SGME 3A3“: WUWfi FOR ANALYSIS OF ELECT ROSYFATEC DUST PRECIPIFATION Thesis for “19 Degree of pin. D. MICHIGAN STATE UNIVERSITY Ross Define Brazee 19.57 [nuts c .9— This is to certify that the thesis entitled Some Pssic Leasnrements for Inelysis of Electrostgtic Unst Precisitetion presented by 7085 D. Frezee has been accepted towards fulfillment of the requirements for - ‘n 1 'I I .. o )0 degree in I (I I‘iC "11,11 TFL 'vllé jfiC: (“Ting 3/91, f/Bmé/ Méjor professor (‘l' (n (I . ‘ ‘_ .. ( ' 5’6. A Al)(.l .1! j ' \f‘ \r- *3 Date 0-169 sen: BASIC MEASUREMENTS FOR ANALYSIS OF ELECTROSTATIC DUST PRECIPITATION By Ross Deline Brazee 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 1957 Approved ROSS DELINE BRAZEE AN ABSTRACT Fundamental information has been developed for eventual application to the design of dust application methods and equipment. Specific areas investigated were: the corona discharge between concentric cylinders, size distributions of dust particles, determination of electrical charge on dust, and analysis of dust precipitation in a cylindrical field. A study was made of three analytical expressions relating the current and voltage for a corona discharge in air between two concentric cylinders in terms of ionic mobility and cylinder geometry. The most satisfactory equation was applied in an indirect experimental method of measuring ionic mobility. The observed decrease of ionic mobility with increase in humidity, differences in positive and negative ion mobilities, and gas density influences on ionic mobilities were explained on the basis of modern gaseous electronics. The log-normal frequency distribution was shown to describe experimentally determined particle-size distributions. An analytical method of predicting total (maximum) charge per unit mass of dust was developed for a concentric- cylinder ionizing charger. An experimental charge-measurement method was also devised. The methods were compared exper- AN ABSTRACT inentally and found to be satisfactory. Disagreement in measured and calculated results was concluded to arise from lowered ionic mobilities in the dust-laden inter- electrode atmosphere. The usefulness of the techniques developed was il- lustrated through a simple analysis of dust precipitation in a cylindrical electric field. It was shown that high but not impractical potentials, would be necessary to overcome the strong influences of air currents. SOME BASIC MEASUREMENTS FOR ANALYSIS OF ELECTROSTATIC DUST PRECIPITATION BY Ross Deline Brazee A THESIS 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 1957 Ross Deline Brazee candidate for the degree of Doctor of Philosophy Final Examination, September 19, 1957, 9:50 A.M., Room 218, Agricultural Engineering Building Dissertation: Some Basic Measurements for Analysis of Electrostatic Dust Precipitation Outline of Studies Major Subject: Agricultural Engineering Minor Subjects: Physics, Mathematics Biographical Items Born, October 9, 1950, Adrian, Michigan Undergraduate Studies, Michigan State University, 1948-1952 Graduate Studies, Michigan State University, 1952-1955, cont. 1955-1957 Experience: Graduate Assistant, Michigan State University, 1952-1955: Instructor, Michigan State University, 1955; Graduate Assistant, Michigan State University, 1955-1957. Member of Tau Beta Pi, Pi Mu Epsilon, Sigma Pi Sigma, Society of the Sigma Xi, American Society of Agricultural Engineers. vi TABLE OF CONTENTS .Page INTRODUCTION . . . . . . . . . . . . . . . . . . . . . 1 Background of the Study . . . . . . . . . . . . . 2 Statement of the Problem in the Present Work. . . 4 AN EXPERIMENTAL STUDY OF THE CORONA DISCHARGE CHARACTERISTICS OF A WIRE IN A COAXIAL CYLINDER . . . 5 Review of Literature . . . . . . . . . . . . . . 5 Experimental Investigation. . . . . . . . . . . . 6 Discussion of Results . . . . . . . . . . . . . . 11 Conclusions . . . . . . . .~. . . . . . . . . . . 15 DISCUSSION OF THE CONCENTRICACYLINDER CORONA DISCHARGE AND IONIC MOBILITY. . . . . . . . . . . . . 16 The Concentric-Cylinder Corona Discharge. . . . . 16 Current-Voltage Equations . . . . . . . . . 16 The Critical Corona Gradient . . . . . . . . 25 Consideration of the Measured Ionic Mobilities of the Corona Discharge Experiment . . . . . . . 25 Influence of Humidity Upon Mobilities. . . . 24 The Effect of Gas Density on Mobility. . . . 24 Differences in Mobilities of Positive and Negative Ions . . . . . . . . . . . . . 26 The Variation in Mobility with the Corona Wire Radius . . . . . . . . . . . . . . . . 27 General Discussion . . . . . . . . . . . . . 27 '='=55u"':sr'2m101.s SIZE DISTRIBUTIONS . . . . . . . . Review of Literature . .-. . . . . . . . . Experimental Measurements . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . DETERMINATION OF ELECTRICAL CHARGE ON DUST . . . Theoretical Maximum Charge per Unit Mass of Dust Charged in a Concentric—Cylinder Corona Discharge . . . . . . . . . . . . . Measurement of Total Charge per Unit Mass of Dust . . . . . . . . . . . . . . . Theory of Measurement . . . . . . . . The Dust Charge Measurement Apparatus Experimental Investigation . . . . . . . . Experimental Method . . . . . . . . . . . . Apparatus . . . . . . . . . . . . . . Procedure . . . . . . . . . . . . . . Discussion of Results . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . ANALYSIS OF A SEMICYLINDRICAL ELECTRIC FIELD FOR CHARGED DUST PRECIPITATION . . . . . . . . . . .Preliminary Experimental Investigation . . Equipment . . . . . . . . . . . . . . Procedure . . . . . . . . . . . . . . Results 0 O O O O O O O O O O C O O O Page 28 28 50 52 52 37 57 38 39 41 41 41 44 45 48 48 48 49 49 viii Page. - . Theoretical Analysis of Dust Particle Behavior ‘ in the Semicylindricai Electric Field . . . . . 49 Analysis Assuming Concentric Cylinders of Infinite Extent . . . . . . . . . . . . . . . 51 Analysis Assuming Concentric Semicyiinders of Infinite Extent . . . . . . . . . . . . . . . 52 Estimation of Charge on a Particle of Given Radius . . . . . . . . . . . . . . . . . . 55 Estimation of Time Required for a Charged Particle to Travel from the Outer to the Inner Cylinder . . . . . . . . . . . . . . . 54 Tue Limiting Electric Potential to Required for Complete Precipitation in Still Air . . . . . . . . . . . . . . . . . . 55 Discussion and Summary . . . . . . . . . . . . . 56 GENERAL SUMAARY . . . . . . . . . . . . . . . . . . . 56 APPENDIX A - EXPERIMELIAL RESULTS . . . . . . . . . . 60 APPENDIX B - THEOREDICAL RESULTS . . . . . . . . . . . 75 REEREI\CES CITE O O O C O O O O O :' ' . O O '- 0 0 O . so ix LIST OF TABLES Table I Page 1 Tube and Wire Size Combinations, Air Velocities, Temperatures and Relative Humidities for Which Corona Discharge Current-Voltage Data Were Taken . . . . . . 10 2 Ionic Mobilities (k) and Corona Starting Voltages (V0) Given by Equations (1) and (15) from.Data of Test No. 7, Positive Corora,. Table I of Appendix A . . . . . . . . . . . 18 3 Air Density Variations in the Corona Discharge Experiment . . . . . . . . . . . . 25 APPENDIX A I Tabulation of Data for Experiment on Corona Discharge CharaCLeristics of a Wire Coaxial with Respect to a Cylinder . . . . . . . . . 61 II Particle Size measurement Data . . . . . . . 70 III Geometric Mean larticle Diameters (dg) and Geometric Stancard Deviations ((7%) for Several Duets .... . . . . . . . . . . . . 71 IV Cnarge measurement Data . . . . . . . . . . 72 Al‘ Pbl‘1l)IX B I Calculated Values for q . . . . . . . . . . 76 10 11 LIST OF FIGURES Page Experimental apparatus for the corona discharge investigation . . . . . . . 7 The cylinder-wire test stand . . . . . . . . 8 The effect of atmospheric relative humidity on the mobility of positive air ions . . . . 12 The effect of atmospheric relative humidity on the mobility of negative air ions . . . . l5 Explanation of Symbols Used in Figures 5 and 4 . . . . . . . . . . . . 14 The effect of atmospheric relative humidity on the mobility of positive air ions, as given by the Parsons equation (1) and the Cobine equation (15) . . . . . . . . . .q. . 19 ‘A plot of equation (15) to show the applicability of the Parsons equation (1). . 21 A plot of equation (16) to show the applicability of the Cobine equation (15). . 22 The charge leakage capacitance measurement circuit . . . . . . . . . . . . 58 The dust charge measurement circuit . . . . 59 The charge measurement apparatus . . . . . . 40 Removal of a dust-coated disk from the cage. 40 L 12 13 14 15 16 17 -xi- Page Schematic diagram for the charge measurement experiment . . . . . . . . . . . 42 The effect of atmospheric relative humidity upon, and the magnitudes of, the total charge per unit mass of dust, q, taken up by micron- ized talc dust in a concentric-cylinder charger: a comparison of experimental measure- ments with predictions of equations (51) and (56) . . . . . . . . . . . . . . . . . . 46 The Chemical Machines Ltd. duster . . . . . 50 The dust charger and the semicylinder . . . 50 Representation of the applied field problem. 51 (a) z - plane, and (b) w - plane . . . . . . 55 APFEEDIX A Positive ion mobility as a function of atmospheric relative humidity, from measure- ments for the concentric-cylinder charger used in the dust charge measurement experiment 75 A plot of duet particle diameters D against cumulative percentage of particles of size less than D for CCC Diluent Dust. 74 APPELDIX B Graphical solution of equation (46) for x under the conditions of the charge -xii- Figure Page measurement experiment . . 