Pestic. Sci. 1993, 37, 133-140

Assessment of a Mathematical Model to Predict Spray Deposition under Laboratory Track Spraying Conditions. I1 : Examination with Further Plant Species and Diluted Formulations*$ B. Terence Grayson,§ Simon E. Pack, Dean Edwards & James D. Webb Shell Research Limited, Sittingbourne Research Centre, Sittingbourne, Kent ME8 9AG, UK (Revised manuscript received 10 November 1992; accepted 1 1 January 1993)

Abstract: Mean spray depositions onto leaves of five plant species (Zea mays L., Vicia faba L., Sinapsis alba L., Glycine max (L.) Merr., Vitis oinifera L.) were measured following spraying of an array of 36 solutions of acetone+aqueous ‘Triton X-100’ varying systematically in composition and properties. The spraying was carried out on five occasions using a standard laboratory track sprayer delivering the equivalent of 600 litre ha-l onto a plane surface around plant height. The results, plotted as response surfaces, showed that there was little variation in spray deposition with solution composition for V. oinifera, there were some slight decreases in deposition with increase in ‘Triton X-100’ concentration on V. faba and S. alba, though not with increase in acetone concentration, and that there were slight systematic increases for G. rnax and large systematic increases for Z. mays with increase in acetone and ‘Triton X-100’ up to concentrations of 350 ml litre-’ and 0.5 g litre-’ respectively. At higher concentrations of these components, there were no further increases in deposition on these latter species.

The results were in agreement with those predicted by a mathematical model derived previously, with the exception of the slight decreases in deposition on V . faba and S. alba and smaller increases in deposition than predicted on G. rnax. The decreases in deposition on the former species were attributed to slight run-off from their easy-to-wet leaves at the higher ‘Triton X-100’ concentrations at the spray volume rate (600 litre ha-l) used. The poor fit of the observed and predicted spray depositions on G. rnax was attributed to the nature of its leaves. These are hairy and it is speculated that the fine hairs, rather than the true leaf surface, played a major role in capturing the small spray drops (115-130pm) created by the laboratory sprayer used in this work.

The observed and predicted spray depositions with a set of diluted commercial- type formulations were in good agreement for Setaria viridis (L.) Beauv., Pisum sativum L., Z. mays, with correlation coefficients ( r ) of 0.985, 0.988 and 0.935 respectively, and also for the more constant depositions on the easy-to-wet species Beta vulgaris L., but slightly less so for Triticum aestivum L. ( r = 0.886) in this test. Overall the model was well-behaved, giving a good prediction of the variation in spray deposition on leaves of a range of plant species, provided that these were not extensively hairy, with variation in the dynamic surface tension of the spray solution.

* Paper presented at the ‘Third International Symposium on Adjuvants for Agrochemicals’, organised by the Physico- 1 INTRODUCTION chemical and Biophysical Panel of the SCI Pesticides Group and held at the University of Cambridge, Cambridge, UK on Systematic variations in spray depositions on four species J Part I : Pestic. Sci., 33 (1991) 281-304. of plants with systematic variations in the natures of the $ To whom correspondence should be addressed. spray solutions, comprising a matrix of aqueous

133 0 1993 Shell Research Ltd

3-7 August 1992.

134 B. T. Grayson, S. E. Pack, D. Edwards, J. D. Webb

surfactant/acetone mixtures, were reported recently.' These results were accompanied by a mathematical model, developed from Young's equation,' that gave a quantitative explanation of the relationship, using in- dependently measured physical properties of the solu- tions and the leaf surfaces.

where &T = volume of spray deposited on any target, T, by any solution S; 4, WG = volume of spray deposited on watchglass WG by solution S; MT = morphology coef- ficient for target, T ; COSO,,~ = contact angle of water on the target, T; CosO,,, = contact angle of water on the watchglass surface; (DST), = dynamic surface ten- sion of solution S at an appropriate surface age; and f = regression coefficient.

The programme of work described in this paper set out to challenge this mathematical model by examining the spray deposition on a further five species of plants with leaves of different surface characteristics from those used in the first set. This work also includes measurement of spray deposition and assessment of the model, using four typical formulation types at two spray-tank dilution rates, on a selected range of plants.

