OVERDUE FINES: 25¢ per w per item RETURNING LIBRARY MATERIALS: Place in book return to remove charge from circulation records ‘8‘ w ' H": :W-h - ‘ M4. ~13ngch STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES: A MATHEMATICAL MODEL FOR PENETRATION FROM DROPLETS AND ITS EXPERIMENTAL EVALUATION By Jose Miguel Leon A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Horticulture 1980 ABSTRACT STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES: A MATHEMATICAL MODEL FOR PENETRATION FROM DROPLETS AND ITS EXPERIMENTAL EVALUATION By Jose Miguel Leon A model has been developed for penetration of growth regulators from small droplets when applied as concentrate, low volume sprays. The model assumes that penetration occurs in two phases: a) from time of application until the droplet solution becomes saturated and b) from saturation until the droplet dries. Other assumptions were tested experimentally: penetrant concentration in the leaf will be considered zero at all times; concentration is uniform throughout droplet; droplet has the shape of a segment of a sphere; the contact angle decreases as the droplet dries but the interface area remains constant; rate of evaporation of water from the droplet is constant; movement of water from the droplet through the cuticular membrane is negligible; the cuticular membrane has a defined permeability coefficient. The model allows predictions as to the effect of droplet size, concentration, dose, interface area and rate of droplet drying on penetration. Penetration per unit dose is predicted to be greater for drOplets of lower concentrations and contact angles. Increasing the rate of droplet drying is predicted to reduce penetration significantly. The model renders penetration independent of droplet size. The model was tested experimentally by applying naphthalene— Jose Miguel Leon acetic acid (NAA) to COWpea leaf discs and using auxin-induced ethylene evolution as a measure of NAA penetration. Two experimental systems were used for NAA application: a) droplets produced with a microsyringe were hand-applied to leaf discs and b) the primary leaves of plants were sprayed with a laboratory apparatus equipped with a rotary porous sleeve nozzle, capable of producing variable spray spectra and of delivering a range of spray deposits. Experimental results generally confirmed the predictions of the model: penetration was more efficient, for a given NAA dose, from solutions of lower concentrations and from droplets with lower contact angles. Increasing the relative humidity (to delay droplet drying) increased NAA penetration. However, penetration was greater, for a given NAA dose and concentration, from smaller droplets, in disagreement with the predictions of the model. However, penetration occurred after the droplets had dried while the model assumes no further penetration from the residue. Smaller droplets resulted in greater contact between the residue and the leaf surface providing for greater penetration from the residue. In memory of my father from.whom I learned the attitudes and values that have made this work possible 11 ACKNOWLEDGMENTS My deep gratitude to Dr. M. J. Bukovac for his dedicated efforts at teaching me how to be a good scientist and for the many hours spent together in stimulating discussions. Thanks are due to Drs. F. G. Dennis, J. A. Flore, C. M. Hansen and G. R. Hooper for serving on my guidance committee. Gratefully acknowledged are the valuable suggestions made by Drs. L. F. Wolterink, C. A. Petty, C. Y. Wang and H. Murase. My special gratitude to my wife Carmen who never failed to give me her unqualified support and gracefully accepted the many sacrifices that my graduate studies imposed on our family. 111 TABLE OF CONTENTS LIST OF TABLES O O O O O O O C O O O O 0 v1 LIST OF FIGURES O O O O O O O O O O O O Vii INTRODUCTION . . . . . . . . . . . . . 1 SECTION I STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. III. A MATHEMATICAL MODEL FOR PENETRATION FROM DROPLETS Abstract. . . . . . . . . . . . . . 4 Introduction. . . . . . . . . . . . . 4 Materials and Methods . . . . . . . . . . 6 Results . . . . . . . . . . . . . . 14 Discussion . . . . . . . . . . . . . 18 Literature Cited. . . . . . . . . . . . 26 SECTION II STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. IV. EFFECTS OF CONCENTRATION, DROPLET SIZE, RELATIVE HUMIDITY AND SURFACTANT CONCENTRATION ON PENETRATION OF NAPHTHALENEACETIC ACID Abstract. . . . . . . . . . . . . . 28 Introduction. . . . . . . . . . . . . 28 Materials and Methods . . . . . . . . . . 29 Results . . . . . . . . . . . . . . 32 Discussion . . . . . . . . . . . . . 41 Literature Cited. . . . . . . . . . . . 44 SECTION II STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. V. EVALUATION OF SPRAY VARIABLES ON NAPHTHALENEACETIC ACID PENETRATION INTO COWPEA LEAVES SPRAYED WITH A ROTARY POROUS SLEEVE NOZZLE Abstract. . . . . . . . . . . . . . 47 Introduction. . . . . . . . . . . . . 47 Materials and Methods . . . . . . . . . . 49 mmflxs. . . . . . . . . . . . . . 53 Discussion . . . . . . . . . . . . . 60 Literature Cited. . . . . . . . . . . . 63 iv APPENDICES Page Appendix A--Methods of Describing Spray Size Distributions . 66 Appendix B-—Geometrical Relationships . . . . . . 74 Appendix C--Equations to Calculate Interface Area . . . 77 Appendix D—-Relationship Between Total Interface Area, Number of Droplets, Droplet Diameter and Total Spray Volume . . . . . . . . . . . 81 Table A1. A2. LIST OF TABLES Page SECTION I Key to symbols and units. . . . . . . . . 9 SECTION II Relative humidity (at 20 0C) of air in equilibrium with different H2504 solutions and approximate drying time of 0.5 ul droplets of NAA solution on the adaxial surface of cowpea leaf discs . . . . . . . 33 Ethylene evolution (nl-disc-Lhruloug"1 NAA) from cowpea leaf discs in response to either 0.6 or 1.5 ug NAA. The residue was washed off after the droplets had dried . 38 SECTION 111 Mass Median Diameter (MMD), Sauter Mean Diameter (SMD) and relative interface area between the spray and the leaf surface for various spray spectra. . . . . 51 APPENDICES Some commonly used mean diameters . . . . . . 69 A spray size distribution . . . . . . . . 70 vi LIST OF FIGURES Figure Page SECTION I 1. Schematic representation of a droplet on a leaf surface . 10 2. Decrease in contact angle with time for 0.5 ul droplets of distilled water and of Xr77 solution on the adaxial surface of a cowpea leaf. Points represent experimental values while lines represent calculated values. . . . l6 3. Decrease in tan(O/2) with time for 0.5 ul droplets of distilled water and of X—77 solution on the adaxial surface of a cowpea leaf and the corresponding regression lines . . . . . . . . . . 16 4. Photographs of two 0.5 ul droplets on the adaxial surface of a cowpea leaf taken at 30 sec intervals. A through J: left droplet, distilled water; right droplet, 0.1 ml-litre'l x~77 . . . . . . . . . 20 5. Calculated QT as a function of dose and concentration . 20 6. Calculated QT as a function of rate of droplet drying . 22 7. Calculated QT as a function of the contact angle. . . 22 SECTION II 1. Ethylene evolution from cowpea leaf discs in response to 1, 2, 4 or 8 five ul droplets of NAA solutions of varying concn . . . . . . . . . . . 34 2. Ethylene evolution from cowpea leaf discs in response to 6 draplets of 0.5, 1, 2 or 5 ul of NAA solutions of varying concn . . . . . . . . . . . 37 3. Ethylene evolution from cowpea leaf discs in response to 6 droplets of 0.5, 1, 2 or 5 ul of NAA solutions of varying concn. Abscissa represents the calculated relative interface area between the droplets and the surface of the discs . . . . . . . . . 37 vii Figure Page 4. Ethylene evolution from cowpea leaf discs in response to 0.75 ug NAA applied in six 0.5 ul droplets of a 250 mg-liter’1 NAA solution in environments of varying relative humidities . . . . . . . . . 