8 " Sodium bromide NaBr.2820 49.9 '9 ’-' Sodium dichromate Na20r207.21120 55.2 " " Sodium nitrite NaN02 59.2 " " Sodium nitrate NaNO3 67.5 " " Sodium chloride NaCl 74.9 " " Potassium chloride KCl 80.7 " " and allowed to cool at room temperature whereupon a suitable ex- cess of salt was added to guard against the possibilities of super— saturation. Where the cost and the amount of salt available per— mitted, it was desirable to use a considerable excess of salt so that mounds of crystals protruded above the liquid surface. It should be cautioned, however, that too much of an excess may re— sult in drying up the solution. For relative humidities above 85 percent the extreme excess of salt is not necessary, though it is still important to have some crystals present in the solution. iEnough of the prepared solution was then placed in the jar to fill it to a depth of approximately one and a half inches. The jar was then sealed, properly labeled, and placed in the corresponding constant-temperature cabinet where it was allowed to stand for at least 24 hours prior to use. As a guide in predetermining the appnoximate amount of salt necessary for obtaining a given amount 0f saturated solution Seidell's encyclopedia on Solubilities of Inorganic and Metal Organic Compounds (42) is probably the best 5°“Pc¢ of’information. {the second method consisted essentially of placing the pre- determined amount of the salt in the empty glass jar or chamber and addingi'the appropriate amount of distilled water to produce the re- quireTl saturated solution. The mixture was thoroughly stirred, whereupon the jar was sealed, labeled properly, and placed in the carresponding constant-temperature cabinet. The solutions prepared as . cordlng to this method were allowed to stand for at least one 59 week prior to use in order to insure complete saturation. The same precaution of providing for an excess of salt crystals in the solution was followed as explained for the first method. Iink and Sears (52) compared both of the above methods and obtained relative humidities which agreed within 0.3 percent. Constant-Humidity Chambers and Sample Containers 'l'wo principal types of containers were employed as constant- hulnidity chambers, namely, one—gallon wide-mouthed glass jars of the type generally used for pickles or mayonnaise in the food in- dustries, and one-half gallon mason fruit jars. The metallic 8ePOW-on type of lids of the former were furnished with a suit- able gasket in order to insure a moisture-tight seal and also as a means of holding the hanger for the sample container. This hanger was made. of a piece of brass wire formed in a loop with a straight section bent at right angles to the plane of the loop and threaded through the center of the circular lid gasket to pro- Vide a. terminal pig-tail hook for suspending the sample container “0'9 the solution. The mason fruit jars were provided with 3990181 lids made of polysterene plastic and similarly equipped 'ith a gasket and hanger. Both types of jars allowed for an ade— quate ratio between the free surface area of the salt solution and the eatimted external surface area of the kernels making up the Gunple. Likewise, the ratio of free surface area of the solution and the estimated external surface area of the kernels making up th e ample. Likewise, the ratio of free surface area of the solution GO to the volume of the chamber above the solution was adequate in both cases. Both of these factors are of importance in determining the time required for humidity equilibrium to be reached, and for restoration of the original conditions after disturbances inciden- tel to the weighing operations. The length of the sample hangers was so adjusted as to bring the sample as close to the surface as was considered safe from the standpoint of minimizing the chances of accidentally splashing the solution over the samples. This height usually varied from one to three inches. Extreme care was “1‘"‘3'8 exercised in handling the jars, and only in very few in- stances were samples ruined by accidental splashing. Figure 2 illuStrates both types of containers described above with the samples suspended in the regular manner. One of the plastic lids used with the mason jars lies on the table to show the gasket and sample hanger; also one of the mason jars is shown with a type of zinc cap used with a few of the jars. _ The sample holders were made of the plastic material previously “Seribed in the form of cylindrical baskets about two to four and a. half inches in diameter and two to four inches high. They were pl"OVided with a handle in the form of a loop made of strands of the “We material. While adhesive cements may be helpful in making the haskets, their use was found objectionable owing to their hygro- scopieity which may: cause the tare weight of the basket to change aPPPI-Ieiably throughout the test period. Accordingly the seams of the baskets were stitched together with strands of the same plastic 61 Figure 2. The two main types of containers used as constant—humidity chambers. Samples are seen suSpended in their regular position above the saturated salt solutions. Figure 3. Constant—temperature cabinet with regular load of constant-humidity chambers. material. Small labels made of aluminum foil on which the code number was typed were attached to the baskets as a means of iden- tification. Temperature Control Six different temperatures were employed for the tests on hygrosc0pic equilibria and drying rates, namely, 40°, 60°, 86°, 100°, 122°, and 140°F. The selection of these temperatures was partly governed by the availability of suitable data pertaining to the relative humidities obtainable with various salts. The 40°F temperature was maintained by thermostatic on—off control in a walk-in type refrigerated cabinet with forced draft air circulation. The 60°F temperature was similarly maintained in a smaller cabinet of the same general dimensions as those showed in Figures 3 and 4. The 86°F temperature was maintained in walk-in type storage cabinet similar to the one used for the 40°F tempera- ture but equipped with a thermostatically-controlled lamp bank as a source of heat and with suitable shielding to protect the constant-humidity chambers against direct radiation from the lamps. The higher temperatures were maintained in wooden storage cabinets provided with lamp bulbs as a heat source, with forced draft air circulation, with suitable oneoff thermostatic control, with a mercury-in-glass thermometer for checking the temperature, with a sheet metal shelf to serve as a radiation shield and as an aid to air circulation, and with a slatted false floor which insured adequate air circulation underneath the jars. Figures 3 and 4 63 Figure 4. Constant temperature cabinet with most jars removed to show construction features. F1sure 6. leighing equipment and general set-up for the weighing operation. 64 shows one of these cabinets in wide-Opened position in order to illustrate all of the above features. In all cases, constancy of temperature was maintained within plus or minus one degree Fahrenheit. Preparation of the Samples The corn samples were either taken directly from the regular stock previously described with no further preparation other than allowing the corn to warm up to room temperature, or from portions Of this same stock previously conditioned to higher moisture con- tents as it was deemed necessary. No specific values of initial moisture content were particularly aimed at, as long as high enough levels were obtained to allow for a wide enough range of desorption Vapor pressure differences and still have the drying process take place in the falling—rate period. This conditioning treatment was Particularly necessary in the case of the samples intended for equil- ibration at high relative humidities. The conditioning procedure followed consisted generally of soaking the required amount of seed in distilled water for a period 0f four to six hours. Throughout the soaking period the grain was kept, inside the 40°F cabinet. The excess water was then drained Off and the kernels spread singly over a sheet of towel paper and allowed to stand at room temperature until all the surface water Md dried out. The seed was then placed in a clean dry jar, sealed t'ightly, properly labeled, and returned to the 40° box until ready t0 “Sec Enough time was allowed to insure moisture equilibrium within the individual kernels. The evening before the test was to 65 be started the jar was removed from cold storage and allowed to re— main overnight at room temperature. The resulting moisture content of the seed conditioned according to the foregoing treatment varied from 37.25 to 45.52 percent, dry basis. No harmful effects whatso- ever were detected as a result of this conditioning procedure. In any case, the samples were made up of anywhere from twenty to thirty singly selected kernels of normal shape and size charac- teristic of the variety. The kernels were spread in a thin layer one grain deep on the bottom of the basket. The basket and sample were then accurately weighed to the closest tenth of a milligram and immediately placed in the correSponding constant-humidity Chamber. This was immediately placed, in turn, inside the corres- I‘Onding constant-temperature cabinet. All necessary information was subsequently recorded on a data sheet eSpecially prepared for the purpose. One separate sheet was.used for each sample and all subsequent data pertaining to that sample was recorded therein. One example of these data sheets is shown in Table II, with typi- cal information pertaining to one of the samples. The time of weighing was recorded to the nearest minute. Drying Rate Data Mensured from the time they were first weighed and placed in the drying chambers at the beginning of the run, the samples were weighed at periodic intervals. The sequence of steps inVOIVEd in each drying operation was as follows: 66 (l) The analytical balance was prepared with the approximate anticipated gross weight of the sample on the corresponding pan. (2) The constant-temperature cabinet was opened, the desired jar was removed promptly and carefully with a steady motion aimed at producing the least possible disturbance of the contents, and the cabinet was reclosed. (3) The lid of the jar was unscrewed and lifted with care, the sample was removed and placed in position on the balance as shown) in Figure 5‘F:5 (4) The weighing pans were released and the actual weighing 01‘ the sample performed. (5) The sample was returned to the jar, the jar was sealed toightJy, and returned to the constant temperaturemabinet. (6) The gross weight and the time of weighing were then recorded on the correSponding data sheet. ‘The whole operation generally required not more than 75 to 9(’ seconds, while the time that the sample remained out of the (trying chamber and the chamber out of the constant-temperature cabixuat seldom exceeded thirty and forty-five seconds respectively. Promptness and accuracy were the objectives to strive for in each weighing operation. irhe weighing intervals adopted for the first series of runs were ill the order of twenty—four hOUrs during the initial stages 0f the tirying process, and were gradually increased after the first two weeks, as the rates of drying slowed down. It was 1300n realized, however, that an observation interval of twenty-four hours was far too long to permit a detailed enough study of the drying rates during the all-important initial stages of drying. In all subsequent runs, therefore, the observations were made at intervals which were in the order of one-half hour for the first eight to twelve hours, twice or four times every day for the next seven to eight days, once a day for the next fourteen or sixteen days, and at longer intervals thereafter as it was deemed appropriate on the basis of the observed drying rates. Determination of Moisture Contents The general procedure followed upon termination of a run for any given sample was as follows: The final gross weight of the sample was obtained as ex- Plfl-ined above and the kernels promptly transferred to a weighing can. The terminal tare weight of the sample container was then determined and recorded after which the basket was returned to its corresponding drying chamber. The weighing can was then Closed and placed in a desiccator for transferring to the oven. The egrregponding data was entered in the appropriate data sheet. The same procedure was followed with all samples due for termina- tion- The weighing cans were then taken to an electric air—oven, Where