3 . . . . . . . . 77 B The variation in total (maximum) charge per unit mass of dust, q, as a function of ionic mobility k, as predicted by equations (51) and (56) . . . . . . . . . . . . .-. . . . . 78 C A sketch of the electric field lines in the space between the field semicylinder and the plant row, based upon the solution (69) by conformal mapping . . . . . . . . . . . . . 79 xiii ACKNOWLEDGMENTS many individuals assisted in making possible the work reported herein. Dr. A.W. Farrall, Head of the Agricultural Engineering Department, made available the research assistantship. The Rackham Foundation and Corn States Hybrid Service provided financial support. Dr. Wesley F. Buchele, Agricultural Engineering Department, as major professor continually provided guid- ance and encouragement. Dr. Donald J. Montgomery, of the Physics Department, contributed many hours of guidance in experimentation and analysis. Drs. Carl W. Hall and Merle L. Esmay, Agricultural Engineering Department, and Dr. Edward A. Nordhaus, Math- ematics Department, served as guidance committee members. Dr. Walter M. Carleton, formerly of the Agricultural Engineering Department and now with the Agricultural Engineering Research Division, United States Department of Agriculture, guided the early phases of the work. Dr. C. D. Reuse of the Physics Department furnished some apparatus for the studies. Mr. James Cawood and the staff of the Agricultural Engineering Research Laboratory gave helpful assistance W 3 xiv ,firl55510n of apparatus. lmfl'y'ilir. Ronald Ehmelink, Mr. Howard Wilson and Mr. Glen "fféghhdenberg gave valuable assistance in instrumentation, L experimental work and analysis of data. Mr. Scott Hedden helped with the photographic work. The author expresses most sincere appreciation to these individuals and all others who assisted in any way. The author also extends thanks to his wife, Hrs. Jean Roth Brazee, for her endurance and encouragement, and for typing this thesis. INTRODUCTION Control of plant diseases and insects is of great concern to the farmer and urban dweller alike. Fracker and others (1954) estimate that the average annual crop losses over the period iota—1951 amounted to about 3 billion dollars from plant diseases, and about one oillion dollars from insect infestations. These figures included field and forage crops, fruit and nut crops, vegetable crops, drug crops and ornamental plants. This less results in a reduction in the quantity and quality of produce available to the consumer, as well as a drain on producer income. Fracker's estimates include all losses whether or not they arise from causes that are preventable with present technical knowledge. The magnitude of the losses raises doubt that present means of insect and disease control are being efficiently used. (Chemical preparations are important for post and dis- ease control. Smith and others (1354) estimate that in the United States, in 1952, about 23 million acres were dusted or sprayed an average of 2.16 times, at a total cost of about 133 million dollars. This cost emphasizes the im— portance of efficient pesticide application to ensure that the investment in control is not a loss. -2- T Ii,g%1ng is an often used, convenient application method, 7;?“it is susceptible to loss of pesticidal material through ' drifting of the dust cloud. Bowen (1951) and Ban (1955) ' found that only ten to twenty percent of the pesticide deliver- ed by a conventional machine reaches the plants. The Michigan State University pesticide-application study was undertaken in 1950 to determine the fundamentals of dust precipitation and thereby provide the basis for improving deposition efficiency. Background of the Study . The work was begun with a study of electrostatic dust precipitation by Bowen (1951) and Hebblethwaite (1952), who found that humpe (1947) and others of France had some success with the method. A dust charging "nozzle“ in the form of a cylindrical condenser was used. Aerosol particles picked up air ions as they passed through the intense field of the nozzle. The potential gradient of the resulting charged cloud was Ilsed to drive the particles onto the plant. Although one hundred percent improvement of deposit- ing efficiency was obtained in some cases, the method was IMDt always successful. Hebblethwaite found that its effec- tiveness fell off with increasing relative humidity. Brazee (15953) reported that electrical breakdown of incidental Inozzle coatings of certain dusts also hindered charging. :result was that high aerosol stream velocities tended to -decrease recovery of coarser dusts. he attributed this to an erosion effect of the aerosol stream.- Recovery of dust was greater for more pubescent and prominently veined leaves. Mathematical and experimental studies by Bowen (1953) showed that assumption of a continuous charge distribution for theoretical analysis was justified. Using this fact, Bowen and Splinter (1955) began a study of dust preci- tation forces. Inertial forces, arising from deflection of the aerosol stream by the precipitation surface, and electrical forces were considered in theory and experiment. Inertial forces were found highly significant, especially for large parti-' cles. The only electrical forces considered were those occurring naturally owing to a charge distribution. Since they depended upon the electric field configuration, they were sometimes as important as inertial forces; in other cases they were negligible. In the ease of very small particles (less than 2 microns radius), it was concluded that electrical forces exerted the only significant effect for useful deposition; In field tests, Ban found that leaves in the outer regions of bean plants had heavier deposits when charged dust was used. However, the recovery for the inner -4- regions (termed hidden leaves) was greater for uncharged dust. He attributed this to reflection of the aerosol stream from the soil surface into the hidden leaf region. Laboratory tests were made by Ben to study the effect of an applied electric field upon precipitation of a number of dusts. The field was supplied by a plane charged screen, having the same charge polarity as the dust. Favorable effects were noted in many, but not all, cases. Finer dusts appeared to receive greater benefit. At the beginning of the studies of this thesis, then, the groundwork had been laid for continued theoretical and experimental study of particle precipitation forces, including externally applied electric fields. Statement of the Problem in the Present Work It was decided that the most fruitful areas of in- vestigation for this work would be: the concentric- cylinder corona discharge and its behavior with variations in relative humidity, analytical description of dust particle size distributions, and determination of electrical charge on dust. These findings, as well as those of previous workers, will be applied to an analysis of dust precipitation in a cylindrical electric field. .AN EXPERIMENTAL STUDY OF THE CORONA DISCHARGE CHARACTERISTICS OF A WIRE IN A COAXIAL CYLINDER A study of the corona discharge characteristics of a fine wire coaxial with respect to a grounded metal cylinder was undertaken. An analytical expression between current and voltage for given ion mobility and cylinder geometry was desired for design of experimental dust chargers, and infor— mation was needed about ionic mobilities and the influences of atmospheric humidity and air velocity upon the corona discharge. Review of Literature Parsons (192%) derives an equation intended to express the current-voltage relation in the corona discharge between a cylinder and a cocxial.rdre. Under such circumstances almost all ionization occurs within a small region surrounding the wire. Outside this region the charge carriers are ions of the same electrical Sign; 1.9., for a positive wire potential, negative ions move toward the wire while the positive ions leave the ionization region and travel outward to the grounded cylinder. In the derivation Parsons accounts for expansion of the ionization region as voltage increases. The final form of Parsons' equation is i - CV(V-Vo)/(Vl"v), (l) ysfjiis the current per unit wire length; V is the applied .3" . vhe=voltageg V6 is the voltage necessary to start the corona, c - 2kro/R2,B , (2) v1 - (ro/p-nnm/ro) 4 V0. (_3) Here k is the ionic mobility (the velocity of an ion in a field of unit strength); rO is the wire radius; R is the cylinder radius; ’8 is the rate of increase of the corona region radius, ri, with respect to applied potential, that is, ri = r0 + '3W-VO). (1+) Experimental Investigation An experiment was made to obtain corona-discharge cur- rent-voltage data. The tests included several sizes of wires and cylinders, and extended over a range of relative humid- ities. The effect of variation in the velocity of air move- ment through the tube was also studied. The effect of an aerosol in the stream was not taken up in this experiment. The equipment was set up in a laboratory chamber for humidity control, as