4O 5. Ethylene evolution from cowpea leaf discs in response to 8 droplets of 0.5 or 1 pl of a 250 mg-liter'1 NAA solution and containing increasing concn of X—77. Addition of the surfactant resulted in changes in surface tension, contact angle and interface area . . 40 SECTION III 1. Ethylene evolution from the primary leaves of 10-day—old cowpea plants in response to spraying with NAA solutions of increasing concn. Spray deposit was 2 ul-chZ. Bars denote standard error . . . . . 55 2. Ethylene evolution from the primary leaves of 10-day—old cowpea plants in response to spraying with increasing deposits of NAA solution (125 mg°liter'1). Bars denote standard error. . . . . . . . . . . 55 3. Ethylene evolution from the primary leaves of 10-day-old cowpea plants in response to spraying with NAA (250 mg-liter-l) at a rate of 2 ul-cm.‘2 and with various spray spectra . . . . . . . . . 57 4. Ethylene evolution from the primary leaves of 10-day-old cowpea plants in response to spraying with NAA (250 mg-liter’l) at a rate of 2 ul-cmF and with various spray spectra. The relative interface area was calculated on the basis of the SMD (Table 1) . . . 57 5. Ethylene evolution from the primary leaves of 10-day-old cowpea plants in response to spraying with NAA (250 mg-liter’l) at a rate of 2 ul-cmfz. The spray residue was removed from the leaves.at the indicated elapsed times after spraying. Bars denote standard error . . . . . . . . . . . . . 59 6. Ethylene evolution from the primary leaves_3f 10-day-old cowpea plants in response to 0.125 ug-cm NAA sprayed in various combinations of droplet size, NAA concn and spray deposits. . . . . . . . . . . 59 viii APPENDICES Figure A1. Frequency distribution of spray spectrum described in Table Al O I O O O O O O O O O 0 A2. Cumulative frequency distribution of spray spectrum described in Table A1 . . . . . . . . . Bl. Segment of a sphere . . . . . . . . . . C1. Interface area between the spray and the leaf surface as a function of the SMD and for various contact angles. . D1. Relative number of droplets and interface area between the spray and the leaf surface as total spray volume and droplet diameter are changed . . . . . . . D2. Relative changes in droplet diameter and number of droplets required to maintain a constant interface area as the total spray volume is reduced . . . . . D3. Relative changes in interface area as both the SMD of the spray and the total spray volume are changed . . . ix Page 72 73 76 80 87 89 91 Guidance Committee: The journal—article format was adopted for this dissertation in accordance with departmental and university requirements. Section I was prepared and styled for publication in Pesticide Science. Sections II and III were prepared and styled for publication in the Journal of the American Society for Horticultural Science. INTRODUCTION Interest in concentrate, low volume (LV) spraying is increasing in the fruit industry. LV spraying allows the use of more compact, less costly equipment and lower spray volumes than dilute application, resulting in reduced energy use and application costs. LV spraying requires delivery of the compound to the target plant in a concentrated solution in a spray with a small average droplet diameter. By increasing the surface-to-volume ratio of the spray, adequate coverage can be obtained with limited spray volumes. Because the total spray volume is reduced, concentration of the compound must be correspondingly increased to insure delivery of an equal dose. Response to foliar-applied chemicals is localized and good coverage is essential. Growth regulators are systemic compounds and must be absorbed by the foliage and translocated to the reaction site to produce the desired effect. With LV spraying, foliar penetration occurs from small discrete droplets of concentrated ' solutions which provide a limited interface area between the spray and the leaf surface, in contrast with dilute application where virtually the entire leaf surface is covered with spray solution. In addition, small droplets dry more quickly and reduce the time for penetration. On the other hand, with LV spraying, the concentrations used are higher, increasing the driving force for diffusion through 1 2 the cuticular membrane and presumably compensating, in part, for the decreased interface area and reduced penetration time. Little is known about the dynamics of foliar absorption of growth regulators under these conditions. The quantitative relation- ships among spray variables (dose, concentration, droplet size, interface area, droplet drying time) have not been critically evaluated and their combined effect on foliar penetration remains to be documented. Field studies on performance of growth regulators applied as concentrate, LV sprays are difficult to evaluate. Spray generation equipment currently available produces a wide (and often unknown) range of droplet sizes, making evaluation of this variable almost impossible. In addition, the physiological responses, such as fruit thinning or prevention of preharvest drop, used to evaluate performance of growth regulator sprays are inadequate to assess penetration peruse. They are the integrated result of a number of steps (efficiency of the spray generation and delivery systems, retention by the foliage, wettability of the leaf surface, penetration and translocation to the reaction site) which cannot be factored out and from which penetration is impossible to isolate. The objectives of this research were: a) to develop a mathematical model for penetration of growth regulators from small droplets which formalizes the relationships among the variables controlling penetration, and b) to evaluate the model utilizing auxin-induced ethylene evolution as a measure of naphthaleneacetic acid penetration and using two experimental systems which allow for critical control of experimental conditions. 3 Developing a better understanding of the dynamics of penetration from small droplets will aid in establishing the conditions under which response to growth regulators when applied as LV sprays can be maximized. SECTION I STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. III. A MATHEMATICAL MODEL FOR PENETRATION FROM DROPLETS STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. III A MATHEMATICAL MODEL FOR PENETRATION FROM DROPLETS Abstract A model was developed for penetration of growth regulators from small droplets when applied as concentrate, low volume sprays. The model assumes that penetration occurs in two phases: a) from time of application until the dr0plet solution becomes saturated and b) from saturation until the droplet dries. Assumptions were made on the rate of droplet drying and on the geometry of the droplet during drying which were confirmed experimentally. The model allows predictions as to the effect of droplet size, concentration, dose, interface area and rate of droplet drying on penetration. Penetration per unit dose is predicted to be greater with lower concentrations and with droplets having lower contact angles. Increasing the rate of dr0plet drying should significantly reduce penetration, while droplet size should have no effect. Introduction Systemic compounds (mainly herbicides and growth regulators) must be absorbed by the tissue before the desired response can be induced.l-7 Within limits, the response to growth regulators increases with the quantity absorbed by the leaf tissue. The cuticular membrane (CMD represents the first barrier to 1,5,8-11 absorption of foliar-applied growth regulators, the driving force for penetration being the concentration gradient across this membrane.1’12’13 S Penetration of chemicals through the CM has been extensively studied using a number of techniques and these results have been reviewed, particularly in terms of identifying and characterizing the environmental and cuticular factors influencing penetration.4’7-10 That movement of