they were placed with the lids removed and placed underneath the Corresponding cans. The samples were thus held at a tempera- ture of .2120!" for a period of seventy-two to eighty hours, which had been previously decided as adequate to achieve constancy of 68 weight. After this period the cans were closed while still in the oven, removed, and placed in an aluminum desiccator charged with activated alumina where they were allowed to cool to room temperature. The cans with their contents were then weighed im- mediately, each at a time, and their weight recorded on the cor— reSponding data sheets. The cans were then emptied, weighed again, and their tare weight recorded. All samples were handled in quick succession, one at a time. Processing of these data yielded the net terminal weights of the samples and their dry matter content. From the recorded initial weight of the samples the instantaneous moisture contents at the various times of obser- vation were calculated. Both the initial and the equilibrium moisture contents were accurately calculated to the closest hun- dredth of one percent. Slide-rule accuracy was judged sufficient for all intermediate moisture content values, even though readings were still read to two decimal places whenever possible. The re- sul ts of all these calculations were entered in the type of data sheet shown in Table II. Irradiation Tests It is a well recognized fact that the drying rate of any given material under a given set of drying conditions is a func- tion of the particular characterisfics of the material. Many GXperimenters have concerned themselves with the nature and dis- t"maul-on of the resistance to the movement of moisture within the 69 grain in response to a drying potential. Several noteworthy ex- planations have been advanced concerning the mechanism whereby moisture escapes from the grain. It has been Specula'ted whether the resistance to moisture transfer is uniform throughout the ker- nel or rather concentrated at some particular site within the grain or at the surface. Oxley (38) has suggested that this resis- tance might be concentrated somewhere below the surface of the grain, basing his judgment on Edholm's findings in experiments on inte mittent drying. 0n the other hand, the suggestion has also been made that the Open tissue at the tip of the corn kernel is PPObably the exit space for moisture during the drying process. It was therefore considered of interest in connection with the in- Vestigation to explore the possibilities of improving the moisture transfer characteristics of the grain with electromagnetic irra- diation. Accordingly a short series of experiments was planned for this purpose. As was pointed out before, the stock of Mayorbela corn from Puerto Rico was used in this series of experiments. Typical samples were prepared from a small batch of seed previously irra- diated with a dose of 106 reps applied on each side of the kernels and placed in drying chambers corresponding to the following drying conditions: 11.1 percent relative humidity and IOOOF; 75.1 per- cent, relative humidity at 1000?; 49.9 percent relative humidity at 14001". Control samples were run simultaneously under the same conditions. The test was repeated following exactly the same 70 procedure, except that the irradiation dose was increased tenfold to 107 reps. Again exactly the same procedure as previously des- cribed was followed in obtaining the drying data of these samples. Results The hygroscOpic equilibrium data for shelled corn obtained as a result of the foregoing experiments and the initial processing 0f the observational data are tabulated in Table II. The table ineludes information on the salt solution employed as constant- hulnidity controller, the corresponding tempe ratures and relative hmllildities, the initial moisture contents of the samples, the cal- culated values of hygroscOpic equilibria, and the duration in hours of the corresponding tests. It should be pointed out that in many cases the runs were extended well beyond the virtual at— tainment of equilibrium and therefore, the duration of the run is not. necessarily to be interpreted as the time required for equili- bration. It is felt that the equilibrium moisture content values Obtainedoare as close to true equilibrium as it is possible to ob- train in such tests. Subsequent processing and analysis of these data will be dealt with in the next chapter. The drying data consists principally of the instantaneous Values of moisture content and their respective times of occur- Pence as obtained from the preliminary processing of the observa- tiOl‘lal data as previously explained. The extensiveness of the data definitely precludes their inclusion here, and only Table 111-— 71 TABLE II EXPERIMENTAL EQUILIBRIUM MOISTURE CONTENTS OF SHELLED CORN AT VARIOUS RELATIVE HUMIDITIES AND TEMPEIMTUELES ————_._ ‘._.___- A- ‘_l- .1“. A ~— a.~.—- .4. ‘. Salt Solution Relative Initial Moisture Eilgfi’iogrgum S1;r:§rilon Humidity Content Content 9, _ m“ - fi _ 3.915353--- *1! , % dd? 11‘, 7i» ..d'b’ . hours 40°F Lithium chloride 14.0 18.20 8.09 1581 Magnesium chloride 34.6 18.40 11.71 1587 Chronic oxide 37.0 18.36 12.27 1943 Sodium chloride 75.9 24.30 20.51 2217 25.90 21.14 69.12 Sodium dichromate 59.3 27.12 16.35 1520 Manganese chloride 53.4 27.22 15.00 1454 60°F Magnesium chloride 33.9 18.42 10.52 1496 chronic oxide 37.5 18.20 11.40 1496 28.10 11.20 390 20.93 11.38 586 23.12 11.08 450 Sodium dichromate 56.6 17.86 13.77 .534 Potassium fluoride 32.35 18.04 10.51 540 Sodium chloride 75.9 18.75 18.23 1496 Potassium nitrate 94.4 43.7 28.7 205 86°F Lithium chloride 11.2 20.77 4.86 925 Potassium fluoride 27.4 24.59 8.10 560 17.95 7.96 1580 “asnesium chloride 32.4 21.75 9.02 900 18.15 8.90 1686 24.25 8.74 1885 23.70 8.97 1613 Chronic oxide 40.0 22.44 10.32 2311 21.66 9.60 689 18.02 9.87 1492 TABLE 11 (Cont.) ‘ Relative Initial Moisture ‘Eq ilibrium Duration Salt Solution Humidity Content 535211? of run percent Mo, % d.b. Me’ % d.b. hours 86°F Potassium: carbonate 48.5 21.14 10.50 941 Sodium dichromate 53.1 18.36 11.90 1687 23.03 11.48 1893 23.98 11.93 1800 23.48 11.88 1914 18.15 11.90 1586 Sodium nitrite 63.3 18.08 13.64 1466 17.86 13.57 814 Cupric clrloride 68.3 23.00 14.89 1638 18.03 14.52 1689 Sodium chloride 75.2 24.85 15.83 1107 20.92 15.83 867 3°41“ bromide 56.3 20.08 12.38 880 P“assium chromate 86.3 21.20 19.28 97 100°F I“him!- chloride 11.1 18.60 .4318 1618 “Regina: chloride 31.9 18.44 8.46 1062 Russian. carbonate 43.4 18.35 9.95 1062 88:11:“ dichromate 50.0 27.79 10.86 1365 Sadium nitrite 61.8 18.49 12.78 1062 m chloride 75.1 18.55 15.28 1061 Anon . 32.82 15.35 839 Poma:um sulphate 79.1 28.85 16.88 856 __ ‘ ium sulphate 96.3 17.61 24.81 242 ... __ _, __ __ __ __ _, __ __ __ __ __ __ __ __ _, _, __ _, __ __ __ Idtdii 122°r ‘UHI chloride 11.4 37.48 3.93 870 44.00 3.83 1188 17.98 4.12 1047 80:11 . ‘1"1 iodide 28.4 36.79 7.48 507 h .4“ -'. 7 M . 7 .1; ‘ 1 '.‘ “I It '7 H1 9"! lg.) ‘1') IU Salt Solution Relative Initial Moisture E uilibrium Duration Humidity Content 00:23:? of run percent “0’ 5 d.b. e’ d,b. hours 122°r Potassium fluoride 20.4 38.10 5.97 1038 Sodium dichromete 47.1 32.28 9.88 1153 Sodium nitrite 59.8 38.35 11.65 1042 Sodium nitrate 68.7 32.11 13.31 506 Sodium chloride 74.7 37.66 14.78 .1040 Potassium nitrate 85.0 37.77 17.74 1047 41.79 17.79 213 17.70 17.33 975 14o°r Lithium chloride 11.2 42.70 3.39 981 Russian fluoride 21.0 43.80 5.21 1304 Sodium iodide 25.3 17.48 . 6.12 981 Sodium bromide 49.9 43.70 8.59 1006 80““ dichromate 55.2 43.58 8.92 170 19.71 9.65 1086 383:: nitrite 59.3 43.12 9.75 994 “has . chloride 74.9 18.33 12.43 941 1m. chloride 80.7 27.40 13.71 168 3011111.. 44.58 14.03 218 nitrate 67.5 28.50 10.78 205 \‘ \“ 74 Vhich partially shows the results obtained for one of the salnples— is offered as an example. Table III-A on the other hand illustrates a form employed for recording the results of further processing 0f the data of each sallple for the purpose of obtaining basic values necessary for subsequent treatments. These basic values include, the moisture contents converted to a wet basis, the free moisture content on a dry basis, the moisture content ratio on a dry basis, the equilibrium relative humidities as given by the constructed experimental isotherms, the equilibrium vapor pressures, pg , Obtained by multiplying the equilibrium relative pressures by the amturation vapor pressure, p8 , of water corresponding to the d'Ving temperature as given by thermodynamic steam tables, and the Values of vapor pressure potentials (pg - pa) as obtained from the difference between the equilibrium vapor pressure and the partial a"Queens vapor pressure, pa , of the drying air. All of the vapor Pressures given in Tables III and III-A are expressed in pounds per square inch absolute. As in the case of the hygroscopic equilibrium data, .further t'I‘Oatulent and analysis as well as the results obtained will be dis- cussed in the next chapter. The results of the irradiation tests are illustrated in Figure 35 which shows the drying curves for one of the samples irra- diated with a dose of 106 reps and its corresponding control sample. Since the point values for both curves were nearly coincident the curve for the control sample was displaced as shown in order to be To; AdL 75 TABLE III EXPERIMENTAL DATA SHEET Code No. 1-3 Salt Solution K2°°3 Temp-.1292 391- Hum-443°“, 35"- Vapor pressure, p8 0.9492 psi Vapor pressure, pa 0.129 psi Bate run started 9Z18Z55 Date run ended 11(1Z55 Duration _l_9_§_2__ hrs. Basket no. __l_(_)__ Tare weight 3.4201 911 Gross weight 13.8353 gm Net weight sample 10.4152 gm Initial water content 1.6155 gm Initial moisture content, Ho l_5_._§_2_ ‘73 w.b. 18.35 % d.b. Final Clio is ture Dete rmination Moisture can no. 8 Date and hour to oven 11/1/55 at 3100 P.1d. Tare weight can 23.9854 gm Date and hour out of oven 11/4 at 5:00 PJA. [eight can + sample .- 33.6707 gm Terminal net wt. 9.6853 El Gross Vt out of oven 32.7899 gm Weight dry matter 8.804% Equilibrium moisture content, 11. 9.08 7% w.b. 11.3 10.00 3 d.b. '-— -..--—-. -.....» Date Time 0 hrs. Gross wt. wt. 11 0 Wt. 11 0 Calculated grams lost-cum. remaining M % d.b. 9/16 a 8:45 0.00 13.8353 0.0000 1.6155 18.35 9:15 0.50 13.7860 0.0493 1.5662 17.78 9:45 1.00 13.7451 0.0902 1.5253 17.31 10:18 1.55 13.7117 0.1236 1.4919 16.94 10:58 2.21 13.6755 0.1598 1.4557 16.52 11:15 2.50 13.6620 0.1733 1.4422 16.36 11145 3.00 13.6377 0.1976 1.4179 16.08 P 12.15 3.50 13.6179 0.2174 1.3981 15.85 :12:45 4.00 13.5988 0.2365 1.3790 15.65 2:15 5.50 13.5507 0.2846 1.3309 15.10 2:45 6.00 13.5375 0.2978 1.3177 14.94 3:15 £6.50 13.5238 0.3115 1.3040 14.80 3:45 7.00 13.5109 0.3244 1.2911 14.68 . . . , . . ll/l P 2:45 1062.00 13.1022 0.7395 0.8760 10.00 \ 76 TABLE IIIA ANALYSIS OF DATA SHEET Sumary from Data Sheet . 0 Code no. 1-8 Salt solution K2603 Temp. 100 F Rel. Hum. 43.473 Ps 0.9492 psia Pa 0.4129psia 11 15.5213 w.b. 11° 18.352 d.b. Duration of run 1062 hrs. Half-reaponse period, 0’} 9 hrs. ' r lie 9.08;! w.b. 116 10.00;! d.b. no - Me 8.35 5% d.b. 9, hrs. 11, percent u - Me H - Me (ll-EL)e Pg Pg " Pa 1 7; w.b. 76 d.b. 7% d.b. 11 - 110 percent psi psi 9 0.00 15.52 18.35 8.35 1.000 86.60 0.822 0.409 0.50 15.10 17.78 7.78 0.931 84.40 0.801 0.388 1.00 14.75 17.31 7.31 0.875 83.40 0.792 0.379 1.55 14.50 16.94 6.94 0.831 82.10 0.779 0.366 2.21 14.30 16.52 6.52 0.780 80.50 0.764 0.351 2.50 14.18 16.36 6.36 0.761 79.90 0.758 0.345 3.00 13.83 16.08 6.08 0.728 78.60 0.746 0.333 3.50 13.70 15.85 5.85 0.700 77.70 0.737 0.324 4.00 13.54 15.65 5.65 0.676 76.80 0.729 0.316 5.50 13.10 15.10 5.10 0.610 74.30 0.705 0.292 6-00 13.01 14.94 4.94 0.591 73.50 0.698 0.285 6-50 12.90 14.80 4.80 0.575 73.00 0.693 0.280 7.00 12.78 14.68 4.68 0.562 72.30 0.686 0.273 7.50 12.66 14.50 4.50 0.539 71.50 0.679 0.266 8-00 12.55 14.38 4.38 9.525 70.80 0.672 0.259 8.50 12.45 14.26 4.26 0.510 70.40 0.668 0.255 13°84 11.78 13.35 3.35 0.400 65.50 0.622 0.209 10°2°°° 9.08 10.00 0.00 0.000 43.40 0.413 0.000 able to plot both curves distinctly. It is evident from the char— acter of the curves that there was no noticeable effect of the ir- radiation on the drying behavior of the corn. Similar results were obtained under the other drying conditions used in these tests, and the curves presented are typical. 