2 EXPERIMENTAL

2.1 Materials and plants

The components, their sources and preparation of an array of spray solutions containing gentian violet

(1 g litre-') and up to 0.9 g litre-' 'Triton X-100' and 500 ml litre-' acetone were reported previously.'

Blank formulations, selected as typical representatives of emulsifiable concentrate (EC), soluble liquid (SL), suspension concentrate (SC) and wettable powder (WP) formulations, with recipes as given below, were obtained from the Analytical and Formulation Chemistry De- partment, Sittingbourne Research Centre.

EC : mixed emulsifiers, (100 g) + aromatic solvents to 1 litre; SL : surfactant (100 g) + water-miscible solvent to 1 litre; SC: dispersing agent (8 g) + structure agent (4 g) + antifreeze (120 g) + biocide (1.5 g) +water to 1 litre; WP: wetting agent (20 g) +dispersing agent (20 g) +inert filler to 1 kg.

Amounts of these formulations, assuming typical active ingredient concentrations (EC, SL, 100 g litre-'; SC, 200 g litre-'; WP, 250 g kg-l), were diluted into tap water containing gentian violet (1 g litre-') to provide spray solutions, so that on application at a volume rate of 600 litres ha-' an active ingredient would be applied at 500 and 1000 g ha-'.

Plants were grown from seed as described previously, except for vine which was propagated from woody cuttings, to the following growth stages : maize (Zea mays, L. cv. Beaupre pau 205) two leaves, 8-10cm; broad bean (Viciafaba, L. cv. Sutton) two expanded leaf pairs, 12-15 cm; mustard (Sinapsis alba L. cv. White Agricultural) first true leaves emerging, 5-6 cm; soybean (Glycine max (L.) Merr. cv. Wells) first leaf pair expanded, 8-9 cm; vine (Vitis vinifera L. cv. Cabernet Sauvignon) two leaves expanded, 8-10 cm; wheat (Triticum aestiuum L. cv. Sicco) first series of trials, expanding second leaf, 10-12 cm, second trial, expanding first leaf, 8-10 cm; green foxtail (Setaria viridis (L.) Beauv.) expanding third leaf, 8-10 cm; pea (Pisum

Broad bean Soybean Vine Mustard

Fig. 1. Plants used for the spray deposition measurements.

Maize

Foliar spray deposition under laboratory track spraying conditions. 11 135

sativum L. cv. Alaska) two expanded trifoliate leaves, 15 cm; sugar beet (Beta vulgaris L. cv. Monotri 95) cotyledons expanded.

The vine plants were left untouched, though maize and pea plants were thinned down to four per pot, broad bean and soybean to three per pot. The apices of pea, broad bean, soybean and mustard were removed with tweezers without touching the surface of the remaining leaves. A typical array of plants, just prior to spraying, can be seen in Fig. 1 or were shown previous1y.l

2.2 Spray method

For the first trial, involving the new species and aqueous acetone spray solutions, the pots of plants were arranged in trays and sprayed on one occasion as defined previous1y.l Replicates were prepared in trays such that each species was in a different location in the spray tray to avoid any bias owing to a particular position in the tray. For the second series of trials, involving a range of

TABLE 1 Contact Angles of Water on Plant Leaves

Plant species Contact angle (") (SD, no. of obs.)

Maize Broad bean Mustard Soybean Vine Wheat Green foxtail Pea Sugar beet cotyledons

130(f8,90) 32 (f 5,72) 50 (f 8 , 5 8 )

127 (f 10,84) 42 (k 9,84)

123 (+4, 60)" 122 ( f 12,85)" 121 (+8,70)" 73 ( f 9 , 70)"

a From Ref. 1.

TABLE 2 Dynamic Surface Tensions of Aqueous 'Triton X- 100'/Acetone Spray Solutions at a Nitrogen Flow-Rate of

6.4 ml min-' in the MBPM Apparatus

Acetone concentration

(ml litre-')

Dynamic surface tension (mlv m-')

' Triton X-100' concentration (g litre-')

0 0.05 010 0.25 055 0.90

0 73 69 61 49 44 42 45 61 60 57 45 43 42

100 54 51 53 45 43 42 225 45 45 45 43 43 42 350 41 42 41 41 40 40 500 35 35 35 36 36 36

species with the diluted formulations, the replicates were sprayed on five separate occasions, again changing location of plants in the spray trays between trials. A 9.5- cm-diameter watchglass, placed on top of the same type of plastic pot amongst the plants in the spray tray, was included in all spray trials on all occasions to provide a uniform target with which to assess repeatability of the spraying process.