materials through the CM occurs by diffusion is 10’14’15 Indirect evidence (such as temperature and widely accepted. light effects) supporting metabolic involvement in cuticular penetration probably indicates an effect on the physical properties of the CM§ or an indirect effect on the concentration gradient across the CMI’6 rather than an effect on the penetration process. Further, movement across the CM represents the rate limiting step in the overall process of foliar absorption of growth regulators.1 Herbicide selectivity and resistance have been attributed, in some instances, to differential permeability of the CM to the penetrant.9’11’14’16’17 Foliar penetration of a growth regulator can be viewed as a physical process of movement of a compound from a droplet through a membrane (CM) into a compartment (leaf). Known laws of diffusion18 apply to this system. We will distinguish between penetration through the CM (the rate limiting step) and absorption (the overall process resulting in uptake of the material by metabolism of the plant and ultimately in a physiological response) as suggested by Sargent.6 Growth regulators are usually applied as dilute solutions 5,19,20 in the form of a spray until the foliage is completely covered with a continuous layer of spray solution. Most studies on foliar penetration of systemic compounds have followed penetration from large droplets or reservoirs, which were designed to reproduce 6 conditions fimrpenetration under conventional dilute spraying. However, information generated with these experimental systems is often of limited value in understanding penetration of growth regulators from low volume (LV) sprays, where the compound is delivered to the plant in a spectrum of very small droplets of concentrated solutions. Spray volume, coverage and penetration time then become limiting. Herein, we propose a mathematical model for penetration of compounds from small droplets formalizing the relationships among the different variables (drop size, concentration, dose, interface area, droplet drying time) which control the process. The model is concerned with the spray as deposited on the leaf surface, independently of the engineering aspects of spray generation and delivery. Materials and Methods In developing the proposed model, the following assumptions were made, some of which were tested as detailed below. Assumptions a.- Concentration of the penetrant in the leaf will be considered zero at all times. Penetration through the CM is rate limitingls and foliar absorbed chemicals are rapidly metabolized and/or bound through conjugation and other mechanisms21 or translocated to other organs22 and are, therefore, removed from the pool. b.— Concentration is uniform throughout the droplet, i.e. there are no concentration gradients. c.— The droplet retains the shape of a segment of a sphere 7 during drying. For the drOplet sizes and contact angles encountered in spray application, this is a reasonable approximation.23’24 d.- As the droplet dries, the contact angle decreases at a rate determined by the rate of evaporation of water from the droplet, but the interface area between the droplet and the leaf surface (SO) remains constant. e.- The rate of evaporation of water (k), expressed as volume evaporated per unit surface area of droplet per unit time, remains constant during penetration. Although the rate of droplet drying for pure water increases with decreasing droplet diameter,25 increasing concentration of the solute in the droplet as it dries will reduce the vapor pressure and minimize this effect. f.- The CM will be viewed as a uniform membrane with a defined permeability coefficient (D) which implicitly accounts for CM thickness.12’13 g.- Movement of water from the droplet through the CM will be viewed as insignificant. Penetration of pure water from droplets is negligible26 and the presence of solutes in the droplet decreases its water potential, further restricting movement through the CM. h.- Penetration of the solute through the CM occurs in two stages: a) from time zero until the droplet solution becomes saturated and b) from saturation until the droplet dries, during which time solute concentration remains constant (Cs) and further evaporation results in precipitation of the material. Mathematical relationships and derivations. As the droplet dries, its volume decreases while the interface area between the droplet and the leaf surface remains constant. Thus, concentration of the chemical in the droplet changes due to a decrease in volume of the droplet and penetration into the leaf. The mathematical derivations of the various elements of the model is described in the next paragraphs. a.- Change in droplet volume and contact angle (see Table 1 and Figure 1). (1) dV = -kSAdt 2 w 2 SA n[ 4 -+11] Since h _ .Ji. w/2 tan 2 1rw2 SA = 20 4cos-——- 2 2 3 _ n w 2 _ NW 0 3 O (2) V———-6 h[3 ——4 +h] -—48 [3tan -—2 + tan —-2:| Then 1Tw3 dV = 4 9 d0 32cos -§- substituting in equation (1) O t w d0 8k 29 ' dt cos -- 2 0 0 9 Table 1. Key to symbols and unitsz. Symbols Description Units D Permeability coefficient of cuticular membrane cm-s- Total quantity of material in droplet at time ug t=0 Time 5 TS Time from t=0 until concentration in the droplet 3 reaches saturation T Time from t=0 until water in droplet evaporates 3 completely k Rate of evaporation of water from droplet cm-s-1 V Volume of droplet at time t ml VO Volume of droplet at time t=0 ml VS Volume of droplet at time t=TS ml 0 Contact angle of droplet at time t degrees 00 Contact angle of droplet at time t=0 degrees 08 Contact angle of droplet at time t=TS degrees SO Interface area between droplet and leaf surface cm SA Surface of droplet exposed to air cm QT Total quantity of material transferred through ug CM from time t=0 to time t=T Ql Quantity of material transferred through CM Hg from time t=0 to time t=TS Q2 Quantity of material transferred through CM pg from time t=TS to time t=T -1 Concentration of material in droplet at time t ug-ml 0 Concentration of material in droplet at time t=0 ug-ml-i S Saturation concentration of material ug-ml 2Units and their symbols were selected in accordance with the International System of Units (SI). See "Standard for metric practice", American Society for Testing and Materials, 1976. 10 ——-- Cutlcular unambnmo Figure 1. Schematic representation of a droplet on a leaf surface. 11 Which, after integration, gives 0 = O __ 4k (3) tan -§—- tan —§9- -;—-t b.— Derivation of Q1. dQ1 -DSGCdt d(CV) = CdV + VdC O. O H II Integrating T s V C dt =— (4) ln[—-3-VO Co] DSO V 0 nwz So 4 Substituting 8 and V (equation (2)) into equation (4) and O integrating 12 P D 2k tan3-9-S- (5) .1EL._£§_.= 2 YQA C = L31.— 8 VS M C = 0 VO Substituting into equation (5) D 1:39 D+2k 08 an 2 Q1=M1" c so 0 tan.-—9—- 2 h d c.- Derivation of Q2' dQ2 = DSOCsdt Q2 = DSOCs(T-Ts) Substituting (T-TS) for its value as a function of the contact angle (equation (3)) = .21.... G9s = Diem .23.. Q2 ”Secs 4k ta“ 2 16k tan 2 13 d.- Derivation of QT' QT = Q1'sz D 3 O D + 2k c tan 2 «Dc 3 T Co 3 00 16k 2 tan ———- 2 L _ from which tan -%f—-can be eliminated. The result is an equation (6) Y“-1 + K Y3“.l — K - o 1 2 Where y..._M_-m_ M = D + 2k 3D /3 =._L__JEL_ 2_9Q_ K1 3 Cs tan 2 /3 =._L..JEL_ 2_§Q_ K2 3 Cs 3 + tan. 2 Equation (6) can be solved numerically by determining the roots for fogl. Since /3 (7) tan ._@.S._ = Ya _C.:.Q_ tan _Q.Q_ 2 c8 2 Q1, Q2 and therefore QT can be calculated. 