78 ANALYSIS AND DISCUSSION It has undoubtedly become evident that the scope of the investigation has touched on two distinct aspects of the water relations of shelled corn: the equilibrium or thermodynamic ro- lationships on the one hand, and the time—dependent rate processes on the other. However closely related these two phases of the problem are-- both from the theoretical and the practical view- points— it has been deemed convenient for the purposes of the analysis and discussion that ~will follow to keep them under separate headings. The results pertaining to desorption equili- brium data shall be dealt with in the first place; the drying rate data shall be considered next. Desorption Equilibrium Data The experimentally determined values of equilibrium mois- ture content for the various test conditions investigated have been presented in Table II. The next step in the analysis of the data was concerned with the construction of desorption isotherms for the temperatures of the investigation. construction of Desorption Isotherms The isotherms were constructed by plotting for each tempera- ture Separately the equilibrium moisture content values (dry basis) as °rd1nates against the corresponding values of equilibrium relative 51"" 79 Chou 3:93 .2 2.3503 .coo son 56 E5... 3:22 5:380 h 9:9... 52.9.53. 9. sgsoq Kip °/o ‘°w ‘suewoo amisgom wnpqmnbg A!" 80 humidity as abscissae. The curves were then drawn as smoothly as possible through the point values corrCSponding to each tempe ra- ture. In the absence of experimental data for relative pressures below 0.10, the lowermost portions of the isotherms could be con- structed by extrapolating the curves to converge at the origin, since it is well-established characteristic of all isotherms that at zero pressure the amount of adsorbate adsorbed is also zero. While a certain degree of uncertainty may still be recognized con- cerning the exact course of the isotherms in that region, whatever inaccuracy may exist must necessarily be very slight. There is therefore little doubt as to the reliability of the isotherms even in that lowermost region, for all practical purposes. The uppermost region of the isotherms beyond a relative pres- sure of about 0.85 presented a similar problem as described above f°r the lowermost region in that not enough data was at hand to complete each isotherm up to saturation pressure. It will be re- me“Ibel‘ed that herein lies one of thejshortcomings of the static methOd in securing hygroscopic equilibrium data at the higher rela- tive humidity, owing to the susceptibility of the samples to molding We" Protracted periods of equilibration. To circumvent this dif- ficulty an interesting method suggested by Bull (12) for extrapo- lating the curves up to saturation pressure was resorted to, with Very slitisfactory results. This method required the plotting of the function a/X as ordinates against corresponding values of X as . a'bcl-Bsae for each one of the isotherms; where a represents the 91 TABLE IV cowu'rulon or DATA FOR a/X VERSUS x PLOTS rmu DESORPTION lsomaas Isotherm Temperature - 100°F ‘ I a a/i Equilibrium Moisture Relative Content, I M/(R..H.) Humidity, (11.11. )9 percent dry basis e Jercent 2.50 1.90 0.7600 5. 00 2.90 0.5800 10. 00 4.30 0.4300 15. 00 5.50 0.3660 20. 00 6.40 0.3200 30. 00 8.10 0.2700 35. 00 8.80 0.2510 40. 00 9.50 0.2370 45. 00 10.25 0.2280 50. 00 10.90 0.2180 55. 00 11.65 0.2120 50. 00 12.49 0.2080 65. 00 13.25 0.2040 70. 00 14.25 0.2038 75. 00 15.30 0.2040 80. 00 16.75 0.2093 35. 00 18.40 0.2163 90. 00 20.50 0.2280 95.00 23.75 0.2500 96.40 24.75 0.2560 97.50 26.00 0.2665 82 852: 05265 .20 Soc .3 . :2 Bowen 3.28:: .o\o 5.25 -2 2:22 55:33 .. .u o\o .2230 2239: Our: 235mg 3 222. 6.822. 222383 2283 2228 moo 6202:: 35:0 385 out 60.: x 028.9. :46 ecu mo 058226 so .2, 0 ac .205 m 959 £25.35 soseeo :6. exec 83 moisture content on a dry basis and X stands for the equilibrium relative humidity. In order,to compute point values for constructing the plots, values of relative humidity were selected at intervals of 5 percent up to 85 percent. Table IV shows the results of the computations involved in calculating the plot for the 100°F isotherm. The same procedure was followed for each of the isotherms. The completed plots are shown in Figure 8. It will be seen that smooth curves were obtained which, though swinging upwards rather abruptly in the low pressure region, do show only moderate changes in slope at, the higher relative pressures. It was thus possible to extrapo- late the curves beyond the last plotted point up to saturation pres- sure without much chance for ambiguity. The values of a/X , given b? the intersection of the curves with the vertical at saturation Pressure, yielded the desired values of equilibrium moisture con- tent corresponding to 100 percent relative humidity. The extrapo- lated sections of the «plots are shown in dashed lines in Figure 8, "file the circles indicate the point values calculated as explained abfive. The three points which appear beyond the plotted curves repre- sent actual experimental values which could be obtained in this re- sion. and which served as a valuable check of the reliability of this procedure. In Table V columns 5 and 6, the values of a/X at 8lI-turation and of the corresponding equilibrium moisture contents, reapectively, are shown for all isotherms. As a further test of the “rt‘ectness of this method the values of equilibrium moisture content thus determined were checked against comparable data from the literature, with gratifying results. Ihile information available 84 TABm V EVALUATION OF a2 AND as FROM PLOTS 01“ FIGURE 8 Isotherm (a/X)2 12 a2 (a/X)s as a2/vm 40°F 0.2693 05.0 17.50 0.330 38.0 2.012 U 60°F 0.2355 67.5 15.90 0.340 34.0 2.008 86°F 0.2100 72.5 15.2 0.297 29.7 2.140 100°? 0.2038 70.0 14.25 0.285 28.5 2.125 122°F 0.1940 65.0 12.6 0.270 27.0 1.905 140°F 0.1615 67.5 10.4 0.240 24.0 1.790 85 on hygroscopic equilibria at high relative pressures is extremely meager, two instances could be found which provided the required evidence. 0n the one hand, Coleman and Fellows (14) reported a value of 23.8 percent on a wet basis as the equilibrium moisture content of shelled corn (yellow dent) at a 100 percent relative humidity and a temperature of 77°F. This is equivalent to 31.20 percent on a dry basis, which, as will be seen from both Figure 7 and Figure 8, represents a remarkably good agreement with the extrapolated values. The other instance was furnished by a completeh—MA adsorption isotherm for maize at 10°C (50°F) taken from an inves- tigation of R. Gave (19) and given by de Boer in his book on ad- sorption. This particular curve was cited by de Boer specifically as an example of an isotherm which exhibits a definite intersection Vith the vertical axis at 100 percent relative pressure. The value of moisture content, given by this intersection was found to be 33'5 Percent dry basis, which again agrees closely with values es— tablished by the method suggested by Bull. Perhaps the greater significance of the foregoing evidence lies in showing that the is"thermal of shelled corn, and prObably of cereal grains in general, do inte rsect the vertical at saturation pressure contrary to the general assumption that the isotherm only approaches it asymptotically. _.f‘ , The significance of the plots of Figure 8 goes beyond serving the purp°39 discussed, and will be referred to again later. 86 Construction of Isosteres Because of the practical usefulness which they may serve it was considered appropriate to represent the eXperimental data in the form of isosteres. Isosteres represent the relationship be- tween the equilibrium vapor pressure and temperature for a given constant amount of adsorbate adsorbed, as given by equation (4). Having obtained isotherms at six different temperatures, the ex- pe rimental data may be used conveniently for representation as isosteres. The procedure involves the calculation of the equili- brium aqueous vapor pressure of the grain at each of the various temperatures for selected values of moisture content. These were obtained by multiplying the values of equilibrium relative pressure, as given by the isotherm curves, by the saturation vapor pressure of water at the temperature under consideration. The values thus determined for each of the moisture content levels selected were then plotted as ordinates against the corresponding temperatures as abacissae. A smooth curve was drawn through the points, which then °°n3titutes the desorption isostere for the particular value of equilibr-ium moisture content. Figure 9 shows a family of desorp- tion iScisteres for shelled corn obtained according .to the fore- going Procedure. The resemblance between the family of isosteres and a Psychrometric chart is immediately evident. Vith the aid of Figure 9 the equilibrium vapor pressure of shelled corn may be readily determined with fair accuracy for any conditions of tem- perature and moisture content within the range of the chart. In sysoq Mp 0/0 wewoo aimsyow ....... 'DTS'd ‘bd ‘smssaid JOdDA wnpqnpbg 87 ..... °F. Temperature, Figure 9 Desorption isosteres for shelled corn ”0 T0 the next section it will be seen how a modified form of the isostere may be useful in the indirect determination of the heats of desorp- tion (or adsorption). Calculation 0f Isosteric Heats of Desorption For equilibrium systems the well-known Clausius-Clapeyron equa- tion, which was first deduced from the Carnot cycle by Clapeyron and later derived from thermodynamics by Clausius ( 9), permits the evaluation of the heat change involved in the transition from one phase to the other. It may similarly be used to evaluate the heat changes involved in adsorption or desorption processes. The equa— tion relates the rate of change of pressure with resyect to tempera— ture, with the changes in heat content and in volume of the system as f0 1 lows .93...- AH (45) dT '1‘ AV Equation (45) may be used directly without integration for processes Whe re dP/dT is approximately constant over the range considered. From a consideration of the isosteres of Figure 9 it is evident that the vapor pressure changes rapidly with temperature and not at all linearly. Therefore, for the grain-water vapor system, dP/dT does “0‘9 remain constant over wide temperature ranges so that equation (45) must be integrated. However, it can not be integrated unless AH and AV can be expressed as functions of temperature or pressure. This can be achieved with the aid of two simple approxi— mations. In the first place, because the molar volume, Vg 9 0f 89 the vapor is large compared with the volume of the adsorbed state, the change in volume AV is approximately that of the vapor itself so that Va 46 A vg () Secondly, if ideal gas behavior is assumed for the vapor the molar volume, vg , is given approximately by Av s RT (47) ' P Ihen this value of AV is substituted in equation (45), H being the molar heat of adsorption (or desorption), it becomes up = dlnP = An (48) cm d'l‘ 'B"T'2 Equation (48) can be integrated whenever A8 is known as a func- tion of T. For the case where AH does not vary with temperature equation may be transformed to d In P = All dT (49) a T2 Vhich, becomes, on integration lnP = - AH l , a 'r + c (00) It will be recognized that this is a linear equation of the type y = ax + b . Therefore if In P is plotted as ordinate against the reciprocal of the absolute temperature, l/T , as abscissa, the resulting curve is a straight line with a negative slape equal to Ail/R and an intercept on the l/T - axis equal to C, the integra- t1°n constant. These straight lines are also referred to as 90 isosteres since they correspond to a constant amount of adsorbate adsorbed, or in the case of grain, to a constant equilibrium mois- ture content. The isosteric plots described above may serve to identify inaccurate vapor pressure data by their refusal to fall on or near a straight line. By constructing such plots and evalu- ating the slopes of the straight lines the isosteric heats of de- Borption can be evaluated. Table VI shows the results of the computation involved in the evaluation of the isosteric heats of desorption by the foregoing graphical method. For the purposes of constructing the plots, the 180 thexm temperatures were first expressed in degrees Kelvin and t1’Ieir reciprocals calculated. In order to use consistent units, the Vapor pressures were converted from lb per square inch, as are mostly expressed throughout this work, to millimeters of mercury as shown, The equilibrium vapor pressures were then obtained for 8elefited values of moisture content by multiplying the corresponding equilibrium relative pressure by the saturation vapor pressure of “ate? at the temperature under consideration, just as it was done in the construction of the isosteres of Figure 9. For the sake of simplicity a semi-logarithmic graph paper "'3 employed and suitable scales laid off on the linear axis for the reciprocals of the absolute temperature and on the logarithmic “‘13 for the equilibrium vapor pressures. Figure 10 shows the com- pleted plots for various moisture content levels. It will be seen that quite satisfactory straight lines were obtained over a 91 aged: hue anoasoo «savages unschon I 2 «90oz ~one.nv~ cwma.an on~m.mm~ mmoo.