shown in Figure 1. Figure 2 shows the test stand holding the cylinder—wire combination under test. Clamps were provided for holding the grounded aluminum— tubing cylinders. Plexiglas insulators held the corona wire in Proper position at the cylinder's longitudinal axis. Figure A.' B. C. D. E. F. Experimental apparatus for the corona discharge investigation. Air circulation outlet. Steam outlet for high humidity tests. Variable speed fan. Cylinder and wire stand. Air velocity probe. Fan for air circulation over wet and dry bulb thermometers (G) for relative humidity measurement. Figure 2. A. B. C. D and E0- The cylinder—wire test stand. Base. Mounting rails. Cylinder clamps with section of aluminum tubing in place. Mounting brackets for Plexiglas connectors between which wire was stretched along cylinder axis. fleet current potential was obtained through elec-_ 15c -§eltage-tripler circuits, one of positive and the =_H -i of negative polarity so that both discharges could be Lastudied. Air movement through the cylinder was controlled by using a variable-speed centrifugal fan, and velocity was measured by means of a Hastings hot-wire anemometer. The meter probe was mounted on a traversing levcr actuated by a solenoid, which allowed positioning of the probe for meas- urements without disturbing the chamber atmosphere. Table 1 shows the tube and wire size combinations, air velocities, temperatures and relative humidities for which current-voltage data were taken. Parsons' equation was written in the form iVl + VD - v20 - iV, (5) where D E CV0. (6) The quantities V1, V6, and C were taken as parameters for adapting Parson's equation (1) to a set of i and V values taken at a Specific polarity and humidity. Fluctuations were smoothed by plotting the data on logarithmic coordin- ates and fitting a straight line. Three i-V pairs were selected from the plot and inserted in equation (5), giving three algebraic equations that were solved for V1, V0, and C. ; .asaeassn swan pm commence on some Iadfinaoo amazofipamg on» mo madaawa on mewso waanfiwbpo pom 090: demo omega an .hpflaaesn o>fipmaoa pceoaom *i .Amov manpwhomEop nasnuhaa ** .Ho>oa hsaofissm * om ¢.Hoa \\MW w.mm mm b.¢w om w.HOH Ho m.>m mm o.¢m mnw.o mm.e oooa nm H.50H mm H.mm Ha n.mm mm b.moa om m.¢m on o.mm om.a mm.¢ oooa a$** ##** om m.mm mm w.mm aaaa *aaa om o.mw an m.mm mm.w mm.v OOOH hm H.m0H no H.¢m on n.0m am ©.moa Hm >.nm on ¢.nm mmw.0 mm.n OOOH m «a «.mHH mm o.sm mm b.¢m mm o.mHH Ho o.>m mm o.wm >m.m mm.n ooow . .... i 8 oooa . mm m.moa mm m.mb mm b.H> no m.moH no n.m> mm m.mb om.H mn.m oom be: . mm >.moa no m.nw me m.mm em H.moa no n.mm ma m.©m mmw.o Om.H oom mo m.mm aw m.©m on o.mm mm ©.Hm em m.wm Hm m.am mw.© om.H oom _ \m.m p .m.m p .m.m p .m.m u .m.m p .m.m **p ~.Eov “.80“ IIIIII . *** A.:HS\.nmv mam SSH ea 309 *nwwm assflwoz $scq moa M hpfiooao> ddcnoo o>apa oz sqoaoo o>HpHmom om m aha omaho>< s. ....mqaam 95 mammaéamaaa .328an m2 62332528 aNHm mag 92 mm? .. .H mama. —.—‘ -11- The constant fl was then determined by solving equation ,3 - r°1n(R/ro)/(V1-Vo). ('7) The apparent ionic mobility k was given by equation (2) in the form k - 0122/3/er. (8) Discussion of Results Numerical results are tabulated in Table I of Appendix A, and ionic mobilities are plotted against relative humidity in Figures 3 and 4. I Trial calculations, which are not presented, showed that Parsons' equation would be fairly suitable as a design equation. In practically all instances the apparent ionic mobil- ity was observed to decrease as relative humidity increased. An examination of the individual points plotted indicates that in many cases the mobilities decreased less rapidly at high humidity. The negative-ion mobilities were in general slight- ly higher than the positive. -here was some tendency for the mobilities to run higher for the smaller wire diameters. The measured ionic mobilities in air are of the same order as values quoted in modern work, e.g., in von Engel (1955) and in Loch (1955). The experimental error in the ionic mo- bilities was estimated to be about i 9 percent. Reynolds number calculations showed that the air flow was turbulent in all cases. The ratio of the transverse to the longitudinal ionic drift velocity (with respect to the cylinders) Test and Symbol for .13 re Curve Individual x 102 Number Points (cm. ) (cm. ) 1 x 1.90 6.82 2 8 1.90 0.655 5 ® 2.58 1.50 4 Q 3.65 2.87 5 E] 3.65 0.655 6 4) 4.92 6.82 7 A 4.92 1.50 h‘ 8 <7 4.92 0.635 -15- varied from about 2.54 x 10‘2 to 0.96. Under these con- ditions no significant effects on the corona owing to air movement were noted with the instrumentation employed. It is important to note that constant temperature could not be maintained with varying humidity, as Table 1 shows, owing to the characteristics of the control system.* Conclusions The experimental method used is convenient-from the standpoint of simplicity in apparatus requirements. The amount of computation in solving the algebraic equations is a disadvantage when treating a large volume of experimental data. Substantial refinement of technique and instrumentation would be necessary to reduce the experimental error. In particular, a well—regulated power supply would be important in maintaining steady readings. The humidity-control system should allow for more exact temperature regulation, since temperature fluctuation may be a major cause of erratic results. More recent work with the method shows consistent ap- Psarance of a slight curvature of a logarithmic plot of the current-voltage data. Hence, it is perhaps an over-simpli- fieation to represent these data by a straight line. Detailed discussion of the ionic-mobility results will be reserved for the section of this thesis immediately following. N” *The reader is referred to Brittain (1954) for a detailed description of the system. . —. ”if"- DISCUSSION OF THE CONCENTRIC-CYLINDER CORONA DISCHARGE \ AND ION IC MOBILITY Two additional current-voltage expressions for the con- centric cylinder discharge will be presented and compared with. Parsons' equation (1). A critical corona-gradient-r: equation for the same discharge will be considered. The experimental ionic-mobility results of the preceding seCtion will also be discussed in the light of modern gaseous elec tronics .-x--::- The Concentric-Cylinder Corona Discharge C u. rrent-Voltage Equa tions . In discussing the current- VOltage relationship von Engel (1955) states a criterion for taking space charge into account in deriving the electric potential distribution between concentric cylinders: when the sIEDace charges between the cylinders become of the same 0 I'der. as the surface charges on the electrodes, space charge muSt be considered. With ID the constant space-charge density, V 1116 inner cylinder potential (the outer cylinder grounded) \ '31- The critical corona gradient is the electric field strength, at r-ro, at which corona discharge starts. The term gaseous electronics refers to the physics of electrical discharges in gases. _ _ _ -17- '15:". g “" capacitance per unit length, the criterion is math- ..- ‘ £511? ' II ,0. volume yvc, (9) I op, 11:) the notation of the preceding section, Fun? 1/ W2 1n(R/ro). (10) For example, with V = 12 statvolts, r0 - 2xlO'2 cm., RIl 1 cm, 1n( R/ro) 2’ 4, space charge may be expected to have notable influence when P'L’ 0.5 statcoulomb/cm.3, or when the number of elementary charges N Q! 109 charges/cmf5 l Von Engel proceeds with his derivation using Poisson's ”nation. The current-voltage expression which results is very COrnplicated. Therefore von Engel assumes that R(21/k )%ln(R/ro)/Vo (<1, and he obtains approximately L i = kVo(V-Vo)/R21n(R/ro), (11) in the notation of the previous section. He further comments that when V>>Vo, empirically 1 0C V(V-Vo), rather than ' V0(V~vo). For radii r>> r0, the electric field intensity vectob E is given by V E = (21/k)% F/r. (12) The conditions of the corona tests of this thesis do not satisfy the approximations made in deriving equation (11). There-f‘ore it is impossible to evaluate the suitability of aqua"sicm (11) on the basis of the experimental data. Cobine (1941) and Thomson and Thomson (1953) give the theoretical current-voltage relation 1 = 2kV(V—VO)/R2 1n (R/ro). (15) ~18? __ _ equation is also deduced by Parsons (1924), but it : flied into the form of his equation (1). '1?" 7 Equation (15) may be written in the form v = [R2 1n(R/ro)/2k] (1/v) + v0. for positive corona, listed in Table I of Appendix A. resul t s agains 1: TABLE 2 . (14) Equation (14) predicts that a plot of V against i/V will yield a straight line, permitting evaluation of k and V0. This procedure may be illustrated with the data of Test No. 7, The for k and V0 from equation (15) and those from Parsons‘ equation (1) appear in Table 2. Ionic mobility is plotted relative humidity, for both equations, in Figure 5. IONIC L’iOBILITIES (k) AhD CORONA STARTING VOLTAGEs (v0) GIVEN BY EQUATIONS (1) AND (15) FROM DATA OF TEST NO. 7, POSITIVE CORONA, TABLh. I 01“ APPENDIX A \ Equation (1) Equation (15) PS rcent Re lative umidity Vo-ze k-xv-w V o k 56 '7 .16 454 9 .50 1210 \ 60 5.86 571 9 .40 954 \ )\ 95 6.58 552 10.0 815 *V0 is given in kilovolts. seek is given in cm.2/statvolt-sec. vi 5': ‘5 '. ! . .