14 Contact angle measurements. Contact angles of 0.5 ul dr0p1ets of distilled water and various solutions of NAA, KOH and a surfactant (X-77, alkyl aryl polyethoxy ethanol and free fatty acids, Chevron Chemical Corp., San Francisco, CA 94104) were calculated, using Mack's formula,24 by recording the height and the width of the image of the droplets projected with a horizontal microscope. Photographs of droplets on leaf surfaces were taken using a Wild M5 stereo microscope equipped with an automatic exposure control unit. To increase contrast, Congo Red dye (0.05%) was added. Although observations on the drying of dr0p1ets on a number of leaf surfaces were made, only data for the upper surface of cowpea (Vigna unguiculata (L.) Walp. subsp. unguiculata cv. Dixielee) are reported since this plant material was used in subsequent work on the experimental evaluation of the model (Sections II and III).27 Results Contact angle and interface area. The decrease in contact angle with time was followed for a number of 0.5 ul droplets of distilled water and different solutions of NAA, KOH and X-77 on the upper surface of lO-day-old cowpea leaves. The decrease in contact angle of 0.5 ul droplets of water or of X-77 solution (0.1 ml-litre-l, surface tension 34 mN-m-l) was measured during drying (Figure 2). These are representative of the results obtained with all the dr0p1ets measured. The decrease in tan ~9—-with time and the regression lines 2 calculated from the data points (Figure 3) represent the 15 Figure 2. Decrease in contact angle with time for 0.5 ul droplets of distilled water and of X977 solution on the adaxial surface of a cowpea leaf. Points represent experimental values while lines represent calculated values. Figure 3. Decrease in tan(O/2) with time for 0.5 ul droplets of distilled water and of X277 solution on the adaxial surface of a cowpea leaf and the corresponding regression lines. 16 125 r 0.1 ml. nun-I x-n comm ANGLE (doom) 8 3 ‘T—'—y¥ O 25 —- O o .. l_ l 1 l o coo woo 1500 was (a) Figure 2 1.?- 1.o - 0'0! 5 O 0.5 - 0.1 nil-mm“ x-n o — L . I . l 0 son woo mo mas (s) Figure 3 17 experimental values of equation (3). For all 20 droplets measured (data not presented) the correlation coefficient was always greater than 0.99, indicating good agreement between the experimental results and those predicted by equation (3). The large differences in slope among these lines reflect differences in the value of 00 and therefore w, depending on the presence of solutes in the droplets. When R was calculated from equation (3) there was good agreement among data for different droplets. The average k for all 20 droplets was 2.4 X 10"5 (SD = 0.216 X 10-5) cm-s—1 with no clear trend as to the effect of the solutes present. The interface area between the droplets and the leaf surface remained constant until the droplet was almost dry (Figure 4), at which point measurement of the width of the droplet became difficult. Predictions of the model. To calculate QT as a function of different spray variables, values for the fixed parameters must be assumed. Unless otherwise specified, the following values, estimated from preliminary experiments, were used: k = 2.5 X 10.6 cmos-l; O = 70°; D = 10"6 cm-s-l; C8 = 1500 ug-ml-l. Although the actual 0 values of some of these parameters are difficult to establish,12 the usefulness or validity of the model is not limited since it deals with trends and qualitative comparisons of the relative changes in penetration as the values of the variables are altered. Equation (6) indicates that Y is independent of drop size (V0). Therefore, tan -%§- (equation (7)) is also independent of V6. For a given set of parameters, both Q1 and Q2 and therefore QT are also independent of Va. A defined dose delivered in a given concentration and total spray volume will result in a constant amount 18 of chemical penetrating the CM, independently of droplet size. The slopes of the lines of predicted QT values for solutions of different concentrations (Figure 5) decrease with increasing concentration, indicating that for a defined dose the amount that penetrates the CM is greater for lower concentrations. By virtue of the previous paragraph, these results are independent of droplet size. Increasing the rate at which the droplets dry reduces dramatically the amount of chemical penetrating the CM (Figure 6). S and therefore penetration increase as contact angle 0 decreases (Figure 7). Discussion The observed change in contact angle with time closely paralleled the predicted values (Figure 2) obtained from equation (3) on the basis of the known parameters 00 and V0 from which w (Appendix C) and k and T (equation (3)) were calculated. This agreement was evaluated quantitatively by calculating the correlation coefficient for equation (3) (Figure 3) which in all cases was highly significant (r>0.99). The change in contact angle is a function of k and of the change in geometry of the dr0p1et. The good fit found between the experimental and the calculated values supports the validity of the assumptions on droplet drying and on which the development of the formal expression of this relationship was based. The reduction in contact angle with time has been studied;28 when 00 was lowered by addition of a surfactant the contact angle decreased more rapidly, 19 Figure 4. Photographs of two 0.5 ul dr0p1ets on the adaxial surface of a cowpea leaf taken at 30 second intervals. A through J: left droplet, distilled water; right droplet, 0.1 mlolitre‘l x—77. Figure 5. Calculated QT as a function of dose and concentration. 01mg) 20 Figure 4 g .— c. - taming-Nun“ l, -n° 0 810‘60-0" 3__ I .2.sx1r‘un-s" 2.. 1+— 0.5 +- L . 1 _ ”no. Illa" m " '- 250 " " 0.5 1 2 DOSEUag) Figure 5 u}— 21 Figure 6. Calculated QT as a function of rate of droplet drying. Figure 7. Calculated QT as a function of the contact angle. 01 (#9) 0mm 0.5 r- 0.1 __ 4.7 P 43 - 4.5 I- 4.‘ - 22 M I: 5 fig C. - “comm-.4 Co I EON-Mn" 0° 8 70° 0 :10'9cm-o" l i 1 l #1 10 so 100 150 n 109(cm-o") Figure 6 u '5»o c. ammo-um." c. - songIm-l D 8 10-6 cut-3'1 k - 2.5x 10'9cm-o" b- 1 50 70 W 110 P - CONTACT ANGLE (dogma) Figure 7 23 as was the case in our work (Figure 2). However, the method used28 did not allow for measurements of the change in volume or in the geometry of the droplet. The accuracy with which contact angles were measured in our work was limited by the experimental techniques used. Mbre critical determinations of the contact angle29 might have resulted in greater differences between the predicted and the observed values.The failure to detect any effect of the presence of solutes on the value of k may have been due to insufficient sensitivity in measuring contact angles, as well as to the low solute concentrations used. However, the overriding goal of our proposed model is to develop a better understanding of the dynamics of penetration of systemic compounds through the CM from small droplets. The ultimate validity of the model rests on the agreement (or lack thereof) between the model—predicted trends in penetration and those measured experimentally. However, penetration is the most difficult component of the overall process to measure accurately (see Sections II and III)27 and is therefore the limiting factor in our ability to critically evaluate the model. Errors in the assumptions used may be of a magnitude below the level of detection allowed by current techniques for measuring penetration. Further refinements in the definition of the other components of the model (such as droplet geometry and rate of evaporation) may therefore be superfluous. The contact angle of the water droplet decreased more rapidly during the later stages of droplet drying than the model predicted (Figure 2). Agreement between the predicted and the observed values was better for the droplet containing X977 (Figure 2) 24 presumably because the surfactant minimized the increase in the rate of evaporation of water with decreasing droplet diameter.25 The model renders QT independent of droplet size for a defined dose delivered in a given concentration or total spray volume. A change in the surface-to—volume ratio of the spray as a result of the change in droplet size (all other variables remaining constant) produces an identical relative change in S and in S . O A The increase in penetration which would result from