~m~ ~eap.ae~ m~ew.~a mama.ne mama.me~ co.” o¢~ mana.ew mae¢.me «mee.oa same.eo mpso.pn eacm.ee ~aec.cm nnmn.am on.» «ma mmoe.n¢ mmwm.~v esve.mm name.nm cem«.wm oc-.—m mowv.e_ newc.ae «a.» co” cv-.mm monm.em c¢ew.nm mooo.~m omm~.a~ esma.m~ mane.w ew~w.~m cm.» as aw~m.- neva.a ooma.m flame.» asem.n aaam.e same.” amnm.m~ be.» cc muaa.v oa~m.¢ mass.” cane.” ca¢m.m ~aav.~ . m~mw.o ~vmm.e as.» as am a x as a a as u 2 em . x «a n a o” a a m a a .m: .sa M\~ m . o . w A ease oasocaomsoa - a o I a: .as a emcee mo oasmueam acae> samuam~msea uoam_ucae> op=~oan<.ho my maze H $3335 338593 Iguassu lrll. r zo . Hammcmsn mo ms flan. pg, mm. Hg. vapor pressure, IL)! [Hill bqull Reciprocal of absolute temperature, Finn Ira l Temperature, °F. 1 l22° I00° 86° 60° I l 9 ..— . 8 —— 7 M°/o d.b. Values of Slopes __ I0 6,200 6 l2 6,| I 5 ... I4 5,800 50 2 l6 5,680 __ I8 5,600 22 5,450 4+— at 20L— 1 9 ‘ 8 7 6 M 'Qi 5“ a ( VT) R M 4‘ Q- Ln = ....L... pg RT W 3* Qi ‘ isosteric heat of adsorption R = universal gas constant M = Moisture content, °/o dry basis C = constant of integration 1N 3J0 IA — 3.20 3.30 3.40 l ‘T— '3? I 3.50 x l02 3.50 93 temperature range from 600 to 12.20F. Over a wider range app-"e- ciable deviations from linearity resulted, as could have been expected in view of the simplifying assumptions involved in the derivation of equation (50). The slopes of the straight lines were then determined and the values of the isosteric heats of desorption evaluated from these by multiplying by 1.9871 calories per degree Kelvin per gram-mole, the consistent value for the universal gas constant, it . The isosteric heats thus obtained are eXpressed in terms of calories per gram-mole. In order to con— vert these values to calories per gram they were multiplied by 18, the molecular weight of water, which is the equivalent of one gram- mole of water. To obtain these values in English units, the con- version factor is 10 I T. cal. = 18 E32 g“). 1b. The Clausius-Clapeyron equation is frequently met in the form of the definite integral. If equation (49) is integrated between the temperatures T and T2 where the equilibrium vapor l PreSSUres are pl and Po , assuming that All remains constant, one 0 b tains AH l 1 AH 1 I In (pa/p) = ----(- -- ) =-~-(---) (51) c. l R T2 T1 R T1 T2 Equation (.51) may be written thus AH a gisosteric _R T1 T2 In ( / ) (,.2) T, - T2 p1 p2 ° '1‘ ' . . hls e(luation rests on all the approximations that were used in tra‘JISforming equation (45) to (50)' 94 TABLE VII CALCULATION 0r ISOSTERIC HEATS or nssonrr10n roe SHELLED coax OVER THE TEMPERATURE RANGE 86° r0 122° F m— At 86°F - 0.6152 psia Saturation vapor pressures: o 122 F = 1.7888 psia Moisture Equilibrium Equilibrium Vapor Isosteric Heats of Desorption Content Rel. Pressure Pressure, psia Total Values Net psrgent 303°K 323°K 303°K 323°K calfmole cal/gm BTU/1b BTU/lb T1 T2 p1 p2 6 0.160 0.205 0.0985 0.3667 12,780 710 1,279 244 8 0.265 0.325 0.1630 0.5815 12,385 687 1,238 203 10 0.400 0.480 0.2460 0.8575 12,110 673 1,210 175 12 0.587 0.617 0.3302 1.1030 11,700 650 1,170 135 14 0.660 0.720 0.4065 1.2879 11,500 638 1,148 113 16' 0.751 0.798 0.4624 1.4280 11,285 626 1,128 93 18 0.825 0.860 0.5075 1.5390 11,080 614 1,105 70 22 0.915 0.940 0.5630 1.6800 10,950 608 1,095 60 26 0.967 0.990 0.5950 1.7700 10,900 605 1,090 55 Equation 8 R T x T 91 (1____22__.x Ln (pz/pl) T - T 2 1 'het1! . . 9i a isosteric heat of desorption, cal. per male #3 I absolute temperature, 0K equilibrium vapor pressure, psia R a universal gas constant, 1.9871 cal. 01(."-J‘111olenl The isosteric heats of desorption 1rare also calculated ac- cording to this equation both as a check on the degree of accuracy obtainable by the graphical method described above, and also to secure more accurate values since the lack of precision which is usually inherent to graphical methods is thus avoided. Table VII _ F“- shovs the results of the computations obtained by this method. L The isosteric heats of desorption are given in three different units as shown, and also in terms of net values. The latter values were obtained by subtracting from the total isosteric heats the 1 3? mean of the latent heats of vaporization of water at 86° and 1220F. Otlunex- Graphical Method Another method employed in evaluating the heats of desorption from the experimental data was 0thmer‘s graphical method of vapor pressure correlation. This method has been recently employed by seve ral investigators ( 17, 80) in determining the latent heats 0f v"riorization of various grains. Based on the Clausius—Clapeyron equation, Othmer derived the fol lowing re lationshil‘ lnp =£3 lnp' + C (53) where L is the total heat required to desorb one mole of ad— Barbed material at a given temperature, L' is the molal latent heat of vaporization of the reference substance at the same tem- Y"Mature, p is the equilibrium vapor pressure of the material, ' p the saturation vapor pressure of free water, and C is a co . . ' nstant of integration. ENE-unit. ..r. ...J“ the 1. _. «..., ~— "h:- WWW”..- _«_‘In '11- . 96 It is evident from the foregoing relationship that a logarith— mic plot of the equilibrium vapor pressure values pertaining to the grain against the saturation vapor pressure of free water at the same temperature will yield a straight line the slope of which represents the ratio of the molal latent heat of the grain to the molal latent heat of free water over the temperature range under consideration. Figure 11 shows such a plot for shelled corn of various moisture contents constructed from the desorption isotherm curves over the temperature range from 40° to 100%”. The method of constructing the plots was similar to that used for the isosteric plots of Figure 11. Using logarithmic graph paper, a suitable scale was laid off on the x-axis to cover the range of water saturation pressures involved. The isotherm temperatures were also indi- cated on the x-axis (top margin) at the appropriate values corres- Ponding to the saturation vapor pressures of free water. A scale was laid off on the y-axis for the equilibrium vapor pressures corresponding to the grain. The equilibrium vapor pressures cor- resWorlding to selected moisture content levels were then plotted on the respective temperature ordinates, and appropriate points ”minted by the isosteric lines. It will be seen that a very satis- fact‘”? fit was obtained over the temperature range selected. As in the case of the plots of Figure 10, deviation from the straight line was already noticeable for points outside of that range. This “3““ was to be expected in view of the limitations inherent to the Clausiuswlapeyron equation, on which the method is based. Equilibrium vapor pressure, nglO? p.s.i.a. 97 Temperature, °F 60° Ln p = g an+C where: 9 f9 5 Q= latent heat of vapor- izotion of grain h = latent heat of vapor- fg izotion of grain C = constant of integration .L.\\. l. J. g 2 ' 3 4 5 6 7 e 9 lo Saturation vapor pressure of water, p$ X IOZ, p.s.i. Figure ll Othmer plots of desorption data for shelled corn of various r"ttblsture levels. 98 In order to determine the differential heats of desorption from the 0thmer plots the slepes of the isosteric lines were measured and their values tabulated as latent heat ratios as shown in Table VIII. As the method is usually applied, these ratios are multiplied by the latent heat of vaporization of water at the tem- perature desired in order to obtain the differential (isosteric) heats of desorption, and so it was done for the purposes of con- structing Table VIII which gives the values in terms of BTU per lb corresponding to eight different moisture levels and to each of the Six isotherm temperatures. Strictly Speaking, however, a more cor- rect procedure should be to apply such ratios only over the tem- perature range for which straight 0thmer plots were obtained, and to multiply the ratios by the mean value of the latent heat of water 0791‘ that range. After obtaining the latent heat ratios from the 0thmer plots these values were plotted against moisture content and a curve drawn through the points. The curve thus obtained is 811°"! in Figure 12. It will be seen that the ratio is quite high for the lowest moisture level and decreases rather rapidly and uniformly with increasing moisture content, leveling off at about 16 pereent (dry basis). This behavior will be examined later in the discussion. Figure 12 should be valuable for predicting heats of desorption corresponding to other moisture levels within the range of the curve. 99 TABLE VIII DIFFERENTIAL HEATS OF DESORPTION FOR SHELLED CORN FROM OTIIMER PLOTS 0F ISOTHERM DATA W ‘7 w *c’ Temperature, °r 40 60 so 100 122 1071.3 1059.9 1048.6 1037.2 1025.8 his, Bro/lb. Moisture Latent Heat Content, Ratio Differential Beats of Desorption, BTU/lb. :ddo. qd/hfg #‘ 8 1.385 1484 1467 1451 1437 1421 10 1.310 1403 1390 1372 1360 1344 12 1.230 1319 1304 1290 1278 1249 14 1.135 1249 1235 1221 1210 1195 16 1.125 1206 1191 1180 1168 1154 18 1.102 1180 1169 1157 1143 1131 22 1.078 1152 1141 1129 1118 1105 26 1.072 1148 1138 1123 1112 1100 Note: hf: - latent heat of vaporization of free water qd " differential heat of desorption \ .Eoo uozocm so .528 Eases 53 «So; 222 so 2:: SEED 2: so co:o:o> N. 839... £25 be o\o .EoEoo Sago—2 «m 1 on m. 9 e. N. o_ lOO rail ..1 v1.11! 1- .... . . .9. . ... .vl. .... ..1v ..o. ... 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L . . .. . . . . . ... 1. . ...v e . 0|...» 4 . . 1 . ... . .9. . .. .... . . . . . .. 1 ...1 ... .. .... . .. . _ i ,_—. -+.-..—_.-._.- _ .— 45—4 -..... , All 11. ) »-_, “L— V l l ; '- -——-+ ....1. 71,..- _ I . . H 01101 1030 luelo-l 101 The Brunauer, Emmett, and Teller Equations Probably the most fruitful approach to the end of elucidating the mechanism responsible for the hygrOSCOpic prOperties of grain was afforded by an analysis of the experimental isotherms according to the Brunauer, Emmett and Teller theory of multimolecular adsorp- tion. The salient features of this theory, which is more often re- ferred to as the B-E-T theory, have been discussed briefly in a pre— vious section. The present discussion will deal in some detail with the application of the theory to the experimental data. It will be recalled that the B-E-T isotherm equation for ad- sorption on a free surface may be written in the form of a two- constant linear equation suitable for testing experimental data. The equation is restated he re for convenience. p l c-l p = + 35 v (p8 - p7 vm c vIn c ps ( ) The constant v is a size constant which depends on the number 0f molecules required to cover the entire surface with a unimolecu- lfir adsorbed layer so that the surface area of the adsorbent can be Ineasured in terms of the cross-sectional area of the adsorbed molecule. The constant c on the other hand is an energy constant the Value of which is determined by the heat of adsorption in the firét unimolecular layer. Because of the simplifying assumrltions involved in the deriva- tion of equation (35) it is only valid in the region of relative pressure values between 0.05 and 0.35 and occasionally up to 0.50. 