-. --.;_-_- ...... - --.... a -- ... -20- '.§ ; . .. ' ,. 1' . :34 Ltion (15) yields results for k about 2.5 times the 2' , l“v5eptable values given by Parsons' equation (1). Equation (1) may be written 1/0 - V(V-Vo)/i(V1-V), (15) and equation (13) may be stated as I R2 1n (R/ro)/2k - V(V-Vo)/i. (16) If V(V—Vo) is plotted against i(Vl-V) for equation (15), and V(V-Vo) against 1 for equation (16), straight lines intercept- ing the origins should be obtained. Figures 6 and 7 show that this is essentially true on the basis of data from Test No. 7, positive corona, Table I of Appendix A. Equation (15) departs from the straight line at higher values of V(V-Vo) and i(Vl-V). Figure 7 indicates that an equation of the form i.a:V(V-Vo), such as (15), represents the current-voltage relation. The mobility results, however, give evidence that the proportionality is probably over-simplified. Meek and Craggs (1955), Loeb, and von Engels discuss the atomic and molecular processes in electrical discharges at considerable length. Photoionization, recombination, attachment and detachment, ionization and excitation by impact and light emission are among the processes known to occur. These will not be taken up here, but they are mentioned to .point out the complexity of the electrical discharge. This complexity is a barrier to the development of more adequate theory than the foregoing. o ,_ ,; ’lflritical Corona Gradient. Cobine, and Thomson and —# .p“ give a semi-empirical equation for the electric old strength E0 at the inner cylinder r I: ro necessary to hater-t: the corona: E0 = so + 9/(ro)% (kv./cm.). (17) Then V9 will be given by v0 = Eoro 1n(R/ro). (18) Von Engel states that in the absence of a theory of breakdown in non-uniform fields it is impossible to calculate V0 and E0 from atomic data, and implies that experimental determination is the only approach at present. He cautions that ac curacy of measurement of V0 is restricted by its dependence upon surface roughness and chemical composition 0f the wire, as well as the polarity. consideration of the Measured Ionic Mobilities of the Corona Discharge Experiment T116 relation between the drift velocity v of an ion through a gas in the field direction and the field strength E defines the mobilities k through v - 1:13. (19) To obtain a satisfactory theoretical expression for the iOnic mobility k which would allow its calculation from atomic and mo lecular data is very difficult. Relationships have been d~erived on the basis of classical kinetic theory, but the 1b predictions always disagreed with observed facts in ..24- some manner. In recent years markers in gaseous electronics have attacked the problem with quantum theory and with modern Inwasuring techniques, but no generalized theory has been advanced. Consequently the following discussion will be largely qualitative. Influence of Humidity Upon Lobilities. Experimentally, the apparent ionic mocility for air decreased as relative humidity increased (see Figures 5 and 4). Tyndall (1958) attributes this effect to the polar nature of water molecules. Loeb found that the presence of polar impurities prompted formation of clustered or complex ions. Sometimes the congiex ions are of a charge specific nature, nmaning that a specific chemical reaction takes place. Loeb states that the robility may decrea§§_or increas§_depending upon the gas and impurities. Apparently, in the case of water vapor in air, the clus- ter ions have sufficiently lar e collision radii to effec- tively lower the apparent ionic nobility. The Effect of Gas DeLsity on mobility. Ehe corona dis- charge experiments of tnis tLesis were carried out under essentially constant pressure conditions of 1 atmosphere. Since temperature was not held constant, variations in air density occurred. The ratio of {as dersitieS/qual is P2401 5y 111/33, (20) where T1 and T2 are the absolute temperatures. Phe density variations are summarized in Table 5, based 3 the temperature .oaomaam>m pod one; when .Ho>oH hanHESQ 30H pd hpmmcoo nww.+.ao>oa hpfiofiesn swan pm hpflmdoo MH< .Ahpflso on on soxmpv pmop do>H0 mo Hopoa hquHES£ 50H pa hpfimdoo aHm|?.Ho>oa hpflwaeofi Eoflvoe pm mpflmcov sad .hpwoflezn o>fipmaoa pdooaom 000.0 00 000.0 00 000.0 00 000.0 H0 000.0 00.0 000.0 00 500.0. 00 000.0 00 000.0 00 00.H 00.0 **** *$** 500.0 00 **** **** 000.0 00 00.0 00.0 5 550.0 50 500.0 00 550.0 50 000.0 H0 000.0 00.0 . Aw 000.0 00 500.0 00 000.0 00 500.0 H0 50.0 00.0 H 000.0 00 000.0 00 500.0 00 500.0 00 00.H 00.0 as... 35.0 ,3 84 no mead g 08; mm 36.0 004 he..." 80.0 mm 80.0 we 08.0 mm 3.0.0 3 $6 004 .... ‘ {\0Q\ .m.m (\NK .m.m $90K .m.m HQ\\0Q\ $0.0 Taov 7&3 mwe snopoo 0>prwoz , wCoaoo o>HpHmom NOHN .. m. mowpwm befimnoa nH< on m .BZWEHmMmNm m0m NHHWZWQ mH¢ .0 qu<fi :' Loeb states that k is inversely proportional to the den- ;‘31ty of gas molecules. In the light of this, comparison of Table 5 with the mobility plots of Figures 5 and 4 may explain (within experimental error) the smaller rate of decrease of mobility with respect to humidity at higher humidities noted in most of the experiments. In such cases the air density at the high humidity level is usually appreciably less than that at the low and medium levels. Differences in Mobilities of Positive and Negative Ions. Negative ion mobilities were found to be higher than the positive. These results are in agreement with those of other experimenters. Loeb describes the "aging" effect which contributes to this mobility difference. He mentions experiments with room air, where initial positive ions had the same elevated mobi- lity difference. He mentions experiments with room air, where initial positive ions had the same elevated mobility of 1.8 cm.2/volt—sec. as the negative ions. However, if the positive ions aged for a few hundredths of a second, their mobility changed sharply to the normally observed value of 1.4 cm2/volt sec. Apparently the mobility change took place in a single act of addition in much less than 10'2 second. Experiments show that in dry air the aging process occurs in less than 1.4 milliseconds, and aging may be delayed by addi- tion of water vapor. The amount of delay depends upon the “ng'ef water vapor. From this one might expect the attitire and negative mobilities to differ less in air of Ilfuigher humidity.- Von Engel attributes the mobility difference in air to a strong tendency of oxygen molecules to attach electrons, whereas this does not occur for nitrogen molecules. As a result, sufficient electrons remain free to show a slightly elevated mobility. The Variation in Mobility with the Corona Wire Radius. The results of the corona experiment showed a tendency for the mobilities to run higher for smaller wire radii (see Figures 3 and 4). There seems to be no cause to expect this on the basis of present theory of gaseous electronics. It seems better to leave this phenomenon unexplained, since it may well arise from failure of Parsons' equation, with its purely classical character, to represent the true physical situation. General Discussion. The agreement of the corona experi- ment findings with the results of others serves to bolster confidence in the work of this thesis. The concentric cylinder discharge is an indirect method of mobility measurement; for more accurate measurements direct methods are recommended. Loeb discusses several direct meth- ods of mobility measurement in considerable detail. -20.. diameters '31 and D2, is . D1 (1(Dl)-Q(D2) = F(D)d.D . (21) D2 The size-frequency curve, F(D), generally does not 1 ,4. J- norms l dist; iou tion out rather a logarithmic- 1...: SD :23 ornal distri “ution. The equation for t c log-no rmc 1 distribution is l l (ln D lr d )2/”(ln\/N.A., (25) where.A\is the wavelength of the illuminating light, and N.A. is the numerical aperture of the objective. A 45X objective with N.A. . 0.85 was used, and for )\= 5500 Angstroms, two lines separated by a distance of z “.../0.6 micron could be resolved. Hence, two particles whose adjacent sur- faces are separated by a distance much less than z will be incorrectly taken as one larger particle. The resolving power in this situation can be increased by use of an oil immersion objective with substage illumination just suffi- cient to fill the aperture of the objective. Resolving power will be an important restriction when a large proportion of the particles have diameters not much greater than 2. The method of analyzing particle size frequency data is quite convenient, and the parameters thereby determined fur- nish an economical means of expressing the particle size distribution for a given dust. The particle size distribution of a given dust is necessary for theoretical analyses of the charging and dynamics of dust particles. DETERMINATBON OF ELECTRICAL CHARGE ON DUST Knowledge of the magnitude of electrical charges on dust particles is important for evaluation of effectiveness of charging methods and for theoretical calculations. Methods for calculating and measuring electrical charge on dust were developed. Theoretical Maximum Charge per Unit Mass of Dust Charged in a Concentric-Cylinder Corona Discharge Ladenburg (1950) gives the maximum charge qo attainable by a spherical particle of radius a in an electric field of intensity E as qo = a [5K/(K+2)] a2, (25) where Arie the dielectric constant of the particle. Equation (26) holds provided a)>O.5 micron. E may be a function of position in the interelectrode space. From equation (21), an element of charge per unit mass of dust, de, is given by com - qo Fug) dD . (27) Since a = 3/2, and F(D) is expressed by equation (22), equation (27) becomes [\lnjo-ln d )2] E [5/(/(K+2)] “2 N e_ 2 (1n (YEW do A] (1% = ’ (28) _l_ 4(277)2 n ln 0% where N =}En is the total number of particles of all diameters per unit mass of dust. Dallavalle (1943) gives an expression for N, based on the log-normal size distribution, of the form log N = '- [log (ew )+ :5 log a + 10.362 (log 0- )2] (29) V g 8 ’ where 6 is the particle material mass density, andCMv is the volume shape factor. For spherical particlesOév =7R/6. Equation (28) must be integrated over all particle di- ameters to obtain 00 D 2 __ 1 .