a greater Se is compensated for by an equivalent increase in evaporation of water from the droplet, with no net effect on the magnitude of QT' A decrease in contact angle however (Appendix C), results in a proportionately greater increase in Se than in SA and therefore in enhanced penetration (Figure 7). The predicted effect of concentration (Figure 5) can be rationalized on the basis that a lower concentration would result in a greater Ts and therefore in a relative reduction in the amount of chemical that is precipitated out of solution during the period in which concentration is saturated. The opposite effect (a reduction in T8) results from an increase in the rate of droplet drying and a corresponding decrease in QT' A number of models have been proposed for cuticular 12’13’30’31 In an effort to simplify the penetration of materials. mathematical treatment, the explicit or underlying assumptions (such as constant volume and concentration of the donor solution) fail to recognize the uniquely dynamic conditions under which penetration of a chemical from a droplet through the CM.takes place. The model proposed here incorporates some of the complexity of the system into 25 the definition and subsequent formalization of the relationships vamong the different variables involved. The model better defines the conditions under which LV Spraying of growth regulators is likely to result in improved performance. Addition of a surfactant to increase the interface area and spraying under conditions which would delay drOpIet drying (such as high relative humidity) are but two of the factors derived from the model which should result in increased penetration and greater efficiency of spray applications. 10. 11. 12. 13. 14. 15. 16. 17. 18. LITERATURE CITED Bukovac, M. J. In Herbicides. Physiology, Biochemistry, Ecology, Volume 1 (L. J. Audus, ed.), Academic Press, New York, 1976, p. 335. Crafts, A. S.; Foy, C. L. Res. Rev. 1962, 1, 112. Hull, H. M. Res. Rev. 1970, 31, 1. Kirkwood, R. C. In Herbicides and Fungicides. Factors Affecting their Activity (N. R. McFarlane, ed.), Burlington House, London, 1976, p. 67. Mitchell, J. W.; Linder, P. J. Res. Rev. 1963, 2, 51. Sargent, J. A. Ann. Rev. Plant Physiol. 1965, 16, 1. Sargent, J. A. In The Transport of Plant Hormones (Y. Vardar, ed.), N. Holland Publishing Co., Amsterdam, 1967, p. 365. Ebeling, W. Res. Rev. 1963, 3, 35. Hull, H. M.; Morton, H. L.; Wharrie, J. R. Bot. Rev. 1975, 41, 421. Robertson, M. M.; Kirkwood, R. C. Weed Res. 1969, 9, 224. Sargent, J. A. In Herbicides. Physiology, Biochemistry, Ecology, Volume 2 (L. J. Audus, ed.), Academic Press, New York, 1976, p. 303. Davis, D. C.; Mullins, J. S.; Stolzenberg, G. E.; Booth, G. D. Pestic. Sci. 1979, 10, 19. McFarlane, J. C.; Berry, W. L. Plant Physiol. 1974, 53, 723. Foy, C. L. Agric. Food Chem. 1964, 12, 473. Franke, W. Ann. Rev. Plant Physiol. 1967, 18, 281. Holly, K. In Herbicides. Physiology, Biochemistry,_Ecology, Volume 2 (L. J. Audus, ed.), Academic Press, New York, 1976, p. 249. Schbnherr, J.; Bukovac, M. J. Physiol. Plant. 1978, 42, 243. Simon, W. Mathematical Techniques for Physiology and Medicine, Academic Press, New York, 1972. 26 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 27 Bukovac, M. J. Symposium on Growth Regulators in Fruit Production. In Acta Hort. 1973, p. 69. Williams, M. W. Hort Rev. 1979, 1, 270. Bukovac, M. J.; Flore, J. A.; Goren, R. HortScience 1976, 11, 389. Donoho, C. W.; Mitchell, A. E.; Bukovac, M. J. Proc. Amer. Soc. Hort. Sci. 1961, 78, 96. Johnstone, D. R. In Pesticide Formulations (W. Van Valkenburg, ed.), Marcel Dekker, Inc., New York, 1973, p. 343. Mack, G. L. J, Phys. Chem. 1936, 40, 159. Zung, J. T. Envir. Letters 1975, 8, 283. Ketel, D. H.; Dirkse, W. C.; Ringoet, A. Acta Bot. Neerl. 1972, 21, 155. Leon, J. M. Ph.D. Thesis, Mich. State Univ., East Lansing, 1980. Sands, R.; Bachelard, E. P. New Phytol. 1973, 72, 69. Guckel, W.; Synnatschke, G. Pestic. Sci. 1975, 6, 595. Becher, P.; Becher, D. In Pesticidal Formulations Research. Physical and Colloidal Chemical Aspects. Advances in Chemistry Series No. 86, American Chemical Society, 1969, p. 15. Price, C. E. In Herbicides and Fungicides. Factors Affecting their Activity (N. R. McFarlane, ed.), Burlington House, London, 1976, p. 42. SECTION II STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. IV. EFFECTS OF CONCENTRATION, DROPLET SIZE, RELATIVE HUMIDITY AND SURFACTANT CONCENTRATION ON PENETRATION OF NAPHTHALENEACETIC ACID STUDIES ON LOW VOLUME APPLICATION OF PLANT GROWTH SUBSTANCES. IV. EFFECTS OF CONCENTRATION, DROPLET SIZE, RELATIVE HUMIDITY AND SURFACTANT CONCENTRATION ON PENETRATION OF NAPHTHALENEACETIC ACID Abstract Penetration of naphthaleneacetic acid (NAA) into cowpea (Vigna unguiculata (L.) Walp. subsp. unguiculata cv. Dixielee) leaves, as indexed by auxin—induced ethylene evolution, was greater, on a per unit dose basis, from small droplets and low NAA concentrations. Penetration was proportional to the interface area between the droplets and the leaf surface and continued from the residue on the leaf surface. High relative humidity slowed droplet drying and resulted in an enhancement of NAA penetration. Addition of a surfactant (X-77) reduced surface tension, improved wetting of the leaf surface and increased the interface area between the droplets and the leaf surface. The resulting increase in NAA penetration was greater than expected on the basis of increased interface area alone, suggesting an additional effect of the surfactant on penetration. Introduction Interest is rapidly increasing in concentrate, low volume (LV) application of growth regulators in the fruit industry (5,27). LV spraying allows the use of more compact, less costly equipment and lower spray volumes than dilute application, resulting in reduced energy consumption and application costs. With LV spraying, foliar penetration of the compound occurs from small discrete droplets. Small droplets dry faster and provide 28 29 a limited interface area between the spray and the leaf surface (11,12, Appendix D, 14) compared to dilute applications where virtually the entire leaf surface is covered with the spray solution (5). On the other hand, with LV spraying the concn used are higher (27), increasing the driving force for diffusion through the cuticular membrane (CM) (19) and presumably partially compensating for the decreased interface area and reduced dr0p1et drying time. The quantitative relationships among these variables (droplet size, concn, dose, rate of droplet drying) have not been critically evaluated and their combined effect on foliar penetration remains to be documented. A mathematical model for penetration of compunds through the CM from small droplets was developed (Section I, 14). It gives the quantitative relationShips among selected variables. Herein, we report on the evaluation of the model using an experimental system based on NAA-induced ethylene synthesis. This property was utilized to develop a bioassay in which ethylene evolution is used as an index of NAA penetration (6). The amount of ethylene evolved was proportional, within limits, to the quantity of NAA that diffused through the CM (estimated by using 14C-NAA, data not published). With this system, the effects of droplet size, concn, droplet drying time, etc, on penetration can be assessed. Materials and Methods Plant material and ggowing conditions. Cowpea seeds were pregerminated in the dark at 30 0C on moist paper towels. Seed coats were then removed to facilitate emergence of the radicle and epicotyl. 