102 If the theory of multimolecular adsorption is obeyed by any system under consideration the plot of the function p/v (ps — p) as ordinates against the relative pressure values as abscissae should give a straight line in the above prescribed region of relative pressures. Furthermore, it is also necessary that the evaluated constants should have reasonable values. An examination of equition (35) will reveal that the values for the constants will be given by the slope and intercept of the linear plot. In the equation, p corresponds to the equilibrium vapor pressure p of the grain which in turn is given by the product of the equilibrium relative pressure and the aqueous saturation vapor pressure, p8 , at the isotherm temperature under considera- tion; v represents the equilibrium moisture content, M , at any time and is expressed in percent dry basis in the present treat- ment. As a first step in applying the equation to the experimental data, the values of the function pg/M(ps — pg) were evaluated for Values of equilibrium moisture content from 1.5 to 26 percent dry basis. Table I shows the results of such calculations for the IOOOF isotherm, by way of illustration. It is well to clarify that. Such a detailed computation of the isotherm is actually not neceasllr'y, as may well be realized from the fact that the. region of “11 idity of the equation is restricted to relative pressures be- tween 0.05 and 0.50. However, it was desired to follow the course of the B-B-T isotherm over as long a range of relative pressures as p08allble, and to determine the full extent of the region of 103 TABLE 11 COMPUTATION or ma non B-E-‘l' mm or THE 100°r ISOTHERM l, f d.b. (pg/9.). pg p, - pg pg/“(p‘a - 1.50 0.015 0.01424 0.9350 0.01015 2.50 0.040 0.03797 0.9113 0.01002 3.00 0.052 0.04930 0.8999 0.01830 4.00 0.087 0.08258 0.8001 0.02380 5.00 0.127 0.12055 0.8287 0.02910 0.00 0.175 0.10011 0.7831 0.03540 7.00 0.235 0.22305 0.7202 0.04380 8.00 0.295 0.28000 0.0092 0.05230 9.00 0.300 0.34170 0.0075 0.00150 10.00 0.430 0.40820 0.5410 0.07550 11.00 0.505 0.47930 0.4701 0.0930 12°00 0.575 0.54580 0.4034 0.1150 14.00 0.088 0.05300 0.2902 0.1570 10.00 0.775 0.7350 0.2130 0.2160 18.00 0.842 0.7992 0.1500 0.2900 20.00 0.892 0.8407 0.1025 0.4130 22.00 0.930 0.8828 0.0004 0.0030 24.00 0.955 0.9005 0.0427 0.8450 20.00 0.977 0.9274 0.0218 1.0350 \ Note: 11 P (Its/11‘ )e '“ter - .0 iature content p8 . gtl‘lilibriun vapor pressure, psia saturation vapor pressure a- 0.9492 psia - equilibrium relative pressure 104 validity of the equation as applied to shelled corn. The next step involved constructing the plots according to equation (35). Figure 13 shows the B-E—T plots, calculated as explained above, for each of the six eXperimental isotherms. It will be seen that. very satisfactory straight lines were obtained in all cases over the range of relative pressures between 0.05 and 0.35. At relative pressures greater than 0.30 to 0.40 the plots deviate with increasing pressure more and more strongly from the straight line. The constants vm and c were next evaluated for each iso- therm from the slepes and intercepts of the respective plots. These values are shown in Table II, columns 4 and 5. From the value of constant c the magnitude of (El - EL)’ the net heat 0f desorption for the first monomolecular layer was also calculated for each isotherm. These values along with those of E1’ the gross heat of desorption (adsorption) are also shown in columns 6 and 7 of the same table. As an example, the computations involved in evaluating the constants for the 100°? isotherm will be 3110'“ here in detail . From the corresponding plot of Figure 12 the value 0f the intercept was found to be l/vhc = 0.0118 from 'hich vm c = 1/0.0118 a 84.8 (c) Th ' e Value of the 810pe was found as follows (0.0007 - 0.0118)/0.40 0.1375 (c - l)/vIn c 105 £500 mm 0 mm m .N. o .m. o. N. .m. Nmk cm mom E 8.0 cm £53.23 Stones .0 .2 m .8 meta ma\oa 8.x cozeomop ao floa Bud .9335 83> o>:o_mm amen Eu 0\0 “Q as H» E 22:00 05> J... Sagas u 2 . 22.3 ... 99mm :\q . 106 owns: 903 .:wcaw mo Edam to; Load: «0 madam cw commoaano :90: was :wcaw has mo Edam non madam aw cobww mm .3 one is 3: amass has .aaoanoo ousumwos accuses aw consensus was mosfish m aswom Edam Lem newscaso mo mates when: has .asoosoo oasamwoe osooaoa a“ vommoamko aw fin aw commoaaxo a“ Eb \a voo~.o mo~o.o cmvo.o mec.o wo.b new ea.» cb.e~ Hw.m mica mn.o moweaobd nopc.o whoo.c oneo.o avc.o nu.n ova mw.m no.m cm.w w1o~ w©.m own nmco.o cmoo.o ammo.o «mo.c on.© goo mc.c mb.m wc.m clog mm.w Nun ~omo.o wmoo.o mmvo.o owe.o nv.o new ou.c mw.m~ m~.m clo~ ma.» oo~ omo~.c c-o.o mmvo.o mac.o oo.h cow ca.» o .mH mm.m clog u~.m cm an-.o vm~¢.o ewoo.o who.o cc.w mam ma.p m¢.m~ c¢.m mica mw.m om wemH.o ngc.o vamc.o vwo.o ow.w mam wc.w oo.em b¢.m mica ca.“ cm I E m“ 4 ... 3 WW . linswom an > o a «— easasmmaaoa o no son sac sowessam Eho com smswwmcwmwsz m.ewasmm ato.se aume n.=omaoe=¢=.r. s H i..u..n-v'.u..i!-ot' "I-I.l' 11“} 1 {I 11' a ‘1‘ 11 1‘11 {I i!!! ‘1‘ 11‘ zmou assqamm mom maz. can .0. 3:03:00 *0 co=o_.o> v. 2:9... 0N. mo 6.22363. 00. cm ow oe ON .¢. , 9.32352 22080" ... 2228 moo .8325 n 1 220.362 530 8 .20; 3 5:05.89, .0 Be... new .26. .638. .955 so 5:90ch we Bo; ... .w ”2mg; 1 Q so»... 6.: uomBEE: o *o 5:2qu0 .8 56330: 23:8 2229.: 0\o u > ”0.22200 .0 3:02:ch “’A 10 ”WM 111 This can be regarded as a mutual confirmation of the empirical method of selecting the point on the isotherm corresponding to a monolayer and the fundamental assumptions underlying the theory of multimolecular adsorption. The use of constant Vm in determining the effective sur- face area of adsorbents has been mentioned. Industrial adsorbents are known to possess enormously large internal surface areas and negligible external surfaces. For instance, the surface area of 8:38 mask charcoal as determined from actual crystal dimensions has been found to be 1940 square meters per gram ( 9 ). In view of the hJ'gr‘oscopic properties of cereal grains it is reasonable to as- sume that they also possess large internal areas available for ad- Borption of moisture. In connection with his studies on the ad- s°rption of water vapor by proteins, Bull (12) determined the areas Of a large number of proteins according to the B-E-T method. He ”9°“th values of surface area for B-zein and C-zein, two of the pmteins in corn, of 0.145 and 0.138 square meters per milligram, respectively. It was considered a matter of great interest to j‘nve'gtigate the order of magnitude of the internal surface area of shelled corn, on the basis of the knowledge of vm values gained from the B—E-T plots. The crucial problem in the application of the B‘E—T method for this purpose lies in the assumption of a molecular area for the adsorbed molecules. In his book on ad- 8‘u‘l’tion, Brunauer gives the following equation for the calculation of “‘0 1e cular are as 112 Area (L) = (4) (0.866) (Li/5.65 N dL)2/3 (56) where 31 is the molecular weight of the gas or vapor, N is the Avogadro's number or 6.023 molecules per gram-mole, and dL is the density of the liquid. This equation assumes that the pack- ing of the molecules on the surface approximates that of the lique- fied gas. Calculation of the molecular area of water from the den- sity of liquid water at 30°C according to equation (56) gives a value of 10.5 12. Based on the finding by Hendricks that a unit cell of the layer crystal montmorillonite adsorbs four molecules of water, Brunauer (9) gives a value of 11.5 12 . De Boer ( 6) states that approximately 1015 molecules of water are needed to 00781‘ one square centimeter of surface at a temperature of 20°C. F°r the purposes of this discussion it was assumed that a water molecule occupies an area of 11.0 22 (11.0 x 10"16 sq cm). Taking the Value of 7m as 7.10 grams per 100 grams of dry grain as ob- tained for the 86°F (30°C) isotherm, there will be n . 7.10 En - 7.10 gm per molecule WN 7.10 23 = 2.375 x 102:3 molecules 18/6.023 x 10 c“uprising a monolayer. The surface area will then be s . 2.315 x 1023 x 11.0 x 10"16 . 26.2 x 107 sq on per 100 grams of dry grain This is equivalent to 262 square meters per gram or 0.262 square meters per milligram, which is about twice the area that Bull re- Pmr‘ted for C-zein. Expressed in terms of acres per 100 grams of infill"- 40.1%» I. ‘ E ., 113 dry grain, the area is approximately 6.5 acres. In view of the foregoing considerations this value for the surface area of shelled corn does not appear unreasonable. The decrease of the 1rIn value with increasing temperature can readily be accounted for in terms of the thermal expansion of the monolayer. It has thus been seen that not. only have the experimental data yielded very satisfactory linear plots over the range of validity prescribed for the B—E-T theory, but also quite reasonable values of the equation constants have been obtained from the linear plots. It can therefore be con- eluded that the water-binding mechanism involved in shelled corn, and probably in all other cereal grains, is one of multimolecular adBOI‘p‘tion. It has been pointed out that beyond a relative pressure of abOut 0.50 the simple two-constant equation fails to describe the course of the isotherm. Beyond that relative pressure the amount 01' water adsorbed increases more and more slowly than it would if gOVEPned by equation (35).~ It should be remembered that equation (35) was derived for adsorption on a free surface; certainly the internal surface of grain is by no means a free surface. Within the range of relative pressures for which the equation holds satis— factorily the influences that restrict the number of layers have generally not yet become strong enough to make themselves notice- able, Beyond that range, however, it becomes necessary to use the three constant equation (38). The B-E-T three-constant equation was derived to take care of the sI'ltuation where only a finite number of layers can be 114 adsorbed at saturated pressure. While there may be other causes for such a restriction, the effect of the pores and capillaries which characterize the surface is probably the most conspicuous. The equation introduces one more constant in addition to the con- stants Va and c of the simple equation. This constant, de- noted by n , represents the maximum number of layers that can be adsorbed on each wall of a capillary. The equation, however, does not take into account the forces of capillary condensation which usually sets in at the higher pressures. It is therefore to be regarded only as a more or less approximation in the higher pressure region. Notwithstanding its limitations the equation can be very helpful in ascertaining the general character of the sur- face, Particularly concerning the size and relative distribution °f the micropores. It is the size distribution of the micropores (pores With radii less than 100 X) that largely determines the shape of the iSOthetm beyond the region of unimolecular adsorption. With the purpose in mind of gaining information in this reSpect the ex- perimental data was analyzed according to the B-E-T three-constant eqlmtion. The application of the three-constant equation called first for the evaluation of constants 7m and 0 according to the simple t"’<>-’(=onsta.nt equation as explained in a previous section. 0ne ob- tains then, by the method of trial and error, the value of constant 11 tJIM best, fits the experimental points. Figure 15 shows the 0 results Obtained with a value of n a- 5 , and n = 6 for the 100 F 115 .353 .2565on 5.3 cocanoo an $39: .....mm of so cozosco .coamcoonm of 2 @5388 322a ....ooo_ .8 Sagas 8:98am m. 059.“. x . 253.5 3.2% 00. om on on om on 6.2.8_ 3:38:33 ES. 358 «23650 .333 33.30.00 2865 85. 2.8 wkoz o¢ on ON ...o: ...:aoo 05 co 3an .3 on :8 .2: 9.26. .3 Bass: E:E_xaE 0523852 2228 u c mmuio m0.3 "£6.23 25-x:bvz x; IIIIII u E _+cx:+ :X2+5_ X0 > _ . x ..,.....H._..: ....f. . : u> q Mp °/o 'A ‘iuawoo aimsgow SISD 116 isotherm. The solid lines represent the calculated curves while the circles and dashed lines indicate the experimental isotherm. It should be noted that up to a relative humidity of 70 percent the value of n = 5 gives almost a perfect fit with the experi- mental isotherm. Beyond that value of relative humidity, however, the experimental isotherm deviates more and more strongly from the calculated curve. At a relative humidity of 90 percent already a value of n a 6 gives a fairly good fit. At a relative humidity 01' 80 percent an intermediate value of n would be required in order to bring about agreement between the experimental and the calculated isotherm. Thus with only two. values of n equation (38) succeeded in reproducing the isotherm correctly up to as high a relative humidity as 90 percent. This can be interpreted to mean that the micropores characterizing the internal surface of shelled Corn are comparatively uniform in size. Both the capillary conden— sation theory and the B-E-T theory of multimolecular adsorption agree that the narrower pores fill up at the lower relative pres- “"98, while the wider pores fill up at the higher pressures. Thus 8‘8 the relative pressure increases the average width of the pores that Still participate in the adsorption process gets larger. In the light of the foregoing results some idea may also be inferred as to the order of magnitude of the average width of the m1“1°Dores which make up the major part of the effective internal surface of shelled corn, at least to a first approximation. Thus it has been seen from the application of the three-constant equation 117 that the maximum number of molecular layers which could be accom- modated on each wall of the average-sized capillary was 5 up to a relative pressure of 0.70, and 6 up to a relative pressure of 0.90. For the purposes of estimation a number of 5.5 may be assumed. It will be remembered from the derivation of equation (38) that it was assumed that adsorption occurs in a capillary of two plane Parallel walls. With this in mind, and assuming a molecular diameter for the water molecule of 2.9 3 it may justly be inferred that the average width of the micropores participating in adsorption up to a relative pressure of 0.90 is of an order of magnitude of 32 3.. The HGrkins - Jura Equation The Harkins-Jura equation afforded another interesting theoreti- cal treatment by which the experimental data could be examined. It will be recalled that when adsorption (or desorption) equilibrium data is plotted according to equation In (pg/p.) = B - A/Mz (40) Straight lines are obtained over the range of relative pressures where the adsorbed gas or vapor is in the form of a condensed film- Having established from the results of applying the B-E-T e‘l‘l’i‘t’ions that the water-binding mechanism involves multimolecular a"morption, the Harkins-Jura equation offered a convenient tool with which to explore further the exact nature of the process. Accordingly, the experimental data was processed as shown in Table II, namely, by computing the reciprocals of the squares of the Values of equilibrium moisture content, dry basis. The plots were TABLE II COIPUTATIOH OF DATA FOR HAHKINS-JURA AND SHITH PLOT Isotherl Temperature - 100°? 