(ln D )2 E [5/(/(/(+2)] (12(EE) N e 2(11'1 C—g)2 d8 dB 430) Qinl O ; 442*”)2 lnog, ' For convenience, let B = E [3K/(K4-2fl- a: i/Mewfi 1n o-g, (51) and 32 : l/2(ln 0’8)? (32) Then 00 21(D/d) -21(D/d.)2 gm 2 a e n g .e s [n 8’] d[1n(D/d8§}. (:55) -oo Upon writing x = ln(D/dg), equation (55) becomes 00 OD ~-82x2+2x l/32 -(sx-l/s)2 l/s2 : Qn-B 6 dx IBe 6 dx =Be (’I'I')2/s.(34) ..w _w Fronlthe definitions (31) and (52), we have finally, 2 em = (1/4) E [SK/(M2)] a: N e 2(lno'g) . (35) -34- We shall make use of Qm in the following sense: The total (maximum) charge.AQ on an element of mass Am large enough to contain many particles, but small enough that the electric field strength may be considered constant over it is given by AQ= Qm Am. (36) Lowe and Lucas (1955) state that charged dust particles, owing to their low mobility, have a space charge effect con- siderably greater than air ions. Lowe and Lucas give the electric field strength E between concentric-cylinder elec- trodes with dust present as 2pSr 1 i +C e i E E = l O ———2—. (r+_l_-) k S 1‘ r (kpasa p 29b . (57) where p = 5k/(K42), S is the effeccive total surface area of dust per unit volume of air, and Co is a constant of in— tegration given by the condition r0 E dr = V, (58) R where V is the applied voltage. If 2pSr<3(1, as it is for the experiments herein con- sidered, equation (37) may be simplified by expanding the exponential term, giving E = [(21/k)(l+2pSr/5H-CC/r2 ] i (59) Q/me __. uffkftien (59) will now be applied to estimating q- ‘1 the to.tal charge per unit mass of dust contained between the cylinders. This quantity is given by Q‘qu qundm . (40) .lzhn .Iirdv- where d7‘is the volume element per unit length, equal to 2'n'rdr, and dm is the corresponding mass element 27Tr3'dr, when r, taken as a function of r only, is the mass of dust per unit volume of air. If f is assumed constant in the region between the cylinders, then from (35), ro q -{[1/2(R2-ro)] .[3K/(K+2)J d2 N 62(lno_8 )2 } Erdr. (41) R E as given by (59) must be inserted in (38) to evaluate Co. This leads to an integral which may be evaluated with the aid of elliptic integral tables such as those of Byrd and Friedman (1954). However, it is adequate and much simpler for the present work to neglect the term 2pSr/5 within the parentheses in (59). Hence, upon writing = (zi/k)%; A: . Oak/2i, (42 a,b) (38) becomes ro v = Eo (Ag + r2)%dr/r. (45) R . . The integration leads to -55- (v/Eo). - (16+ rim-(AS + R2? + (1/2)Ao m{-[(A§+R2)%+AOJ /[(A§+az)%-Ao]} + (1/2)».o ln{[(A§+r§)%-Ac:l /BA§+P§)%+AOJ}. (44) If we set x . rO/Ao; §=R/ro; A=V/Eoro, (45 a,b,c) then Ax = (1+x2)%-(1+§2x2)’$'-1ng + ln{[(l+§2x2’)%+1]/[( l+x2)%+l]} . (46) It remains to determine x, which contains A0 =(COk/2i)§, with-Aland E experime tally known. Equation (46) may be solved graphically from a plot of the right-hand member of (46) as a function of 1:. Then the intersection of a straight line through the origin with slope.[idetermines x. The quantity q can now be obtained by applying equation (41). We find e2(ln 0‘8)2 _. i q = {El/2(R2-rgfl . [BK/(Kir2fl d: N no) r0 ‘ (A§~+-r2)% rdr/r. (47) R Upon neglect of r3 compared with R2, we may define . 2 X: (1/2R2)Eo[3K/(/<+2)] d: N Juno—s) '(48) I ‘ _;_L_ (‘3 + r2)2 dre R Integration yields (2q/X) = roufi + rid-Rug + 122% 2 2 2 a 2 2 1} -(Ao/2)ln{ [ (A0 + a )+R]/[(Ao + R ) 43]} ~(AE/2)ln{ [ (Ag + r§)%-ro]/[(A§ + r§)%+ro]} ,(50) 01‘ q = (XrE/zxz) {2:(1 + x2)%. gm + §2x2)% -ln [(\/1+€212 +§x>/(1/1+x2+x)1} . (51) With x given by equation (46), q may be immediately calculated. Measurement of Total Charge per Unit Mass of Dust Theory of Measurement. The electrical charge Qc on a system of known capacitance C may be determined by measuring the potential V, through the relation QC - CV. .(52) Since the potential arises from an electrostatic charge, a low-drain instrument must be used. A vacuum—tube electrometer is convenient and has adequate charge sensitivity for the systems studied. The system capacitance may be determined by measuring the rate of charge leakage through a known resistance Rs, as -58- ~5hnwn in Figure 8. A charge is placed upon the system by contact with the battery (E) and a voltage reading is selected Contact -—e> C i_________‘ E P —4ll|l|—-‘ ”r i K\\~—__;”/,-———-Electrometer Figure 8. The charge leakage capacitance measurement circuit. for time t equal to zero. A series of time-voltage readings are then taken as the charge decays through the resistance Rs. A straight line of slope —l/RSC should be obtained when the logarithm of voltage is plotted against time. The known resistance Rs must be large enough to allow timed measure- ments but small compared with the electrometer leakage resist- ance. C is then given by c - t/Rs 1n (VG/Vt), (53) where V0 and Vt are potentials at t-O and t=t respectively. The Dust Charge Measuremggt Apparatus. Figure 9 is a schematic diagram of the dust charge measurement circuit, and the assembled apparatus is shown in Figure 10. A Keithley model 210 electrometer was used. Thin aluminum disks of 10.7 centimeters diameter were used for dust collection. Steel-Screen Cage Detachable Collector \ Plate I .\ / Electrometer \\ y/ Figure 9. The dust charge measurement circuit. To make a charge measurement a disk was clamped in place inside the steel-screen cage (see Figure 9), which shielded the disk from stray electric fields, but allowed dust to reach it. The cage was held in the dust cloud to collect a sample. After the potential was recorded, the disk was removed with tweezers, as shown in Figure 11, and the amount of dust collected was determined by weighing on an analyti- cal balance. The total charge per unit mass q was given by q - Qc/mc: (54) where me is the mass of dust collected. Experimental Investigation An experiment was conducted to evaluate the reliability of the charge measurement method. Its results were compared Figure 10. The charge measurement apparatus. A. Electrometer. B. Screen cage with disk in place. C. Connecting coaxial cable. Figure 11. Removal of a dust-coated disk from the cage. -41- _%fi those predicted by equation (51): and equation (41) With 'E assumed constant [see equation (56)]. Experimental Method Apparatus. The laboratory chambers of the corona-dis- charge experiment were used. A concentric-cylinder ionizer with re - 1.50 x 10'2cm., R = 3.65 cm., and a wire length of 25.4 cm. was used for dust charging. The wire was of solid steel; the outer electrode material was aluminum. The charger was operated at a positive potential of about 14 to 18 kv., with 1 held constant at 1.89 x 104 statcoulomb/cm.-sec. A plane screen grid was placed normal to the axis of the charger at its outlet end. The grid was held at a positive potential of 10 kv. The positive grid, or "ion-trap", allowed the charged dust to pass, but prevented free air ions from reaching the collector disk and causing erroneous readings. The collector-disk cage was located about two feet from the charger. It was placed away from the direct aerosol stream to prevent erosion of the dust deposit. Electrometer voltages were continuously recorded by a strip-chart recorder con- nected to the electrometer output. A schematic diagram of the apparatus is shown in Figure 12. Procedure. Micronized talc dust with d8 = 5.74/u.and CE = 2.80 was used. This dust material has a mass density 6- 2.8 gm./cm:5 and a dielectric constant kf- 6.5. A series of dust exposures was given to each collector .ucoawaodxo pcoaohdmwoe owadno on» how Eeawwflp oHpmaonom .ma oadwfim %% II. II II II. II. II. nopoauao> poemfimom haadsm hl\.eeoq hamasm hamnsm owdpao> owapao> magnum 9050 w IIII mam aoeom m n Hm +. . I .+ A Ti LN. I! h p I_ ,; _ pofimfiaaa< aouoafiw M aovaooom.lli .o.Q Iliaouoanpoon We noacaz sopoapao> . pnoSoadmsoz m condufiesaw 90% m consumfimom .