2.3 Measurement of spray deposition

The plants were harvested as follows: maize, three or four of the second leaves; broad bean, three leaves from each pot; mustard, both cotyledons from 8-10 plants; soybean, four primary leaves from each pot; vine, two expanded leaves; wheat, green foxtail, sugar beet, pea as

TABLE 3 Dynamic Surface Tensions of Spray Solutions at a Nitrogen

Flow-Rate of 6.4 ml min-' in the MBPM Apparatus

Formulation application

(g a.i. ha-')

Dynamic surface tension (mN m-')

rate Formulation type

EC SL sc WP

500 43 56 69 68 1000 40 52 69 68

TABLE 4 Estimated Morphology Factors (M,) and Variances Explained between Observed and Depositions Predicted by Equation (1)

Speciesltarget Combined data set Previous data set

M , Variance M , Variance explained explained

(%)

Maize Broad bean Mustard Vine Wheat Green foxtail Pea Sugar beet cotyledons

Glass rods Residual sum of squares

Weighted residual sum of squares

Regression coefficient

0.77 98.0 0.45 98.0 0.54 97.7 0.7 1 99.9 0.3 1 95.6 0.63 98.6 0.89 98.6 0.65 98.3

0.09 99.4 38.3

4.8

7-5

0.33 0.64 0.94 0.65

0.09

964 98.6 98.9 98.6

99.4 20.7

4.1

6.8

136 B. T. Grayson, S . E . Pack, D . Edwards, J . D . Webb

previously and their weights measured before they were washed in acetone+water (1 + 1 by volume) and the concentration of gentian violet measured.' The surface areas of each sample of the harvested plants were obtained by reference to a regression of weight versus surface area, measured by a surface area meter (Delta-T Devices Ltd, Cambridge), on samples from the same batch of plants.

2.4 Measurement of contact angles

Contact angles with water were measured on all species,' to ensure that the natures of the plant leaf surfaces were consistent on all occasions. Mean values and standard deviations were determined from at least 58 measure- ments (Table 1).

Vine: observed

2.5 Measurement of dynamic surface tensions

Dynamic surface tensions were measured for all spray solutions using the maximum bubble pressure method (MBPM) described in Ref. 1. Values, measured at a nitrogen flow-rate of 6.4 ml min-l found to be optimal in the previous studies' with the described apparatus are given in Tables 2 and 3.

2.6 Mathematical model analysis

The spray-deposition data obtained from the aqueous acetone solutions on the five plant species in this study were added to those data given in the previous paper and the whole data set submitted to a non-linear least squares multiple regression analysis using the mathematical

Vine: predicted

Bean: observed

(a)

Bean: predicted

(b) Fig. 2. Observed and predicted spray depositions. (a) Vine; (b) broad bean.

Foliar spray deposition under laboratory track spraying conditions. I1 137

Maize: observed Maize: predicted

Soybean: observed Deposit;; a

N

E m 4.8

Soybean: predicted

D e p o s i t ; ; a N

G rn 4.8

(e> Fig. 2-contd. (c) mustard; (d) maize; (e) soybean.

138 B. T, Gruyson, S. E. Puck, D. Edwards, J . D. Webb

model given in eqn (1) with values for the dynamic surface tensions obtained as in Section 2.5, as discussed previously.' This analysis estimated the morphological factors for each of the new species and re-estimated the regression coefficient (Table 4).

3 RESULTS

The five plant species chosen for these further studies of spray deposition provided an extension to the range of leaf-surface wettabilities over that reported previously,' as indicated by their measured contact angles with water (Table 1). These different leaf surfaces brought about very different shapes to the spray deposition response surfaces with the array of aqueous ' Triton X- 100 '/acetone solutions (Figs 2(a)-(e)). As with depositions on the plant

surfaces in the previous study there are non-systematic perturbations in these response surfaces that are attri- buted to experimental scatter. There are no systematic variations in deposition with change in solution com- position for vine. There are some decreases in deposition on broad bean and mustard with increase in 'Triton X- 100' concentration, though not with increase in acetone concentration. There appear to be large systematic increases in deposition on maize and smaller systematic increases in deposition on soybean with increase of both 'Triton X-100' and acetone up to concentrations of 0.5 g litrecl and 350 ml litre-l respectively.