118 W.“ ll ' moisture content 93/13. a relative vapor pressure ll, 5 d.b. 1!, 7o w.b. pg/p8 1 - (pg/p8) ln(l - pg/ps) 24:23:.) 3.00 2.91 0.05 0.95 0.050 —--- 5.50 5.22 0.15 0.85 0.162 330 6.50 6.10 0.20 0.80 0.223 236 7.75 7.20 0.25 0.75 0.288 167 8.10 7.50 0.30 0.70 0.356 153 8.80 8.10 0.35 0.65 0.430 129 9.50 8.66 0.40 0.60 0.505 111 10.25 9.30 0.45 0.35 0.600 95 11.00 9.90 0.50 0.50 0.694 83 11.65 10.45 0.55 0.45 0.800 74 12.45 11.07 0.60 0.40 0.918 64 13.25 11.68 0.65 0.35 1.050 57 14.35 12.45 0.70 0.30 1.205 49 15.35 13.30 0.75 0.25 1.385 42 16.70 14.32 0.80 0.20 1.610 36 18.25 15.42 0.85 0.15 1.900 30 19.25 16.13 0.875 0.125 2.080 27 20.50 17.00 0.90 0.10 2.300 24 23.50 19.00 0.95 0.05 3.000 18 Note; _ 31 ps Relative vapor pressure 0.? 0.4 03 0.2 119 \ Horkins-Juro Equation \ '00:"- \ p \86°F 9 A Ln —- = B- —2- -e ( p5 ) M \\ \ \ M = moisture content of grain gm/gm dry basis \°\ — 60°F 3 = constant \\ \ Values of Constants \ o i \°\ - F A A “—— _— \ 40° 0.0l605 0.1268 “30°F 1 60° 0.0l340 0.|l59 86° 0.0ll00 0.|050 \ lOO0 0.00982 0.099l \0\ I220 0.00586 0.0925 \ I400 0.00584 0.0765 \ _ \\ \ \\ | 30 50 no 130 LJ\L I l p F"'Qlalre I6 H-J plots of desorption isotherms for shelled corn. 120 then constructed on semilogarithmic graph paper as shown in Figure 16. It should be noted that the plots yielded very satisfactory straight lines in the case of all isotherms, over the range of values of the function l/M2 between approximately 10 or 15 up to about 90. Translated in terms of moisture levels in the grain and of relative pressures, these values represent approximately ranges between moisture contents and relative pressures near satura- tion down to about 10 percent dry basis and about 0.40 to 0.45 relative pressure. According to the theory, these results indi- cate that in these ranges the adsorbed water occurs as a condensed film. It should be remembered that the amount of water necessary t'0 Complete the first unimolecular layer over the surface was given by the constant vm of the B-E-T equation as 7.1 percent dry basis (“Veruge of all isotherms). It would seem then that shortly after this first layer is completed, i.e., upon adsorption of enough a~dditiona1 molecules to account for the difference between 10 per— CEDt dry basis obtained above and the value of vm , two-dimensional Condensation sets in to form a more or less continuous film which then constitutes the new surface for further adsorption. Interestingly, further analysis of the Harkins-Jura plots pro- duced additional evidence that lent support to the above theory. It has been pointed out that Liang (34) correlated the Harkins— Jill's and the B-E-T equations and found that the square root of the “We: A , of the Ha] plot actually corresponded to the value of vm 0f the B-E-T equation. Some confirmatory evidence to that 121 ”o it 0.4 0.3 Equilibrium relative vapor pressure 0.2 ‘ ¥ I .1 p Ln p_g =B-A—2 __ s M Pg _ \n\ —— relative vapor pressure 95 \ \ M = moisture content of grain, gm/grn dry basis \°\ Ln 0.80—Ln 0.335 _ \— A 74_20 -0.0|605 \\ VA— : V0.01605 : O.l268 1 I 1 L I 20 40 so ICC 120 I so I W Flgu'e l7 Deiermlnaiion of the H-J constants for the 40° CIEsorption isotherm. effect has been reported by other investigators. For instance, Hogan and Karon (26) found good agreement between the values of A?! and V111 in their analysis of desorption equilibrium data of rough rice. Also Dunford and Morrison (15) obtained similar results in their work on the adsorption of water vapor by proteins. Yet an ”Hr analysis of the H-J plots obtained for the desorption data of this a _l investigation yielded values for A“7 correSponding in the average to values in the neighborhood of 10.35 percent dry basis. The order of magnitude of these values is approximately one and a half times ' j that of the vm values. It is interesting to note, however, that this average value of A11f corresponds rather closely to the general order of magnitude of the values obtained from the range of linear- ity of the same H-J plots as marking the probable onset of two- dimensional condensation. It may be inferred from the foregoing that while the val-values do serve as a measure of a first uni- molecular layer, this is not necessarily continuous over the whole internal surface, there remaining probably lesser active portions 0" the surface still available for adsorption. The molecules com- Prising this layer are probably characterized by a fairly uniform heat of adsorption. Then upon further adsorption on the remaining bare portions of the surface, and conceivably even on top of the first layer, a point is reached where enough lateral interaction between the water molecules themselves will develop to cause the formation of the condensed film as indicated by the analysis of the “'0 Plots. The heat of adsorption involved in this latter part of 123 the process is most probably of a lesser order of magnitude than that characterizing the initial adsorption, but still appreciably higher than the heat of liquefaction. In fact, referring back to Figure 12, which shows the variation with moisture content of the differential heats of desorption, it will be appreciated that probably even successive layers will involve heats of adsorption in excess of the heat of liquefaction even though decreasing in magnitude, It would appear then as if the influence of the surface forces of the grain could still reach outwards beyond the first unimolecular layer. It is conceivable that the principles under- lying the polarization theory of adsorption postulated by de Boer and Zwikker may well play some role in this connection. This is all the more probable in view of the highly polar nature of the “ate r molecules. The Smith Equation The Smith equ.:.tion, which is applicable over the higher Pressure region where the two-constant B-E-T equation breaks down, was also employed for correlating the experimental data. The Smith equation is w : Vb - W. In (1 "P/Ps) (42) 'hel‘e, it will be recalled, w is the moisture content expressed on 8- vet basis. As a first step in applying the equation, the f“fiction —ln(l - p/ps) was computed for the relative pressures at lutelWals of 0.5 and at shorter intervals wherever it was convenient 19‘! 58 3:05.. .2 mEtofofl 3:983 “so 303 5:5 m. N.m ad ¢.N 9.333 33> a 2522 Esta—:33" Wannabe: Aoa\ 1; 5.3-33 u 3 a 3:035 6350.»; «.....Em ON 9.. -.v 5 0.. N._ «No he was. 8+ «Mn 2 m as 0.0 8:9“. we «a ox . we. 3. v m as V0 0v. mm. 00. mm 0m 9. mo ass £5.28 8:33 ‘0 «33> sysoq lam °/o M ‘waiuoo aimsgow 125 to define more accurately the limits of linearity in the plots. The corresponding moisture content values were then converted to the terms required by the equation, namely, on a wet basis. The same was done for each of the isotherms and the plots then con- structed as shown in Figure IR. In columns 2 and 4 of Table XI, the computed point values for the lOOoF isotherm are shown as an example of the above procedure. An examination of Figure 18 will show that the plots gave good straight lines extending between values of the logarithmic function of about 0.6 on one end and 2.0 to 2.3 on the other. These values correSpond to a range of relative pressures from about 0.45 up to about 0.90 which is very nearly the prescribed range of validity for Smith's equation. It has been mentioned that Becker and Sallans (4) found essentially similar results when applying the equation to their desorption isotherms of wheat. They also suggested a graph- ical method for defining the intermediate approximately linear rti'gion of the isotherm. This method consists - plotting the data. according to both the B-E-T two-constant equation and the Smith equa- tion on the same graph, and then drawing a straight line tangential to the Smith curve and intersecting the B-E-T curve at its point of inElection. Their method was tested on the experimental desorp- tion isotherms for shelled corn with very satisfactory results. Prior t'0 constructing the plots, an adequate number of point Vflluea Was comfluted for each curve by using the values pFeViOUSly obtained fol- the respective constants of each equation. Figure 19 illustrates 126 .552 Soc: 2238.25 of 055030 .6 .352: c 05652: 53:33 525 uco Hum of 2 96.680 ooze—a moOO. 6 Eco .um__onm mo E.o£8_ 8:90me 8 959.... m 8.3% 5.25:: 252.5 00. Ca 8 on 00 On O¢ Om ON 0. o 4 4 . .... .... .....A. .. .. ... ... .-. .... .... ... . .. .... to - H4). oo......\. 0.... ....+ ...a . ..v...6. ...s a.. a... ... .. .. .. .. . .vr. .... .... ....u .... .... 0.. . . ,.-. ... .... ... ...e ... .v.. ..vo coo>t.o4¢c90.vl..o our. ... 40,- 1.. ..v. ..-. ... .. .n., ..I. .. v . u. . ...; .... .I. .o. . ... . . . ., .. . . .. . .. .., .. .. . . -. . .. .. . . . . .. . . .... o... v- .... .... o. . . ....l - . . ...a . ...n ... . ...A . . . . ... ... .. .v . .....L .. . ..ve _ .... ... 1 . . . . ... ... . .. .... .... ... .q. ... .. ; Quit ...?QJO... ...o. ... .... a . It- ... ..- -... . u . . .... .... b. )‘n. to. , 4 . .... .... .... .... .... .. .... .... .... .... .... .... ...- . . . .. .1 ... ... .. o I... . -.. . ....... .... . .... . . . . ... ... ... .. . .... .... ...1 ... a... ..4. .... . . .~ .... ... .... ..n.. . . .. .... ...-. ... . .. . . .... ,. ..., ... ... .... .. ... .... ... .... . . . .. .... .... .> ..ov. .... . .. .. . .... . . u. . .... . . ... ... . .. ...: . .... ., . . . ,. . ... .. . . .. .... .. . .... .... ... . . ... .. . . . . ...- ... .... ... ... . . .. It . #7 o 4 r a ‘9; o .0 I. u 4 vv v c. t .0 O; I. . - one I 4‘ . v t t 4 to C v A.‘ iv I y . v D Y .. O A n q . o o s .. .. n. r - q I t. . I a a.-. u v N v o. o .4. . Nil... 0 u . . . . 5.4. f . . -.el. ...Y... o a; l r .... . o is a. v . ill. L at .09.. J l a 0 b l . r 1 1 . o i . v v 0 -.. A av l . a e 9..., o J . _ . to or¢ . . .01 ‘\ . n .fi. . . ... 1. .. . . . L- - - .. . 04”.- o L ' Khan... M - --..f .- 713.... 5 . . . - L---fi . -. IffiO : , 1.......:.. . - 3;..3. .” 5,. 4 ...v ..+ 9 O ..J,W¢... m . , TH - T. - O. a . .. . a _. - -. .. .. .i 1 1.. . .0 fold- . .. -. 1.- L . . .H. .k\.. . V - . .w - . . mi N. . ...: . .. . . - . - . . - . . .m— . .. a. . . -fi -- r: i- I - . . H . we. .. c e For- who—o e A 0. Bonn; 695.0 ".3 L 009 a... mum m .. N A n AQ\QVI_ 00.22 Ht ..2 \ a 4 . -..... 3+ _ CI— .3 u 2 E3535 ...:Ew O ....x xx -ilx _ a . a _ II’IO.IIII trill-I. 53.5 .5 .. > "m 009 a... a 595.: as . "successes Hum q Q0 E> . . _ _ a... .: 5 ~ m5: . 5 N: .