__ In. Emfindnooz aces“; 533330 I 92.8me $3 , I I I I I I J 7| I II II I. II'IIIII‘IIIIII owao one sea eouooHHooIIJ/Iifiv . + _ _ s3 mam AI efiofiofl _ JJI+IV a + I_ _ II +. IEflmaw _ _ _ I I _ fiesta oa IIuUI II _ _ _ de$W\h(\ \\\\\\\\\N. _ nomamno dam pmsa mesa 8H o 328 I_ F IIIII L nonseno dam ll'llllllllllll aonadno mcwpmsm -43- disk. In this manner sufficient dust was accumulated to make the deposit weighing error small. The voltage vy.was allowed to stabilize at each exposure, and then the charge was drained off through a known resistance, R The latter procedure 8. resulted in a decay curve on the strip-chart for capacitance determination. The quantity q was then calculated with a modified form of equation (54), n q = 2 CT n0} VY/mc, (55) Y 'Y=l where no is the total number of exposures, C Y.is the measured capacitance at exposure Y} and mo is the mass of dust collected. Charge measurements were made at a dust feed rate of 0.641 gm./sec. and an average charger—air velocity of 915 cm./sec. These figures give a value for f of about 1.65 x10"5 gm. dust/cm.5 of air. Twelve exposures were given to each disk. Measurements were made at relative humidities in the neighborhoods of 40 and 60 percent. Positive-ion mobility data were obtained for the charger by the methods of the corona experiment. The data were cor— rected for air density variation and adjusted to give the accepted dry-air posigive-ion mobility. ' Since assumption of constant B in equation (41) leads to a trivial integration, E as given by equation (12) was in- serted to obtain -44- 2 q . (1/4; {mi/kfi’ [SK/062)] d2 N 92(lncrg) } (56) The ionic mobility information was used with equations (51) and (56) to obtain the approximate variation in the predicted q, as a function of relative humidity, for comparison with measured q values. Discussion of Results The charge measurement results and a plot of ionic mobil- ity against relative humidity are given in Table IV and Figure A, respectively, of Appendix A. Results of q cal; culations using equations (51) and (56) appear in Table I of Appendix B. - The error in the average measured qL values was estimated at about i 6 to 8 percent, which agreed approximately with the standard error of the mean qav: s, given by n s - E (qav «1J2 n(n-l) L= l e NIH (57} The outer electrode of the charger invariably became heavily coated with dust during the exposure series with a given disk. Some systematic error in comparing the measured and calculated q values may be expected as a result. A slightly non-linear response of the recording system with respect to the electrometer was noted. This was an important error source in the capacitance measurement. It should have little effect upon the static voltage readings, since fre- quent meter-recorder comparisons were made. A sample graphical solution of equation (46) for x is given in Figure A of Appendix B. The measured and calculated q values are plotted as functions of relative humidity in Figure 13. The measured values were in general much higher than the calculated. The discrepancies are probably a result of lowered ionic mobilities in the presence of dust and im- purities in the charger atmosphere. It is also possible that some additional charging effect may have existed in the I vicinity of the ion trap. This could be tested by varying the ion trap potential. Equations (51) and (56) predicted an increasing charge effect with increasing humidity, in direct opposition to the observations of this experiment and those of Hebblethwaite (1952)- Figure B of Appendix B shows the predicted decrease in q as k increases. The values for q predicted by equations (51) and (56) differ only slightly. This indicates that for some applica- tions assumption of constant E in the interelectrode space would be an adequate approximation. Conclusions With careful instrumentation, the method of measuring charge will be quite satisfactory. The theoretical charge equations do not account for reduction in charging effect with increasing humidity on the basis of ionic mobility. The shortcomings of the theory are -45- - I ' ' :II" I . _..I..--__--._._-..- .. -; :: '. : “5 I : ' . II 2 . -.. .. I 'I 3 .; : - .: : . I I I :' 5"? 1I-—-* "'4‘- r‘- -I- ~ ' --..-i .._._-.- -*- "I . . - -O I ' I g,“ I I i" . .E. . . - ----- run-m. -- "*““""'T" --~I“ _- - I3 '- - . : a : : i ! a 0 : - : ; I I I I ' ' 43 - . I J z . 3_ : II ; : I I I I .. :1" : ' : : I : I .n . r -r *--r- I ----- "~r-- "I r e—~- JI— v - ' - . ' I I ' f: - 7 III—II “‘1. ' I\T" I I 'II” T'" I --O' i I '__ 1 I\ ".‘I g I : "e" .1. r . 4E5- : : : I: I 2'” ' I . : : : :I":' ea , -... .. .-. .... .. a s a a a - "" I I i e ' a: ' I I I .‘E . -- ° I - - I- - ID I I i I g. I I I I ' : : m .. ---; ..- -—;- I ' ' .._-_L-_-;. In: I ‘ i : t : : . : : ' : . - : ' .I I . : : : : ' . L IE}, i s ; lo a 2 a , I _ . 5-; I - - I“ . 'I - """"" I 'I'” " "I'm —- 47-“ ‘5 I ' I ' I I I ' I : ' .52 II I I I i L I . ' I 4' ... _ ___.. ....EQMATI--N.(IPQ “a; ___. .- IS I “2““. ‘- —.-.-_-___1-_- TI’E“ +7 I “I .__... i z +5 #47 ewe a . ' I - ' I I : ' ' ' : ' : I I 1---- - 1'. ”I ...... .I . . .3. .. . .1" 1,--- I Io I I i i i I ' I (II : I 20 I I 4 i I ‘I SCI : I8C I 1.00 "Atmospheric R‘eIatTive 'Humi d‘iIty',"R§.H.' 4-? (fieré'er'Ith—M -_ g r ‘ I *”""'T“" I'm-t M“ ‘ .._T__.-_ --- I“ -I- T . _ I I ' - , I : . I P '- ur --rs. .The.-Iff.e.c .5. .of..a_tmp.sgheIriq..rela tive humidityupon. ‘7' "'; and 'hel gndtudes .f the tbtal cherge per unit; I nxa'ssi-of—dmstr-qj-ftaaer’x: u by x icrux ’rze'd‘taitc—du‘st‘ - _ --.-1..n:.a conCIn.tr_iQ-cy11 nder Ghanaer‘ia. aeamparieonaf I experimental meaerermehtI with predictions of E. :- : equations \5iqunp (06:). v ; ; I I . . I . I I . . .I ...__._1._;__ ......l.. ...I ._1.-_.. ........ I. .1- --L- L. .I:::. I I ' _I II 3' :I:.. I 1 I I a; . ii; ~47- ‘ ;'in part attributable to its cluesical nature,.apart ITItrup the more predominant effect of impurities in the inter- electrode space. ANALYSIS OF A SEMICYLINDRICAL ELECTRIC FIELD FOR CHARGED DUST PRECIPITATION. Ban (1955) performed laboratory experiments which indi- cated the effectiveness of an applied electric field for dust precipitation. The following study was undertaken to extend this concept to a semicylindrical field. Preliminary hxperimental Investigation A preliminary study was conducted with rows of beans planted in field plots. This was a qualitative study of the applied field under conditions less favorable than previous laboratory tests. Attasorb dust with d8 8 1.2Q/4, OE - 2.27 and. 6- 2.45 gm./cm.5 was used. Eguipment. A field crop duster supplied by Chemical Machines Limited of Winnipeg, Manitoba, Canada was used. It was fitted with a concentric cylinder charger having a wire length of 25.4 cm, a wire radius r0 - 1.50 x lO'2cm., and outer electrode radius R I 5.65 cm. Positive corona was employed throughout the test. The electric field "hood" was of semicylindrical form, with a length of 107 cm. and radius of 21 cm. The material was galvanized steel sheet, and it was uninsulated except at the edges. The semicylinder potential was a positive 18 kv. The semicylinder was mounted so that it passed over -49- the plant row as the machine moved forward. The duster is shown in Figure 14, and the position of the charger relative to the semicylinder is shown in Figure 15. Procedure. Bean plant rows were dusted and operating characteristics of the semicylinder were qualitatively noted. The dust charge per unit mass q was determined by the charge- measurement method. Results. In spite of the fact that the semicylinder was set close to the soil surface, slight air currents and the aerosol stream from the charger swept the dust cloud from the semicylinder before any appreciable precipitation could occur. It was impossible to hold the potential when the semicylinder touched the plants, which indicated that the plants act as grounded conductors under such circumstances. This obser- vation was tested further with a bean plant set in a metal can. A charge placed on the plant by an ionized air stream could be held if the plant and container were isolated, but if the plant and container were grounded the charge was im- mediately lost. Charge measurements gave q = 4500-: 500 statcoulombs/gm., with V Q{l4 kv. and i “1189 x 102 statcoulombs/cm.-sec. at 50 percent relative humidity. Theoretical Analysis of Dust Particle Behavior in the Semi- cylindrical Electric Field General simplifying assumptions made are that the plant row may be represented by a semicylinder (concentric with Figure 14. The Chemical Machines Ltd. duster. The conventional lateral dust distribution tubes were removed to allow mounting of the charger and semicylinder. Figure 15. The dust charger and the semicylinder. -51- _ Fat to the electric field semicylinder) and that the dust .Iymrticles obey Stokes' law. Space charge is neglected so that the electric potential distributions satisfy Laplace's equation. Analysis Assuming Concentric Cylinders of Infinite Extent. It is assumed that the problem may be represented by two concentric cylinders of infinite extent, as shown in Figure 16. This discounts edge effects, but greatly sim- plifies the analysis. The inner cylinder, r - a, represents the plant row at potential U(a) = O, and the outer cylinder, r = b, represents the semicylinder at U(b) - V. Figure l6. Representation of the applied field problem. The potential distribution satisfies Laplace's equation, VZU = o. (58) If the potential is a function of r only, in cylindrical coordinates V2U(r) = (l/r){d [r dU(r)/dr]/dr}= o. (59) Integration of (59) yields U (r) = 01 ln r+02, (60) p;- I [V 1n(r/a)] /ln(b/a). ffetric field intensity vector, E, is g ' E . - [V/r ln(b/a)] (2%); (6‘2) ‘ " ”T,the inner surface of the cylinder r = b is insulated s of a dielectric kfof thickness (b-h), then U1 - 05 in r + C4, (a E rgf h), (63) U2=C51nr+C6,(hér5b). (64) A~tr-a,U1-o;atr-h,U1-U2andE1-KE2; ' at r - b, U2 8 V. The solutions are U1 . v 1n(r/a)/[(1/K)1n(b/h) + ln(h,/a)J, (a 5 r e h), (65) U2 - v{1-[(1/K)1n(b/r)]/[(1/K>1n(b/h)+1n(h/afl} . (h f r f b),(66) E1 = - (vF/r2)/[(1/K)1n(b/h)+1n(h/a)], (a 5 r 5 h), (67) and E2 - —(v?