30 Healthy seeds of uniform size and radicle length were planted in disposable AC—4-8 "Cell Paks" (Geo. J. Ball Co., W. Chicago, IL 60185) using PROMIX BX (a peat-lite soilless medium, Premier Brands Inc., Canada) as a growing medium. The containers were held in a growth chamber at a 16-hr light (25 0C) 8-hr dark (20 oC) cycle. Lighting was provided by 12 fluorescent lights (GE F48T12—CW- 1500 Cool White) plus 8 incandescent lamps (GE Rough Service Inside Frosted SO/RS). Average radiant flux density (400-700 nm) was 27 W-m-z. The containers were rearranged daily to insure uniform exposure to the environmental conditions. Emergence generally occurred on the 4th day. Plants were watered as needed with the last watering 24 hr prior to excision of leaves to prevent moisture stress in the experimental material. Experimental_p£ocedure. The primary leaves of 10-day-old plants were collected and 2 discs were excised from each leaf with a sharp No. 15 cork borer (23 mm diam) with the midrib running through the center. The discs were placed, abaxial side down, in 100 X 15 mm disposable petri dishes containing 40 ml of distilled water, which were floated in a constant temperature water bath maintained at 25 DC. Average radiant flux density (400-700 nm) at the level of the discs was 15 W-mI2 provided by a bank of 6 fluorescent lights (ITT F36 T12/CW/RS Cool White). Droplets of NAA solutions were applied to the adaxial surface, avoiding major veins, with a microsyringe equipped with an automatic dispenser. This procedure allowed production of uniform droplets as small as 0.5 pl (985 pm diam). Penetration of NAA proceeded for 12 hr, 31 after which the discs (2 per replicate) were placed (abaxial surface facing the walls) in 15 X 85 mm glass vials containing 0.5 m1 of distilled water. The vials were sealed with serum stoppers and incubated at 30 0C for 4 hr. The ethylene content of the air in the vials was determined by gas chromatography (Varian 1440, Varian Associates, Inc., Palo Alto, CA 94303) using a flame ionization detector and a 100 cm steel column packed with activated alumina. Operating temperatures were: injection port, 130 oC; detector, 150 0; column, 80 0. N2 flow rate was 0.25 ml-s-l. Unless otherwise specified, a completely randomized experimental design was adopted, with 6 replicates (2 discs per replicate) for each treatment. NAA solutions. All test solutions contained 50 mg-liter-1 KOH to raise the pH of the medium and increase NAA solubility, in addition to 0.5 ml-liter-1 X-77 (alkyl aryl polyethoxy ethanol and free fatty acids, Chevron Chemical Corp., San Francisco, CA 94104). Flasks containing the NAA solutions were stored in the dark to avoid photodecomposition (7). Solutions were prepared fresh for each experiment. Penetration from NAA residue. Either 0.6 or 1.5 pg NAA were applied to leaf discs in the required number of 0.5, 1 and 2 p1 droplets of 100 and 250 mg-liter-1 NAA solutions, respectively. After the droplets had dried, the remaining residue was removed with distilled water by rinsing the treated surface with a wash bottle. In every other respect the experiment was conducted as described above. Effect of relative humidity. Four leaf discs (20.6 mm diam) 32 were placed in 60 X 50 mm disposable petri dishes containing distilled water which were floated on 500 ml of various H2804 solutions (Table 1) in 600 ml glass beakers. The beakers were tightly sealed with polyethylene film and the discs were allowed to equilibrate for 2 hr. Six 0.5 pl droplets of a 250 mg-liter-1 NAA solution (containing no X—77) were applied to the adaxial surface of each disc through the polyethylene film which was repaired after each application with transparent adhesive tape. The experiment was conducted in a growth chamber at 20 0C under the lighting conditions described above. A split-plot (completely randomized) experimental design was used in this experiment. Effect of surfactant. Solutions of varying surface tensions were prepared by adding increasing concn of X-77 to the test solution (250 mg.liter-1 NAA). Surface tension was measured with a surface tensiometer (Fisher Mbdel 20, Fisher Scientific Co., Pittsburgh, PA 15219). Leaf wetting was indexed by measuring the contact angle as described previously (Section I, 14) on 2 X 5 mm sections of primary leaves of plants of the same age and from the same group as those used in the penetration studies. For each Xr77 concn, 2 contact angle determinations were made on each of 4 sections obtained from each of 5 leaves (for a total of 40 measurements). Results Ethylene evolution for a given NAA concn was proportional to the dose applied, which was altered by increasing the number of 5 pl droplets applied to the discs (Figure 1). The slopes of the lines decreased with increasing concn. 33 Table 1. Relative humidity (at 20 0C) of air in equilibrium with different H2804 solutions and approximate drying time of 0.5 p1 droplets of NAA solution on the adaxial surface of cowpea leaf discsz. H2804 concn Relative humidityy DrOplet drying timex (ml-liter—l) (Z) (min) 200 90 82 400 55 34 700 8.5 18 2Contact angle: 105.40. ySource: Handbook of chemistry and physics. The Chemical Rubber Co., 1970, p. E-40. xTime required for 50% of the droplets to dry out. ETHYLENE EVOLUTION (nI-dlsc‘1-hr'1) 34 25 ' 500 20 - 100 15 L m. 10 - 'NAAconcontmlono Inna-mar" Numborolsmdtoplou 5 P- o 1 A 2 I 4 o 8 0 I. L l l J A 0 5 10 15 20 NAA nose ( pg disc") Figure l. Ethylene evolution from cowpea leaf discs in response to l, 2, 4 or 8 five p1 droplets of NAA solutions of varying concn. 35 When dose was altered by applying a constant number of droplets of increasing volumes, response was curvilinear (Figure 2). For any given dose, the slopes of the lines were greater for the lower concn and decreased with increasing dose (increasing droplet volume) for any given concn. Ethylene evolution was proportional to the calculated interface area between the droplets and the leaf surface (Figure 3). When the response data were corrected for differences in interface area, ethylene evolution for a given NAA concn was essentially constant (data not presented) and independent of dose. Ethylene evolution was reduced when the NAA residue was removed after the droplets had dried (Table 2) compared to experiments where the residue remained on the leaf surface. Response per unit dose was greater for the lower concn but droplet volume did not affect response. Drying time increased with relative humidity in the environment in which NAA application and penetration took place (Table 1) resulting in enhanced ethylene evolution (Figure 4). Increasing Xr77 concn reduced the surface tension of the solution through the critical micelle concn (CMC) (about 0.1 ml-liter-l Xr77) (24) and lowered the contact angle of the droplets on the leaf surface beyond the CMC (Figure 5). Ethylene evolution was higher for the same NAA dose in solutions which produced lower contact angles, thus greater interface area between the droplets and the surface of the leaf discs (Figure 5). 36 Figure 2. Ethylene evolution from cowpea leaf discs in response to 6 dr0p1ets of 0.5, 1, 2 or 5 p1 of NAA solutions of varying concn. Figure 3. Ethylene evolution from cowpea leaf discs in response to 6 droplets of 0.5, 1, 2 or 5 pl of NAA solutions of varying concn. Abscissa represents the calculated relative interface area between the droplets and the surface of the discs. E‘I’HYLENE EVOLUTION (nl-dioc‘1-hr") ETHYLENE EVOLUTION (nl-dloc"-hr1) 37 25- 15" 10.. CID. mung a. ICIE NM 008E( ’39- one") Figure 2 DROPLET VOLUME (pl) 35 0.5 1 2 5 fi T j I 15" 10- .L 1 1 2 3 RELATIVE INTERFACE AREA Figure 3 38 Table 2. Ethylene evolution (nl-disc-l-hr—lopg-l NAA) from cowpea leaf discs in response to either 0.6 or 1.5 pg NAA. The residue was washed off after the droplets had driedz. Droplet volume Number NAA concn (mg-liter-l) of (pl) droplets 100 250 0.5 12 1.73y 0.87 1 6 1.82 0.84 2 3 1.82 0.90 then the residue was not removed (Figure 2), ethylene evolution for the same droplet volumes and NAA concn ranged between 5.2 and 11.4 nl-disc’lohr'lopg'1 NAA. yMeans within a column were not significantly different by Tukey's w procedure (P = 0.05). Concn main effect was significant by Tukey's w procedure (P = 0.01). 