~\\:F \ _. .. ,_ \vm r m a a . M‘-—. - -h——_. up 0/0 w ‘iualuoo amlsgow 127 the results of the plot for the 10001“ isotherm. A comparison of the resulting composite curve with the 10001" experimental isotherm of Figure 7 showed nearly perfect agreement over the range of relative pressures from 0.15 up to about 0.82. It may therefore be concluded that the foregoing method is eminently successful in predicting the intermediate approximately linear region of the desorption isotherm. Henderson's Equilibrium Equation One objective of the investigation was to test the correctness of Henderson's equilibrium equation in describing the shape of the isotherm and in accounting for its temperature dependence. Hender- son's eqution involves two constants, k and n , which are held to depend only on the characteristics of the material; their values should entirely govern the shape of the curve at any given tempera- ture. The equation is - k T It: 1 a— g- a: e (43) 8 If 0‘19 evaluates the constants k and n from the eXperimental 180thehn data and then calculates a complete isotherm from equation (43) on the basis of the values thus obtained for the constants, the ex"Lent to which the calculated curve agrees with the eXperi- mental isotherm may be considered a measure of the equation's valid- lty in characterizing the shape of the isotherm. Moreover, if Hen- d , ergon.8 equation accounts correctly for the temperature dependence or the isotherm one should be able to calculate the curve at any t'emper'it'i‘a1re on the basis of the values previously determined for 128 constants k and n . Conversely, the values for constants k and n should remain constant for any given material regardless of the isotherm temperature. According to the foregoing criterion, the first step in testing equation (43) involves therefore the evaluation of the equation constants from the experimental data. This was accomplished for each experimental isotherm of Figure 7. by selecting two appro- priate points on the approximately linear portion of the curve, and substituting the corresponding coordinate values in their reSpective places in the equvtion. The resulting equations were then solved simultaneously. To illustrate, the calculations involved in evalu- ating the constants for the 122°!" isotherm are shown below. At a. relative pressure of 0.30 the equilibrium moisture content of shelled corn, as given by the 122°? isotherm of Figure 7, is 7.65 percent, ‘dry basis. Substituting values in equation (43) _ k (122 + 460) (7.65)n e l " 0030 l m” ‘ meflnwfi Transposing and taking logarithms, k (582) (7.65)n - In 1.43 - 0.3577 R (7.65)n a 6.146 x 10"4 Again tfiliing logarithms In R + n (in 7.05) = 1n 6.146 - 4 (In 10) In R + 2.0347 n . - 7.3940 (a) vili gig. d I 129 Similarly, at a relative pressure of 0.70 the equilibrium moisture content given by the same isotherm is 13.62, and substituting per- tinent values in equation (:13) ~ . n l " 0.70 = e - k (088) (18062) Going through exactly the same steps as before, a new relationship is obtained as follows In R + 2.6180 n a - 6.1829 (b) SOIVing equations (a) and (b) simultaneously, In k + 2.0347 n =- - 7.3940 In R + 2.6180 n = - 6.1828 0.5833 n a 1.2112 n 3 2.08 Substituting now the value of n in equation (a) In R + (2.0347) (2.08) - 7.3940 In R - 11.6261 COnVerting to common logarithms: log k = - 11.6261 x 0.4343 log k = - 5.0492 By definition 0 k -.= 10.5.0498 and l/k 2 105.0492 Taking common 10garithms log (l/k) l/k 5.0492 x log 10 = 5.0492 antilog 5.0492 130 By referring to a table of common logarithms l/k . 1.120 x 105 Taking rec ipro cals k a 8.93 x 10‘6 The same procedure described above was followed for each of the remaining five isotherms. Table IX, columns 2 and 3, shows the values of constants k and 11 thus calculated. It will be seen that the values of the equation constants show a definite dependence on temperature. The variation with_temperature appears to be par- ticularly pronounced in the case of constant k which increased steadily from a value of 1.90 x 10".6 at 40°F to a value of 9.68 x 10-5 at 14001“. Constant n , on the other hand, decreased from a value of 2.47 to a value of 2.08 at 122°F, increasing again t0 2.20 at 140°F. This behavior of the constant n of exhibiting a reversal of its change trend at the upper extreme of the tempera- ture range may seem a little anomalous, and may reflect a certain degree of ambiguity in the values of equilibrium content obtained at this elevated temperature. A closer examination of Figure 7 will reveal that the 140°F isotherm exhibits an increased downward displacement as well as a slight deformation as compared with the family of isotherms as a whole. It is conceivable that too long a“ exhosure of the grain samples at a temperature of 14001" may have resulted in abnormally high weight losses throughout the latter part of the equilibration period, due to changes other than normal w ater desorption. Such contingency would appear to be a definite 131 «£5503 8:988 .2565on £3 8.6:? €8.85: 2 @5288 3.86 328 _o comEQEoo ON 959.... mg . 00: \fi: £252. 222mm 5853 .8 -custoaxo 2355 0 3:32.23... . I . . a ._ ._ Q .. 23%.: 3:: 2.3 "202 . . a . : a . 9 9 ON.N mmd tr H3 mud EN #000. .. him om... m 00¢ ; c ob. x x as“: 3:228 *0 322, 6:58.8me .0. N sgsoq Mp O/ow ‘auaguoo OJNSQOW W . .., L.“ :25... H mm; ... x w. N "cot—Sum fis- 132 limitation of the static method in obtaining hygroscopic equilibria at elevated temperatures. It should be stressed, however, that the foregoing observation can not by itself be regarded as conclusive evidence against the reliability of the 140°F eXperimental isotherm. Nevertheless, it strongly suggests the advisability of inquiring into the matter further in order to decide upon the applicability of the static method to studies in hygroscopic equilibria at elevated tem- peratures. In view of the results discussed above, concerning the varia- tion of constants k and n with temperature, it can be concluded that Henderson's equation fails in accounting correctly for the tem- Perature dependence of the isotherm. Some knowledge as to the he— hEWior of these constants with varying temperature should be useful, however, in predicting the position of the isotherm at any tempera- ture Within the range of the investigation. When the values of both °°“Sti"nts were plotted against temperature the smooth curves shown in Figure 2| were obtained. In the absence of more exact values for the equation constants, Figure 2' should therefore be helpful 1" lroviding suitable values for the calculation of isotherms at a“? temperature within the range of 40°F to 140%“. AS a rough check on the reliability of the foregoing FPO- CEdure in calculating hygroscopic equilibrium data for intermediate t’emperadian-es, a comparison was made between values thus calculated “1‘ a tem t f 7""r d th ted b c 1 [an and Fel— pera ure 0 . an ose repor y 0 en lows (14) for yellow dent shelled corn at that same temperature 133 40 SOD|DA U .58 3:05... .8 8:03am £8335: .6 ..c: 25 ..v... 3:228 no ooconcoaou 8220an... _N 8:9... me .2223th ow on. ON. 0: 00. cm Om Oh om on Ge 0 _ . 4 v... . .... .. .... ... . . .. ... ... .. . .. .. . .... .... .. ...1.... ....L .. .. ..... .L ...L. .. . .s ¢ott. .... u... ... .. .. . .. ... .. . . .... .. . .....v.... ... .o ... ..... .. .... .... .. . .. 4. . . ..4 .... 1 .-.. ...t ...- ... . ... . ... . .. . . . .. . ., .L . ..... . ,. . . l .. .... ... .. ... .... .... , .... ... ... . .. . . .. .. .... ... . . .. ..c .... . . .. ., . ....Awtot.l.o a. ..v.v H H . .v .. . - ., 1 L z . .. -. H 1 . d .U- M. 5.“; I L . - .. 7 -. L L 1 W H l . I 0 % p. N L . . .-L . q l . L.....H 117 a . lg L J . a. 5;... .L\A.:.. L ...L.. . e .. . . .. v H «A ..Ht . .. V L is. . ..L L . \ L. .... H I L 171 g L -L H. l 4 L L L 3.. L... - H L L . . w . . + - n . , A F” ..H. 4 L . , IL -LH...¢ ., ... t ... Y . ., ‘Ivl 1 O A” . \‘wea: L .... L N H}..- _._'~. 7- .LLLL “,....-.“4 ..-- -.. .. . LLL LL -.~~4» ' O. J 1. ~—>-__L 1H-,.N~. 1L? FL L 1L. s _ I r— —-——— b.._._.. Mk“. L > - “L4 JR... ...L.---.s.-L.£. L .-. “54L”-..L -~4 j” -" 5. . . L L... e L L L L . H L L L... ill Hal ...-él 11191.1».--3 Tali! » . J . .rlxl _ .L L n. L w. 4. 2L . L L1 L L .. _V L1 L L L. L12 ”LL T 1.. r If 1-w...-1-..rtlvw$¢o1 L wlvtl L. H 4r a L. . t“ L N. . L L. .L .. ...L .... .L. .N. L L L L L .. .- L. L1. n h. H‘4r—o-fi ._ L . L L. -ILi: I I Q I ”I 6 l O i J -LLL- - L L I l l l [L l- 99: x >1 :10 serum 134 for various relative humidities. The results of this comparison are tabulated in Table XII. The table shows he values reported by Coleman and Fellows (wet basis), the some values converted to a dry basis, the values calculated us explained above, and also, corresPonding values which were visually interpolated from the ex- perimental isothexms of Figure 7. It will be seen that up to a relative humidity of 60 percent the agreement between the cal- culated values and those reported by Coleman and Fellows was fairly satisfactory, with considerable deviation occurring at the higher relative humidities. These results are in accord with those dis- cussed further below and afferd proof of the adequacy of the method. 0n the other hand, the agreement between the reported Values and those visually interpolated from the experimental iso- therms was much closer throughout the whole range of relative humidities. This latter observation may be regarded as confirma- tory eVidence of the reliability of the experimental isotherms. In order to determine whether Henderson's equation succeeds in describing the shape of the isotherm throughout its entire range, the isotherms were calculated by fitting equation (43) with the res . . - pective values of constants k and n . Enough p01nts were Calculated to enable following the course of the isotherm throughout, the entire range of relative vapor pressures. These calculated curves were then compared with the experimental iso- therms. Figure 20 shows such a comparison for three of the iso- them'so It will be seen that for the relative humidity range 135 TABLE XII COHPARISON OF DATA 8! COLEMAN AND FELLOWS WITH CORRESPONDING VALUES CALCULATED ACCORDING TO HENDERSON'S EQUATION AND EXPERIMENTAL coms'nm'rsl Equilibrium Data by Coleman and Fellovsz Calculaged Visually relative Reported values Converted values values interpolated . . , percent values from 32:23” .5323. agrfiifi. dry bu“ 33::ng 15 6.40 6.84 6.40 6.5 30 8.40 9.17 9.00 9.16 45 10.50 11.62 11.40 11.72 60 12.90 14.80 13.60 13.75 75 14.80 17.35 16.50 17 .00 90 19.10 23.61 20.40 22.50 100 23.8 31.20 28.00 31.25 \ 1/ Experimental constants obtained from Figure 21 , for 77°F as follows: °°n8tant K a- 4.05 x 10.6; constant 11 c 2.31 2 / Data. by Coleman and Fellows for yellow dent shelled corn at 77°F, / taken from Table 1, Chapter 11 of Reference (28). 3 calculated by substituting interpolated constants in Henderson's equation. 4/ 0btained from Figure 7' LUU from 20 percent to 60 percent there is an excellent agreement between the calculated and the experimental isotherms. However, beyond that range the eXperimental isotherms generally deviate markedly in an upward direction from the calculated curves. It should also be noted that while the experimental curves show definite intersections with the vertical axis at saturation the calculated curves approach this axis asymptotically. Below 9. relative humid— ity of 0.15 to 0.20 the tendency of the eXperimental isotherms is towards slightly lower equilibrium moisture content values than the equation calls for, even though the extent of the deviation may be considered negligible. It is evident from the foregoing that Henderson‘s equilibrium equation can'only be expected to yield good results in predicting hygroscopic equilibria of shelled corn When apprOpriate values of the equation constants are used according to the temperature, and then only below a relative pres— sure 01' about 0.70. It is also quite likely that varietal charac- teristics may introduce appreciable variations in the values of the constants as may be inferred from a comparison between the con- stunts previously calculated by Henderson and those herein evalu- ated fI‘om the experimental isotherms. Henderson (23) gave two sets or Values calculated from data of two different sources as follows: Value of 1: Value of n Temperature 1.10 x 10’5 1.90 77°F 1.59 x 10"“ 2.68 77-8301" 137 When compared with the values reported in Table IX it will be seen that while they appear to be of the same order of magnitude, the differences are such as to suggest appreciable influence of varietal characteristics . 