/Kr2)/[(1/K)1n(b/h)+1n(h/a)], (h 5 r e b). (68) gnalysis Assuming Concentric Semicylinders of Infinite @53223. The problem may be represented as shown in Figure 17 (a), and solved by conformal mapping* as outlined by Churchill (1948). The solution is comparatively easy to obtain *Kober (1957) gives many conformal representations useful in treating such problems. U: f i U=O u (a) z - plane (b) w - plane Figure 17. for the region in the w — plane. This solution may be trans- formed to the z - plane by using the transformation z - ew to get . 00 “J U = (4V/7T) (r/a)n:-(r/a)'n;. sin n'B, (69) 2 (b/a)n -(b/a)'n n' n-l E where n' =(2n-l), l é (r/a) é (b/a), and O f 95 7T. Estimation of Charge on a Particle of Given Radius. It is justifiable to assume a uniform surface charge density for dust on the basis of Ladenburg's (1950) equation (29) and experiments by Splinter (1955). The particle surface area Sm per unit mass of dust material is given by Dallavalle (1945) as log Sm - log (%/€%)-log c1g — 5.757(log O'g)2- ('70) where 0% is the surface shape factor. For rounded particles ‘__— ag/CKV is about 6.1; for "worn" particles, 6.4; for "sharp" particles, 7.0; for angular particles, 7.7; and for spheres 6. Then the charge per unit surface area Qs is Qs = ‘l/Sm- Dallavalle gives the surface area Sp for a particle of star 3 as sp = 043 32. Hence, the estimated charge per particle qois qo‘ Q3 as 92' (71) diam- (72) Estimation of Time nequired for a Charged Particl Travel from the Outer to the Inter Cylinder. Stokes' gives the llmiEiL; velocity v for a force F, aLJ The parLicle till requir: a time it = tance dr. b from r = b to r = a is l.JLU x lo - ,arLlc.e at r=L, in a U \;I. bulb.) "lic; LL. tel-val a . dl/[Cod/LTFVDJ = 67177:) :OLL—iit’)l.’ll\n./ cfl/iiqo‘F. L travel witfl 1 Liver; by (62), (75) -55- plane. Here’I‘is the length of the semicylinder and vf its uniform forward velocity. It is assumed that the particle remains in the original plans, which denotes a still medium. Equation (75) represents a limiting case, since a large proportion of the particles will require less time to reach the depositing region. The Limiting Electric Potential VG Required for Complete Precipitation in Still Air. Examination of equation (75) shows that toC(l/D). hence, to approach 100 percent deposit- ing efficiency, vc - [57Tv7(b2-a2) Vf Sm ln (b/a)]/2q 043T dm, (77) where dm is the minimum diameter observed in particle size measurements. Equation (77) is based on the simplification that the surface which encloses all particles approximates the lateral surface of a frustum of a cone of altitude if. The axis of the cone is imagined to coincide with that of the cylinders, with the periphery of its base of radius b containing the leading edge of the semicylinder. The other base is of radius a, with its periphery on the inner cylinder in the plane of the semicylinder trailing edge. The conic surface moves with the semicylinder. The actual case will vary from the above depending on air turbulence and the manner of introduction of dust, and should be accounted for with a more appropriate mathematical model. -57- E}: I: -¢H;-analysis serves to illustrate application or some iV-the theory, methods and information developed in the _ preceding investigations of this thesis. GENERAL SUMMARY The Parsons equation (1) is suitable for use in designing experimental cylindrical dust chargers. It provides an indirect means of measuring ionic mobilities through study of the concentric-cylinder corona discharge. A direct mobility measurement method, however, would be preferable for more accurate work. Many of the ionic—mobility phenomena noted experimentally were explained in the light of modern gaseous electronics. The decrease in ionic mobility with increase in atmospheric relative humidity arises from the formation of cluster ions in the presence of the polar molecules of water vapor. The fact that negative air ions are more mobile than the positive is attributable to positive-ion aging effects and the non- existence of electron attachment to nitrogen molecules. The experimental variation of mobility with corona wire radius could not be explained, unless it perhaps arose from the classical nature of the Parsons equation. The log-normal frequency distribution was shown to describe all particle size distributions studied. The analytical and experimental methods of dust-charge determination were concluded to be satisfactory. However, the analytical expression does not explain the reduced charging effect at high humidity. Disagreement between -59- calculated and measured charges was attributed to greatly ' reduced ion mobilities in the presence of dust and imp ; purities in the interelectrode space. The usefulness of the measurement theory and methods 1 developed was illustrated with a simple analysis of a semi- ‘ cylindrical precipitating field. To overcome strong in- fluences of air currents, high though not impractical potentials would be required for its successful use. A much more detailed analysis would be necessary for proper estimation of the applied potential. APPENDIX A EXPERIMENTAL RESULTS APPENDIX A EXPERIMENTAL RESULTS TABLE I TABULATION OF DATA FOR EXPERIMENT ON CORONA DISCHARGE CHARACTERISTICS OF A WIRE COAXIAL WITH RESPECT TO A CYLINDER Explanation of Symbols and Units. 21. r0: Wire radius in centimeters. -2. R: Cylinder radius in centimeters. :3. R.H.: Relative humidity in percent. 4. 1: Current per unit wire length in microampereakentimeter. 5. V: Wire potential in kilovolts. I"6. C: Given in microamperes/centimeter-kilovolt. *2. V1, V 1 Given in kilovolts. b. p: Eactor in Equation (5) expressing enlargement of ionization region with increase of wire potential, given in centimeters/statvolt. 9. K: Apparent ionic mobility in (centimeters) /statvolt-second. * Parameters of Parson's equation (6). * * * Test 1e 'r'o"-"'6.82 x 10-2 R - 1.90 ' 1 Positive Corona RTHZ 21 64 92 i V i V i V 0.536 13.75 0.536 13.00 0.536 14.00 1.292 14.00 1.292 14.00 1.292 14.15 19.26 15.00 5.345 14.8 5.345 14.85 30.95 15.75 11.63 14.05 11.63 14.90 38.77 16.20 19.26 15.50 19.26 15.60 . 39.95 16.30 30.95 16.40 3d.’/‘/ 16.60 38.77 16.65 Test 1 continued. -52- TABLE I Continued Positive Corong R.H. 21 . 92 C 0.796 0.434 0. 73 V 17.2 16.9 17. v35 12. 12.5 12.6 0.0146 0.0154 0.0144 k 277 160 197 Nggative Corong R.H. 30 64 98 i V i V i V 0.536 13.50 0.536 14.00 0.536 12.05 1.292 13.60 1.292 14.15 1.292 13.15 19.26‘ 14.70 19.26 14.60 19.26 14.20 36.77 15.00 30.95 15.20 30.95 15.00 35-77 15.50 39.77 15.45 c 0.650 0,551 0.704 v1 15-4 16.0 15.7 vb 13.1 13,0 12.3 0.0292 0,0227 0.0200 k 453 16 338 Test 2. r0 - 6.35 x 10-3 R = 1.90 Positive Corong R.H. W2 6 97 i V i V l V 0.530 5.15 0.530 5.20 0.530 5 30 1.270 5.65 1.276 5.70 1.276 5.05 5.264 7.20 5.204 7.30 5.264 7.60 11.50 7.30 11.50 7.50 11.50 /.70 19.04 0.30 19.04 6.55 19.04 6.90 30.60 9.65 30.60 9.00 30.60 10.30 30.33 10.35 30.33 10.65 30.33 11.20 - 63- TABLE I Continued Test 2 continued. Positive Corona R.Hg ’42 97 c 1.99 1.76 2.05 V1 13.5 13.1 15.2 Vb 3.67 3.76 3.67 0.00111 0.00116 0.000944 k 566 532 497 Negative Corong R.H. 42 63 96 i V 1 V i V 0.530 5.05 0.530 4.90 0.530 4.55 1.276 5.40 1.278 5.40 1.278 5.05 .26 6.65 5.26 6.60 5.264 6.60 11.50 6.60 11.50 6.90 11.50 7.10 19.04 7.40 19.04 7.60 19.04 6.05 30.60 6.50 30.60 6.60 30.60 9.30 36.33 9.00 36.33 9.35 36.33 10.15 c 1.34 2.09 2.63 v 9.61 11.6 14.1 Vi 3.57 3.69 3.46 , 0.00169 0.00137 0.00102 k 52 735 692 issi_3- , r0: 1.50 x 10—2 R = 2.36 U Positive Corona , R.H. 32 63 93 A 1 V i V 1 V A 0.541 7.60 0.541 7.60 0.541 6.05 1.302 6.30 1.302 6.35 1.302 6.65 5.386 10.10 5.366 10.30 5.366 10.70 11.72 10.30 11.72 10.45 11.72 10.95 19.40 11.50 10.40 11.65 19.40 12.40 31.19 12.10 31.19 13.50 31.19 14.2 J 39.07 13.65 39.07 14. 0 39.07 15.30 1 -54- TABLE I Continued Test 3 continued.’ Positive Corona R.H. 32 63 gr; 0 1.36 0.630 1.13 v 16.1 14.2 18.3 V35 6359+ 609# 5.90 _ 0.00235 0.00315 0.00184 k 551 337 370 Negative Corona .59 R.H. 32, 95 1 V 1 v 1 V 0.541 7.60 0.541 7.55 0.541 7.15 1.302 6.30 1.302 6.15 1.302 7.60 5.366 9.65 5.366 9.60 5.366 9.90 11./2 10.00 11.72 10.00 11.72 10.20 19.40 10.90 19.40 11.05 19.40 11.50 31.19 12.30 31.19 12.50 31.19 13.15 39.07 13.00 39.07 13.35 39.07 14.20 V1 15.4 14.1 17.9 V0 6.40 6.91 5.44 0.01254 0.00315 0.00163 622 451 n52 Test 4. r0: 2.67 x 10‘2 R - 3.65 Positive Corona R.H. 27 61 96; i V i V i V 0.541 10.95 0.541 11.20 0.941 11.00 1.302 11.00 1.302 12.15 1.302 12.00 5.306 14.65 5.306 15.20 5.306 15.50 11072 15005 11072 1}.)0 11072 150k! 19.40 16.90 19.40 17.55 19.40 16.15 31.19 19.30 31.19 20.15 31.19 20.90 39007 20070 39.07 21. DO :3," 007 22elIO Test 4 continued. TABLE I Continued Positive Corona R.H. 27 01 96 c 1.04 0,977 O -1 VO 8.46 6.35 5 1+ 0.00239 0.00221 0 0195 k 450 br04 negative Corona 3 R.H. 23 59 9* i V i V i V 0.541 10.00 0.541 11.05 0.541 10.35 1.302 11.30 1.302 11.05 1.302 11.50 50;)UU 13.00 9.300 lfl‘q'A/O )ojOU l /Q\O 11.72 13.70 11.72 14.5 11.72 1;.15 QLI‘O :1.)th 130110 10.05 l/‘OL‘FO lI 05.0 :ol/ 1101- / 31019 10065 31.19 1‘;er 370U/ 10. 