39 Figure 4. Ethylene evolution from cowpea leaf discs in response to 0.75 pg NAA applied in six 0.5 pl droplets of a 250 mg-liter’ NAA solution in environments of varying relative humidities. Figure 5. Ethylene evolution from cowpea leaf discs in response to 8 droplets of 0.5 or 1 pl of a 250 mg-liter’1 NAA solution and containing increasing concn of X-77. Addition of the surfactant resulted in changes in surface tension, contact angle and calculated relative interface area. 40 «u- I (52 muffins. NEH-ma 2.5 " a 5 ‘ 2.0 r- :L; £8525 20.535 uzuatfi. 1.0 '- 3 2 4| 0 gm «II _ a J o I .8223 322 8.228 n .m. w w m w w . . . .4 . II4IIIIIIJ I A—IEZE. 2032“... uguzam w L» 1 In. W m m I a .0. I M... mm a... d .uo .4” W l I.» m .4 u m E u N as In m M a .m In . ,m. o l. .l .m ... w. o. — p _ h b b u m m w s o I AT... .7020 . .5 202.342 mzwgzm x-n CONCENTRATION (ml - Imfl) Figure 5 41 Discussion Ethylene evolution was linear with dose for a given NAA concn only when droplet volume was constant (Figure 1). When droplet volume was altered, linearity of the response was lost (Figure 2). The response was not saturated within the range of doses used in the experiment (Figure 1). Ethylene evolution per unit dose, given by the slopes of these lines, decreased with increasing concn, indicating that NAA penetration was more efficient at lower concn. The slopes also decreased, for a given concn, with increasing droplet volume (Figure 2) indicating greater penetration efficiency from smaller droplets. A given NAA dose will thus result in greater penetration if delivered in solutions of low concn and in smaller droplet volumes. These findings are consistent with earlier reports (3,6). When increasing droplet volumes were used, penetration was linear with the relative interface area between the droplets and the leaf surface (Figure 3). Correcting for differences in interface area rendered penetration essentially constant for a given NAA concn and independent of dose. This suggests that the enhanced ethylene evolution resulting from an increase in droplet volume can be explained principally in terms of the increase in interface area rather than in dose. Removing the NAA residue after the droplets had dried (Table 2) reduced response. Penetration per unit dose was greater for the lower concn but droplet volume did not affect response when NAA dose and concn were constant. Some penetration continues after the droplets dry (4,9,15,26) 42 and even from NAA dust (16,18). Our results support these findings and suggest that the greater penetration observed from smaller droplets may have been due to penetration after the water evaporated. For a given dose and concn (and therefore total volume) smaller droplets produce a greater interface area (Appendix D, 14). Thus, more of the residue would be in contact with the leaf surface after the droplets dry. This would result in a greater opportunity for penetration from the residue and therefore greater response (Figure 3). Increasing the relative humidity prolonged drying time (Table 1) and increased penetration (Figure 4) as reported previously (1,2,15,17). Penetration in this experiment was lower than in others where similar doses were used, probably because it was conducted at a lower temperature and light was reduced by the polyethylene film covering the discs. Both factors markedly affect penetration (10,25). In addition, no Xe77 was used and the contact angle of the droplets on the surface of the discs was higher, resulting in reduced interface area and therefore lower NAA penetration. Adding Xr77 reduced both surface tension and contact angles and correspondingly increased the calculated relative interface area (Figure 5). NAA penetration (Figure 5) paralleled interface area through a Xr77 concn of 1.0 ml-liter-l. Greater Xr77 concn produced no further reduction in surface tension and only a small decrease in contact angle, but a significant increase in penetration (Figure 5). Although the main role of surfactants as spray additives is to reduce the surface tension of the solution and thereby increase wetting of the leaf surface (8,13,23), in some instances they may also affect penetration through direct interaction with the compound 43 (8,22), facilitating diffusion through the CM (2,21) or acting as humectants (19,20,23), thereby delaying droplet drying. Some of these effects were evident in our experiment because the Xr77 effect on penetration cannot be explained solely in terms of increased interface area. Our results agree in general with those predicted by the penetration model presented in Section I (14) except for the effect of droplet size. Droplet size affected overall penetration, while the model rendered penetration independent of droplet size. However, NAA penetration continued after the droplets had dried, while the model assumed no further penetration after the water evaporated. The experimental procedure used magnified this effect for penetration is probably enhanced by incubating the leaf discs at high humidity and temperature. These results, in conjunction with those reported in Section III (14) and the model presented in Section I (14), provide a guideline to aid in establishing the values of spray variables required to maximize penetration and thus the response. The ultimate values adopted in actual spray application will be affected by other factors such as the capabilities of the application equipment and the nature of both the compound and the leaf surface. 1. 10. 11. LITERATURE CITED Babiker, A. G. T., G. T. Cook and H. J. Duncan. 1976. Further studies on the influence of adjuvants and humidity on the penetration of bean leaves (Phaseolus vulgaris) by amitrole. p. 93-98. Ig_ N. R. MCFarlane (ed.). Herbicides and fungicides. Factors affecting their activity. Burlington House, London. . and H. J. Duncan. 1975. Penetration of bean leaves by asulam as influenced by adjuvants and humidity. Pestic. Sci. 6:655-664. . Buehring, N. W., L. O. Roth and P. W. Santelmann. 1973. Plant response to herbicide drop size and carrier volume. Trans. . Bukovac, M. J. 1965. Some factors affecting the absorption of 3-chlorophenoxy-a-propionic acid by leaves of the peach. Proc. Amer. Soc. Hort. Sci. 87:131-138. . 1973. Foliar penetration of plant growth substances with special reference to tree fruits. Symposium on growth regulators in fruit production. Acta Hort. 34:69-78. Crabtree, G. D. and M. J. Bukovac. 1980. Studies on low volume application of plant growth substances. I. NAA-induced ethylene production as a means to evaluate spray parameters. Pestic. Sci. (In press). Crosby, D. G. and C. S. Tang. 1969. Photodecomposition of 1-naphthaleneacetic acid. Agric. Food Chem. 17:1291-1293. Foy, C. L. and L. W. Smith. 1969. The role of surfactants in modifying the activity Of herbicidal sprays. p. 55—69. In Pesticidal formulations research. Physical and colloidal chemical aspects. Advances in chemistry series. No. 86. American Chemical Society, Washington D. C. Greene, D. W. and M. J. BukOvac. 1971. Factors influencing the penetration of naphthaleneacetamide into leaves of pear (Pyrus communis L.). J, Amer. Soc. Hort. Sci. 96:240-246. . and . 1977. Foliar penetration of naphthaleneacetic acid: enhancement by light and role of stomata. Amer. J. Bot. 64:96-101. Hartley, G. S. and R. T. Brunskill. 1958. Reflection of water drops from surfaces. p. 214-223. IE J. F. Danielli, K. G. A. Pankhurst and A. C. Riddiford (eds.). Surface 44 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 45 phenomena in chemistry and biology. Pergamon Press, London. Johnstone, D. R. 1973. Spreading and retention of agricultural sprays on foliage. p. 343-386. IQ_W. Van Valkenburg (ed.). Pesticide formulations. Marcel Dekker, Inc., New York. Leece, D. R. and J. F. Dirou. 