138 Drying Rate Data The analysis and discussion of the preceding sections have dealt with the equilibrium aSpects of the investigation. The time- rate relationships will now be considered. Drying Curves It has been explained that throughout the equilibration period of most samples, sufficiently detailed data were obtained to enable accurate construction of drying curves and subsequent cor- relation of the drying data. Upon termination of any given run the observational data were processed, as shown in Table III for one of the samples, so that the equilibrium moisture content as well as the values of moisture content at each time of observation were calculated. On the basis of these calculated data, drying curves were constructed for each sample by plotting the moisture content Yelues (dry basis), against drying time in hours. The large number 01' curves so obtained precludes including them all here; however, Curve A of Figure 22 illustrates a typical example of this kind 01' curve. In general, very smooth curves were obtained by joining all experimental points with hardly any point deviating significantly from the curve. As is characteristic of drying in the falling-rate per-10d, the curves exhibited continually decreasing sIOpes approach- ing asymptotically the correSponding equilibrium moisture content Values. These drying curves enabled ascertaining what was the in- stantaneous moisture content of the samples 0t any time during the d 0 ”lug process . x I Idlirdjb-Im 139 dv ‘aoualallgp 81055810 JOdDA 'y'so ((Dd .bd) .58 3:93. *0 9E5 .63 £5 5 3:22:80 .896: $06 was $23.23 32:; ..o «E: 5:» cozoto> mm 2:9“. 3:0: ¢ 66:. ax to 558.3% so 3.5: 286:. mac: taxman 62:3.802 a D N. o .W .8 W O m 8W 8W ammo "gov: . n a mwmo n A v: a on... "s V: a 831:; x 5:22:30 .322. 89: ,.o mw:_o> o and 00.0. mmd. VMV m000. .252 .2 oz rm use 93: o: sysoq bp was 18d ‘lualuoo aJnlsgow 140 For comparative purposes it was desirable to reduce the drying curves of the various samples—in which the initial moisture content showed some variation—to some common basis. This was accomplished by computing the values of the moisture content ratio, (ll - "13)/(Mo - M.) dry basis and plotting these, instead of the moisture content values, as ordinates against the drying time. In this case, all points on the ordinate axis start at a value of 1.0 regardless of the initial moisture content of the sample. Curve B of Figure 22 shows such a cum as a result of plotting the same data of curve A according to this procedure. A18 0 Figures 25, 27, 29, 31 and 33 give this type of curve for other drying conditions. These curves not only facili- tated further correlation of the data but enabled the determination of h‘11'--response periods for each of the samples. It will be recalled that a knowledge of this factor‘ for any given set of drying conditions is 0f great value in drying calculations. These values were obtained by reading from the drying curves the value of drying time corres- ponding to a value of the moisture ratio of 0.50. Table XIII shows the values thus obtained for various drying conditions. Factors Affecting the Half-Response Period A 8tndy of Table XIII reveals that the most important single factor affecting the length of the half-response period is tempera- ture. The higher the temperature the shortenwill be the period of half‘response for any given set of conditions. Next in importance to the temperature factor in determining the length of the half— res ponse period seems to be the initial moisture content, Mo . 141 TABLE XIII VALUES 0? HALF-RESPONSE PERIODS FOR SHELLED CORN UNDER DIFFERENT DRYING CONDITIONS Rel. Hum. pa Mo Me No - Me jA p)0 0} percent psia fl d.b. % d.b. % d.b. psi hr. 40°F 14.0 0.0170 26.96 7.78 19.18 0.0967 26 34.6 0.0421 27.30 11.80 15.50 0.0724 20 53.4 0.0640 27.22 14.90 12.22 0.0504 29 59.3 0.0722 27.01 16.35 10.66 0.0417 18 75.1 0.0914 27.47 20.50 6.97 0.0236 26 60°F 12.8 0.0328 27.20 6.35 20.85 0.2235 16 33.9 0.0369 26.80 10.52 16.28 0.1681 10.5 37.5 0.0861 27.50 11.10 16.40 0.1538 11 54-0 0.1385 27.50 13.30 14.20 0.1178 12.8 56-0 0.1451 27.50 14.10 13.40 0.1022 11 75-9 0.1945 27.20 18.20 9.00 0.0618 13.5 86°F 11-2 0.0689 20.77 4.86 15.91 0.4817 11.2 32-4 0.1993 21.75 9.02 12.73 0.3619 7.0 43-5 0.2676 21.14 10.50 10.64 0.2860 7.5 56-3 0.3464 20.08 12.35 7.73 0.1944 7.0 63.6 0.3894 17.86 13.57 4.29 0.1169 11.5 75.2 6.4626 20.92 15.83 5.09 0.0050 5.5 33-3 0.5309 21.20 19.28 1.92 0.0284 6.50 100°]? “-1 0.1054 18.60 4.78 13.82 0.7081 17.0 3L9 0.3038 18.44 8.46 9.98 0.5088 10.0 43'4 0.4129 18.35 9.95 8.40 0.3958 9.0 5°°° 0.4746 27.79 10.86 16.93 0.4717 6.0 142 TABLE 1:111 (6061,.) Rel. Hum. pa No “a I"o ' no (Awe 0% percent. psia fl d.b. % d.b. % d.b. psi hr. 61.8 0.5866 18.49 12.78 5.71 0.2250 9.5 75. 1 0.7128 32.82 15.35 17 .47 0.2364 5.25 79.1 0.7508 28.85 16.53 12.32 0.1984 8.75 85.6 0.8125 34.54 18.60 15.94 0.1367 18.0 122°r 11.4 0.2039 44.00 3.83 40.17 1.5849 3.0 11.4 0.2039 37.48 3.83 33.65 1.5849 3.25 20.4 0.3649 38.10 5.97 32.13 1.4239 3.0 28.4 0.5080 36.79 7.48 29.31 1.2808 3.0 47.1 0.8425 32.26 9.88 22.40 0.9463 3.75 74.7 1.3362 37.66 14.78 22.88 0.4526 5.5 140°? 11.2 0.3235 42.70 3.39 29.31 2.5651 2.0 21.0 0.6066 43.80 5.21 38.59 2.2820 2.0 25.3 0.7308 44.03 6.12 37.91 2.1578 2.0 49.9 1.4443 43.70 8.59 35.11 1.4443 3.0 74.9 2.1635 16.52 12.63 3.89 0.4825 4.5 55.2 1.5945 43.70 , 8.59 34.66 1.2938 2.75 143 It was evident that under the same external drying conditions, the higher the initial moisture content the shorter the- half-reSponse period tends to be. This behavior may at first seem rather anoma- lous in View of the fact that the free moisture content corresponding to the higher Rio-value must also be higher, thus increasing the a- mount of water that should desorb within the half—resyvonse period. However, it should be noted that as the moisture content of the grain increases, the additional amounts of water involved in the desorp- tion or drying process are apt to be bound by ever-decreasing forces and are therefore more easily desorbed. Thus the increased initial drying rt! te that results from a higher initial moisture content more than compensates for the increased amount of water to be removed. It toll-Owns from the foregoing that both the equilibrium moisture content and the free moisture content also have an important bearing in de te I‘mining the extent of the half-response period. For instance, as the equilibrium moisture content approaches the lower-most values- where the binding forces of the grain exert the strongest influence- the deSOrption rate becomes slower and slower with a consequent in— crease of the half-response period. It would appear then as if the imp°rtant factor concerning the free moisture content is the moisture range onr which it occurs. Referring to Figure 12, which shows the variation of the 0thmer latent heat ratios with moisture content, it may be inferred that beyond a moisture level of 18 percent, dry basis, the binding forces are more nearly uniform and therefore the latter effect may become less noticeable. Other factors which may 144 come into play as the moisture level is lowered, to account for the foregoing behavior, are the increase in overall diffusion resistance and the probable decrease in the diffusivity of the grain. Determination of Drying Rates In an attempt to obtain a simple analytical expression for the drying rate which may obviate the need for graphically differentiating the drying curves, the same data used in obtaining the last mentioned type of curves were plotted on semilogarithmic graph paper. The values of [11018 Lure content ratio, (M - Me)/(Mo - Me) were plotted as ordinates on the logarithmic scale against drying time on the arith- metic Scale. The plots yielded excellent straight lines over re- stricted regions of the curve with sharp changes in slope occurring at more or less regular intervals between the linear portions. This behavior is shown in Figure 23 which represents the semilogarithmic Plot of the drying curve of Figure 2 . Figures 26, 28, 30, 32 and 34 also illustrate the same type of curves for other drying conditions- W , The f0 Pegging results prove conclusively that the exposed drying be- haviol. of shelled corn obeys an eXponential law analogous to Newton's 1" of cooling, but with rate constants which are only valid over re- stricted ranges of moisture content. This relationship may be formu— late (1 thus 4:9- 11 - Me = (Mo -— Me) e (5?) OP . M - Me — {m (58) M - M " ‘ fn—h __._._M_ 145 0.9 0.8 0.7 —- 06-— 0.5 —- 0.4— 0.3 — T .0 M- Moisiura ratio, ~29- 0.07 0.06' 0.05 0.04 Mo. Ma r K3: 0.0324 Temp. RH. IOO°F. 43.4 0.03 —- M-M Ln 9 =-K€- MdMe Mo Me i835 IQOO o.oz(g——i\l 1 1 l /|_L D 20 30 K4: 0.0l5 “‘0‘ Me 8.35 Time ,9- Hours Figure 23 Semilogarithmic plot of moisture ratio Showina behaviour of role consio nt K. 40 50 vs. time curve of Figure 60 22 146 It will be seen from the senilogarithmic plots that as many as four or five different and ever—decreasing values for the rate constant took place in governing the drying process over the first 72 hours of drying. Interestingly, there appears to be some cor- relation between the number of values for the rate—constant oc- curring over the drying period and the theoretical number of molecu— lar layers estimated by application of the B-E-T three-constant equation as constitting the adsorbed water. It might well be in- ferred that the value of the rate constant is to a certain extent related to the particular layer Aof molecules that is being desorbed, and hence to the particular intensity of the binding forces that OPPOSe the process. The changes in value of the rate constant may 8:180 reflect changes in the moisture diffusivity of the kernels as dr"Ying proceeds. The values of the drying rate constants were determined for the Various drying conditions and are given in Table XIV along With their corresponding ranges of applicability. The latter are GXPrOssed both in terms of moisture content, percent dry basis. The drying rate values were obtained by measuring directly the slopes of the linear semilogarithmic plots, while the limits of the corresponding ranges of validity were determined from the values which marked the beginning and end of each linear portion of the curve. 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N.o . _ ”0.0 r ‘ -C0_U_ 000 50 WCOsu ”was 0 ”GD—O . . . _ . . . . . . . .... ... ... .... a . .vv. .... .... ,... Y- > ~ . . .... .... .... . . v ‘ n a . . . re o 1w . O. o I . o .o. . .. .... ... 0.0 .r ”0.0 , . _ . . .... .... ' . o . . . . .. . . ' 'l . i. . . .e r:.! V w [:0 4‘ o .. V . . . ,. r. . .... ‘ co— gam oc.a . V. . ... a W , . ... . ... ... u o o h ... . .1 a . .. .uov 4 4 ’ O . . . ~ 1 . . .. .. . .... ..v. . A . . ... ....._. . c . A .. ... . .. ...i . .. . . .. ... . ¢ .. .. ... . .. .. . .... I . . . . .... .. . It , .e.. .. , f ... . . a o .. ... _ _ :16... v... . ..H. . , . .... — ‘096 . _ _ . _ 7 . ... .7 _ n . o._‘lnlll.||l _ . , . .. ... .. .. . .. o . .. H.. b . .. . 160 The pronounced effect that the moisture level appears to have on the magnitude of the mass transfer coefficient is un- doubtedly related to the relative intensity of the binding forces acting on the vatenfimolecules. In view of the sharp stepwise changes that occur in the values of both the drying rate constant k and in the mass transfer coefficient K.g as drying proceeds it seems logi- cal to infer that the resistance to desorption stems essentially from the tenacity of the binding forces, and that the relative intensity of these remains relatively constant as long as the molecules of one particular layer are being desorbed, falling off abruptly as desorp- tion from another layer begins. It would appear from the above con- siderations that the law of eXponential decay gOVerns throughout the entire drying process with the proviso that the rate constant as- sumes a correspondingly lower value for each of the adsorbed layer molecules. The exceedingly low drying rates that are observed at very low'moisture levels are most probably due to the very high ad- sorptive|fbrces acting on molecules which are adsorbed on particularly -active centers of the internal surface and perhaps also on the sharp- est cracks or crevices of the porous structure. The general behav- iour of the heats of adsorption at the various moisture levels ap- peaaw; to lend support to the above concept. ‘9.» I. [.udfinv'b-llal .- . _ 161 1r I'l'll'l"! m~.o n n_.o n.o~ u “.5" po.~ n~.c n a~.c m.p~ a w.w~ ma.¢ mm.o o~.~m mmmo.o m.m~ on upoo.o n nv~o.c u w~.a_ o~.o mnao.o I nnmo.o o¢.om u n.vm pu.c nonc.c : nvvo.c cm.vw n m.um vo.~ om.m~ om.»m ava~.o a.np on nvc.c u owo.c “.m— u m.n~ wv.m cwo.o a m-.c a.n~ u m.m~ mm.¢ «_po.o u oom~.o om.w~ u «w.wm ”a.” n.o_ ow.mm memc.o m.mm cm I wn_c.c u no.a~ m».p mp_o.o u u~m¢.o n~.om n na.vm on.- ammo.o u canc.o mm.nm u go.pm op.vc n~.e~ ~o.~m mmuo.c n.an ov u nmdo.c u cm.nm c.m on~c.c u op_c.c om.nm u pv.s~ a.v~ o.om bv.um v_wo.o “.mp cw cvo.o n ono.o mp.m~ n ~m.e~ ‘ no._ ono.o a «pc.o om.a_ u cm.o« mo.n v»o.a : ”mo.c on.c~ u om.vm po.- . . pwo.o a cao.o om.wm n ca.em co.on oo.w cm.cm cpdc c c v~ ow u 0 o a “an a a c u z . “mg.uom .a.u & .n.e x «as a mo ail h£\ a v a K O o d hauumndomamc no mmwcdz mg a a. .— 415 .988. 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