00 9.07 20. 35 C 0.089 1,07 0 12 vJ-O 7'.()9 U04U ’/ 0.00300 0.002111)” 0 225 k 556 550 1‘29 Test 20 r . 0.3) x 10‘3 R = 3.65 Positive Corona {1.17102 :36 ()1 , 97 i V i V i V 0. 530 0. 40 0. 530 0. 70 0. 530 0.00 log, log/U 'IQUS 102(k) U01; 5. 204 10. 95 5. 204 11.10 5.204 11.00 11.)0 1102) llojU lloU) ll. )0 12.00 19.04 13.10 1,.04 13. 65 15.04 14.30 30.00 10.15 30.00 10. 05 30.60 17.05 38.33 17.70 38.33 10. 20 30.33 10.05 TABLE I Continued Test 5 continued. Positive Corona 61 RoHo 26 1/ C 2.06 1.90 1.79 V1 26-6 28.9 30.0 Vo 4.24 4.40 4.47 0.000490 0.000493 0.000474 k 881 802 Ne ative Corona R.H. 36 97 1 V 1 V 1 V 0.530 0.35 0.530 0.35 0.530 0.20 1.278 7.35 1.278 7.35 1.278 7.40 5.284 10.40 5.284 10.70 5.284 11.15 11.50 10.05 11.50 11.00 11.70 11.40 19.04 12.05 19.04 13.20 19.04 13.00 30.00 14.90 30.00 15.70 30.00 10.30 38.33 16.20 38.33 17.15 38.3 18.00 c 1.01 1.04 2.18 V 23.8 23,1 30.0‘ ' v: 4.30 3.93 4.10 0.000023 0.000572 0.000407 k 1070 885 959 Test 6. r = 0.82 X 10'2 R = 4.92 Positive Corona R.H. 37 60 * i V i V i V 0.542 10.30 0.542 19.15 1.300 19.50 1.306 19.95 5.400 20.70 5.400 23.30 11.75 20.80 11.75 20.80 19.40 22.20 19.40 22.20 31.27 23.45 31.27 23.35 39.17 24.45 39.17 24.50 -67- TABLE I Continued Test 6 continued. Positive Corong R.H. 37 00 * c 0.453 0.514 v 25.4 24.9 v}, 10.8 19.2 0.0102 0.0152 k 730 1250 Negative Corona R.H. 35 00 * 1 V i v i V 0.542 19.2’ 0.542 19.00 1.300 19.00 1. 00 19.85 5.400 22.30 5. 00 22.70 11.75 21.00 11.75 21.05 19.46 22.30 19.46 22.30 31.27 23.65 31.27 23.00 39.17 24.00 S g.515 0.499 2 «7 25.6 vi 18.4 10.4 0.0121 0.0123 k 991 982 *Data could not be obtained because of failure of the par— ticular wire-cylinder combination to function Satisfactorily at higher humidities. Test 7. r0- 1.50 x 10-2 TABLE I Continued R = 4.92 Positive Corona 6O R.H. 30 93 i V i V i V 0.522 10.10 0.522 10.10 0.522 10.50 1.266 11.35 1.206 11.50 1.206 12.00 5.157 15.80 5.157 10.15 5.157 10.95 6.528 16.90 6.520 17.30 6.520 10.05 13.00 21.15 13.00 21.05 13.00 22.00 20.05 24.60 20.05 25.15 20.05 26.20 20.57 27.00 20.57 20.45 29.80 29.45 29.20 29.55 C 0.000 0.035 0.697 V 42.1 0.4 44.0 V0 7.10 5.00 0.58 0.000746 0.000612 0.000695 k 434 371 52 Negative Corona i V i V i V 0.522 9.25 0.522 9. 0.522 9.35 1.206 10.00 1.200 10.05 1.206 11.00 5.157 15.30 5.157 15.50 5.157 16.25 6.526 16.40 6.528 16.50 6.52 17.40 13.06 19.90 13.06 20.50 13.06 21.50 10.70 21.05 15.65 21.80 14.40 22.15 C 0.001 0.000 0.530 31 33.0 30.3 30.3 0 0.03 5. 2 5.42 0.000967 0.000041 0.000843 k 422 403 324 Test 8. r0- 6.35 x 10'3 TABLE I Continued R - LI"092 Positive Corona R.H. 30 61 296 i V i V 1 V 0.494 7.30 0.494 7.45 0.494 7.05 1.216 0.00 1.216 9.10 1.216 9.60 4.070 13.55 4.070 14.10 4.070 14.00 6.175 14.70 6.175 15.35 6.175 16.00 12.35 19.15 12.35 19.90 12.35 20.55 10.96 22.70 18.96 23.60 10.96 24.20 25.13 25.00 25.13 20.70 31.34 20.65 C 1.01 1.05 0.956 V 60.4 40.4 49.6 V0 3-32 3-90 3-92 0.000195 0.00020 0.000277 k 605 12 455 Negative Corona R.H. 30 50 96 1 V i V 1 V 0.494 7.30 0.494 7.15 0.494 7.10 1.216 0.00 1.216 0.65 1.216 0.90 4.070 13.40 4.070 3.55 4.070 14.30 6.1/5 14.55 6.175 14.00 6.175 15.70 12.35 10.30 12.35 10.05 12.35 1;.00 10.29 21.05 17.51 21.30 15.99 21.00 C 1.40 0.926 1.02 V1 56.5 41.1 46.4 V0 2.95 3.56 3.70 0.000237 0.000330 0.000290 k 600 536 522 -70- TABLE II ' PARTICLE SIZE MEASJRLHLHT DATA Dust Attasorb CCC Diluent* Copper Sulfate** Particle Number Percent Number Percent Number Percent Diameter in Smaller in Smaller in Smaller Group Group Than Group Than Group Than (microns) Upper Upper Upper Limit Limit Limit <1 1.62 35 10.35 39 11.57 2 0.99 1.62- 3.24 264 88.46 101 65.28 62 31.53 3.24— 6.48 32 97.93 67 85.16 69 05-52 6.48- 9.72 7 100.00 13 09.02 36 03.25 9.72-12.96 0 -——— 25 96.43 13 09.65 12.96-16.16 0 —-—— 5 97.91 9 94.08 . 16.16—19.44 0 —-—— 5 99.39 6 97.04 ! ‘ 19.44—32.40 0 —-~— 2 100.00 4 99.01 ‘ >32.40 0 -——- 0 ———- 2 100.00 I Total 1 Particles 338 ~--- 337 ———- 203 --—- ” Measured * CCC Diluent is 97.73% calcium carbonate, with the remain- ing percentage consisting of miscellaneous compounds. ** This copper sulfate dust contained a small amount of inert ingredient. -71- TABLE III GEOMETRIC MEAN PARTICLE DIAMETERS (dg) AND GEOKETRIC STANDARD DEVIATIONS ((7%) FOR SLVEHAL DUSTS Commercial Nature d Designation of 02 of Dust (microns) Dust Attasorb Micronized** 1.20 2.27 clay CCC Dilucnt 97.73% 2.73 2.29 calcium carbonate Copper Sulfate Some inert 4.65 2.26 ingredient present Standard* Some inert 5.75 2.78 Copper ingredient present Sulfate Micronized* Hydrated 3.74 2.60 Talc magnesium silicate * From data obtained by Ban (1955). ** The term ”microniaed" 1neicates undergone a special fine grinding treatment. that the material nus Averages -72- TABLE IV CHARGE MEASUREMENT DATA Relative q (statcoulombs/gm.) .umSG paoSHHQ ooo hog G sac» mmoa onqm mo moaofippdm no mowdunoohon o>wudeEdo pmSHamd Q myopofiwac maowundg pmsc mo poam 4 .m ohswwm Q hepoEaHO cane mama pcoohom .m.mm mm Om Or Ow on 0H #41 Ho.u r-i (.0 0 W . -74- \ Ilull... . . ..... l..| .Jnu w o (suoaotm) - q ‘Jeqawerq exorqaeg APPENDIX B THEORETICAL RESULTS . . _ .... .. . _ 4w “2- ;g ...—:ca—u. ,- - .- "53(411. .. TABLE I CALCULATED VALUES FOR q Dust: Micronized Talc. Percent Equation (56) Equation (51) Relative q* x q ‘ 9 Humidity (X 102) . 0 2610 -3.54 2720 20 > 2650 -3.70 2720 I 7 1 80 2750 . -4.05 2820 100 2760 -4.25 2860 *q given in statcoulombs/gm. U : o SOIL SURFACE U : o. . h I,” Figure 0. A sketch of the electric field lines in the space .' between the field semicylinder and the plant row, ‘ based upon the solution (69) by conformal mapping. 9 . .l' l ... O O 0 O I 110' 10. ll. Ban, Nguyen T. Contributions to Electrostatic Dusting: , 1. Application of Polarography to Dust Deposit Evald uation, 2. Effect of Ionized Current Intensities and Effect of Shielding on Dust Deposition. M.S. thesis. Michigan State University, 1955, 92 numbered leaves. 'Brazee, Ross D. Brittain, Robert W. Byrd, Paul F., and Friedman, Morris D. « G REFERENCES CITED‘ Unpublished ‘Bowen, Henry D. Electrostatic Precipitation of Duets for Agricultural Applications. Unpublished M.S. thesis. Michigan State University, 1951, 76 numbered leaves. Bowen, Henry D. Electric and Inertial Forces in Pesticide Application. Unpublished Ph.D. thesis. Michigan State University, 1955, 150 numbered leaves. Deposition Evaluation For Agricultural Dusting Research. Unpublished M.S. thesis. Michigan State University, 1953, 97 numbered leaves.' ' The Effect of Plant Surfaces on Pesticidal Dust Deposition. Unpublished M.S. thesis. Michigan State University, 1954, 150 numbered leaves. Handbook of Elliptic Integrals for Engineers and Physicists. Springer-Verlag, Berlin, 1954, 555 pp. Churchill, Ruel V. Introduction to Complex Variables and Applications. McGraw-Hill Book Company, Inc., 1948, 216 pp. Cobine, James D. Gaseous Conductors. McGraw—Hill Book Company, Inc., New York, lst ed., 1941, 606 pp. Micromeritics, the Technology of Dallavalle, J. M. Pitman Publishing Company, New York, Fine Particles. 1943, 428 pp. Losses in Agriculture. Fracker, S. B., and others. June 1954, United States Department of Agriculture, 190 pp. Hampe, Pierre. Le Poudrage Electrostatique des Vegetaux. Reprint of the proceedings of a conference of La Ligue de Defense contre les ennemis des Cultures. Paris, 1947, 19 pp. Translated by Peter Hebblethwaite. I" e #1- 12. 15. 14. 15. 16. 17. 18. 19. 20. 21. 22. 25. -31- Hebblethwaite, Peter. The Application of Electrostatic Charging to the Deposition of Insecticides and Fungicides on Plant Surfaces. Unpublished M.S. thesis. Michigan State University, 1952, 117 numbered leaves. Kober, H. Dictionary of Conformal Representations. Dover Publications, Inc., 2nd. ed., 1957, 208 pp. Ladenburg, R. Untersuchungen uber die physikalischen Vorgange bei der sogenannten electrischen Gasreinigung: I Teil: Uber die maximale Aufladung von Schwebeteilchen. Annalen der Physik. 4(1950), pp. 865-897. Loeb, Leonard B. Basic Processes of Gaseous Electronics. University of California Press, Berkley and Los Angeles, 1955, 1012 pp. Lowe, H. J., and Lucas, D. H. The Physics of Electro- static Precipitation. Static Electrification, British Journal of Applied Physics, Supplement No. 2, Institute of Physics, London, 1955, pp. 40-47. Meek, J. M., and Craggs, J. D. Electrical Breakdown in Gases. Oxford University Press, London, 1955, 507 pp. Parsons, Samuel R. The Current-Voltage Relation in the Corona. Physical Review. 5 (May‘l924), pp. 598-607. Smith, Richard K., and others. Agricultural Statistips— 1954. United States Department of Agriculture, 1954, 607 pp. plinter, William E. Deposition of Aerial Suspensions of Pesticides. Unpublished Pn.D. thesis. Michigan State University, 1955, 164 numbered leaves. Thomson, J. J., and Thomson, G. P. Conduction of Electricity Through Gases. Volume II. Cambridge University Press, London, 5d Edition, 1955, 608 pp. Tyndall, A. M. The Mobility of Positive Ions in Gases. Cambridge University Press, London, 1958, 95 pp. von Engel, A. Ionized Gases. Oxford University Press, London, 1955, 281 pp. J..v\ _ . “I \ \- :SE B‘a‘lL’! JUN-l 14:99; a 9.130% I», M'Tllfillfllllfllfllfllfiflflfllflilflfliflfflllll'ES