1977. Organosilicone and alginate adjuvants evaluated in sprays foliar-applied to prune trees. Commun. Soil Sci. Plant Anal. 8:169-176. Leon, J. M. 1980. Studies on low volume application of plant growth substances. A mathematical model for penetration from droplets and its experimental evaluation. Ph.D. Thesis, Mich. State Univ., East Lansing. Luckwill, L. C. and C. P. Lloyd-Jones. 1962. The absorption, translocation and metabolism of 1-naphthaleneacetic acid applied to apple leaves. J, Hort. Sci. 37:190-206. Marth, P. C., L. P. Batjer and H. H. Moon. 1945. Relative effectiveness of sprays, dusts, and aerosols of naphthalene- acetic acid on harvest drop of apples. Proc. Amer. Soc. Hort Sci. 46:109—112. Middleton, L. J. and J. Sanderson. 1965. The uptake of inorganic ions by plant leaves. J. Exp . Bot. 16:197-215. Mitchell, A. E., W. Toenjes and C. L. Hamner. 1948. The use of dusts and concentrate sprays to prevent pre-harvest drop of McIntosh apples. Mich. Agric. o 2 Lu 8 g 60 - Volume U. In .->.- '< _________________________________ 5' so : I I I! : I 8 . I I I 40 I- I g i I I ' : I I I I so - I : I I I I i I 20 I- : E : I ' I ' I I I 10 _ : I ' I ' I NMDE MMD 0 _ \I 1 I 1 {I I O 50 100 150 200 250 DROPLET DIAMETER ( pm) Figure A2. Cumulative frequency distribution of spray spectrum described in Table A1. APPENDIX B GEOMETRICAL RELATIONSHIPS Sphere 3 5D Volume V = 6 Surface S = NDZ From the above relationships, the following can be derived S 6 V D 1/3 1/2 6V S D 2: = -— TI TI S3/2 v = —— 6111/2 S = (6V)2/3fl1/3 Segment of a sphere. See Figure B1. 2 1 2 1 w 2 Volume V = --nh (3R-h) = --flh 3 -——-+ h 3 6 4 Curved surface S = 25Rh = flDh 74 Flat surface 75 76 I'W/2 Figure Bl. Segment of a sphere. APPENDIX C EQUATIONS TO CALCULATE INTERFACE AREA Interface area of one droplet with the leaf surface. (See Figure 1, Section I). The interface area between a drOplet and the leaf surface (SO) can be calculated by applying the formulae in APPENDIX B if R, h and w are known. Although this is not normally the case, S can 0 still be calculated on the basis of other readily measured parameters such as the contact angle (0), the volume of the droplet (V) or its diameter in flight (D). O h tan -—-= 2 w/2 w 0 h = -——-tan -- 2 2 2 TI 6V w3 0 3 O = 3tan — + tan --- 8 2 2 F 6V ‘1” O 3 O 2 n<8tan-§—-+ tan 2 ) 77 78 Since 2 w S = 1r -— O 4 P - 6V 2’3 So 7 " o 3 o 1r(3tan — + tan -—-) 2 2 .. .1 Since 1TD3 V = 6 1TD2 So ' 3 o 2/3 (3tan —§— + tan -—2:-) Total interface areajer unit volume of 8131;1- For all the droplets (Ani) in one size class with mean diameter Di’ the total interface area SO would be 1 1T 2 S = D An 91 (3tan —-(3 + tan3 —2 ’2/3 1 i For all the droplets in the spray 1r 2 S = ID An OT (3tan -C%- + tan3--g--)2/3 i i 79 Since the total volume of the spray, V is equal to T2 The interface area per unit volume of spray, S , would be 0V S 2 s = OT = 6 XDi Ani o o 3 o 2/ 3 3 V VT (3tan —-2 + tan ——2 ) 23Di Ani ZDiZAni 1 But -—-—7;———-= (See Appendix A) 2Di Ani SMD Therefore 6 1 So = o 3 o 2/3 V (3tan T '1' tan T) SW The relationships between SMD, contact angle and relative interface area per unit volume, are depicted in Figure C1. It is evident that the total interface area per unit dose will change inversely with concentration for a given SMD. 8O 125 - 300 IN - 5 N - E 75 E ( '6' 2 so - C III .- E 25 *- L 1 I 1 l J 8ND (pm) Figure C1. Interface area between the spray and the leaf surface as a function of the SMD and for various contact angles. APPENDIX D RELATIONSHIP BETWEEN TOTAL INTERFACE AREA: NUMBER OF DROPLETS, DROPLET DIAMETER AND TOTAL SPRAY VOLUME As total spray volume and droplet size are decreased in going from dilute to low volume spraying, the total number of droplets produced and the total interface area between the spray and the leaf surface change dramatically, the magnitude of the change depending on the relative changes in total spray volume and droplet size. These relationships are important because the number of droplets determines the extent to which coverage of the foliage can be accomplished with a given spray volume while the total interface area determines the total area through which penetration of the growth regulator takes place. If we assume an ideal spray spectrum delivered in m. uniform 1 droplets of diameter D1, the total volume of spray delivered will be If the spray is delivered in m droplets of 2 diameter D2, the total volume of spray delivered will then be 81 82 Therefore V m D On the other hand _ 2 SO - leOD1 1 Where 11' K = O (3tan —@— + tan3--9---)2/3 2 2 2 So In2KoD2 2 Therefore 8 2 G)2 .. m2 I32 2 So m1 D1 1 And since 3 m v /D (1)-1) 2 = 2 1 m1 V1 \D2 3 O V D (1)-2) 2 = 2 1 S V D (Appendix C) 83 Example If total spray volume is reduced by a factor of 10 while the diameter of the dr0p1ets is reduced by a factor of 5 v D -——3— = 0.1 and -——l— = 5 V1 D2 Then m 2 = 0.1 x 53 = 12.5 m1 And S 02 = 0.1 x 5 = 0.5 s 01 This means that the total number of droplets has increased by 12.5 times while the interface area has been reduced to half. In order to maintain a constant interface area for a given reduction in total spray volume SO2 v2 = 1 and -———-= N S V 01 1 D1 1 = N --—- (From equation (D-2)) D2 D 2 g N D1 m D1 3 l 3 1 = N -—-—- = N -——- 8 -—3- (Equation (D-1)) m D N N 84 Therefore “‘2 =__1_ m1 N2 Example If total spray volume is reduced by a factor of 10 V N=-—2—=Ol V1 So D __2_.___0.1 D1 While m l 2 = 2 = 100 m1 0.1 This means that in reducing the total spray volume by a factor of 10, 100 more droplets of a diameter 0.1 times that of the original ones need to be produced in order to maintain the same interface area. No other combination of droplet size and number of droplets will satisfy the condition of providing the same interface area for a given reduction in total spray volume. There are only two variables (droplet number and droplet diameter) and by imposing two conditions on the system (total spray volume and interface area) both degrees of freedom are accounted for. The above relationships are illustrated in Figures D1 and D2. In the case of a spray with non-uniform size dr0p1ets, similar calculations can be made if the SMD of the spray is known. 85 S0 = KS 1 and S0 = KS 2 1 SMD 2 SMD 1 2 Where 6 K = S (3tan £— + tanB—g-)2/3 2 2 Therefore S 02 = V2 SMD1 SO V1 SMD2 These relationships are illustrated in Figure D3. 86 Example If the spray volume is reduced by a factor of 10 and droplet diameter is reduced by a factor of 5 ---= 0.1 and -———-= 0.2 The relative number of droplets (nz/nl) is equal to 12.5 (left axis, solid line) while the relative interface area (S6 /S6 ) 2 1 is equal to 0.5 (right axis, broken line). 87 ‘LOOO" "100 100- ..10 E? ca .5 :0 I: .4 n. C) E 10- -1 u. (D c: u: a: Si :: 2 us 2: ’2 d c 1- -o.1 04- 4mm RELATIVE SPRAY VOLUME (Va/V1) Figure D1. Relative number of droplets and interface area between the spray and the leaf surface as total spray volume and droplet diameter are changed. s )--- 91 92 RELATIVE INTERFACE AREA (S / 88 Example If the spray volume is reduced by a factor of 5 We would need 25 more droplets (broken line, left axis) of a diameter 0.2 times that of the original droplets (solid line, right axis) to obtain the same interface area. 89 10,000 r- , - 10 1,” - d 1 E N EL en E _l O. O “a“ a 100 — .. 0.1 O I III-l D 2 D 2 III E S I.“ C 10 .. - 0.01 1 . L 1 . J 0.001 1 0.1 0.01 RELATIVE TOTAL SPRAY VOLUME (V2/V 1) Figure D2. Relative changes in droplet diameter and number of droplets required to maintain a constant interface area as the total spray volume is reduced. RELATIVE DROPLET DIAMETER (Dz/D1) -— 90 Example If the spray volume is reduced by a factor of 10 and the SMD is reduced by a factor of 2 V SMD -—-2—- = 0.1 and ———g— = 0.5 v1 SMD1 The relative interface area (S9 /S9 ) is equal to 0.2. 2 1 91 10'- en";- \. 1,. N 9% < Ill 1 < Ill 0 < ll. C Ill .- E Ill E < —l Ill m 0.1 h- .015 RELATIVE SMD (8M02/SMD1) Figure D3. Relative changes in interface area as both the SMD of the spray and the total spray volume are changed. “IIW‘THmymmmmwmES 886