The flat response surface for vine is in accord with the easy-to-wet nature of its leaf surface shown by the low contact angle with water (Table 1). The slight decreases in deposition on broad bean and mustard may have been attributable to run-off from their easy-to-wet leaves

TABLE 5 Observed and Predicted Spray Depositions of Gentian Violet from Two Spray-Tank

Dilutions of Standard Formulations on Five Plant Species

Formulation Application Gentian violet deposition @g cm-z) type ratea

( g a.i. ha-') Green Wheat Pea Sugar Maize foxtail beet

EC

SL

sc

WP

500

1000

500

1000

500

1000

500

1000

Obs. SDb Pred. Obs. SDb Pred. Obs. SDb Pred.

Obs. SDb Pred. Obs. SDb Pred.

Obs. SDb Pred. Obs. SDb Pred.

Obs. SDb Pred.

2.56 0.12 2.4 1 2.83 0.38 2.56 2.29 0.06 1.72

2.32 0.19 1.97 1.82 0.15 1.03

1.91 0.07 1.13 1.97 0.14 1.18

1.90 0.26 1.18

0.37 0.04 1.18 0.54 0.12 1.26 0.38 0.03 0.8 1

0.49 0.09 0.94 0.24 0.03 0.43

0.24 0.04 0.48 0.23 0.02 0.5 1

0.23 0.03 0.5 1

2.94 3.36 0.47 0.25 3.38 3.45 3.72 3-15 0.19 0.43 3.59 3.49 2.06 2.99 0.35 0.28 2.40 3.19

2.52 3.05 0.33 0.17 2.14 3.37 1.08 3.74 0.26 0.56 1.41 2.92

1.09 3.75 0.34 0.34 1.55 2.96 1.10 3.63 0.22 0.60 1.61 2.97

1.15 3.57 0.21 0.44 1.63 3.00

1.95 0.42 2.77 2.65 0.24 2.97 1.96 0.34 1.85

2.13 0.26 2.17 0.92 0.05 0.92

1 .oo 0.25 1.05 1.24 0.2 1 1.12

1.27 0.6 1 1.12

a Assuming a.i. concentrations of 100 g litre-' for EC/SL, 200 g litre-' for SC and 250 g kg-l for WP formulations.

Standard deviations of observed results.

Foliar spray deposition under laboratory track spraying conditions. II 139

(Table 1) at the higher 'Triton X-100' concentrations at the spray volume rate (600 litre ha-l) used. Nevertheless, the results clearly show that it would be unnecessary to reduce surface tensions of spray solutions by adjuvants, etc. in order to increase spray deposition on such surfaces and that it may even be slightly detrimental to deposition at high volume rates. The curved response surface for maize is intermediate between those for wheat and pea,' both similarly difficult-to-wet species, and shows that a reduction of surface tension below that of water would be required for efficient spray deposition on maize and species with similar leaf surfaces.

The contact angle of water drops on soybean (Table 1) was high, suggesting that this surface is also difficult to wet and therefore should give a marked curved response surface of spray deposition with change in solution composition. However, the adaxial surfaces of the first (and subsequent) true leaves (but not the cotyledons) of soybean are extensively hairy. When measuring contact angles, small drops of water placed on the leaves could be seen to be attached to the hairs, sometimes without contact with the true surface. The measured 'contact angles', really between the drops and the hairy surface, were large (mean value - 127") although the transfer of drops from the syringe needle to the leaf hairs was easy, in contrast to that with smooth, difficult-to-wet surfaces (wheat, pea, green foxtail, maize). Under the spraying conditions of this work it can therefore be understood that the small drops (1 15-130 pm) created by the hydraulic nozzle would be caught by the leaf hairs irrespective of the surface tension of those drops, to give a shallow-curved response surface, as was observed (Fig.

The formulations used in the second series of trials were chosen as representatives of normal types of EC, SL, SC and WP formulations, without active ingredients but diluted to typical concentrations that would be used in normal practice, as described in Section 2.1.

Increase in their concentrations decreased their dy- namic surface tensions and increased the volumes of spray deposited for the EC and SL formulations, but not the SC and WP formulations, on four of the plant species-green foxtail, wheat, pea and maize (Table 5). The increases on any one species varied, but ranged up to 40% of the deposition of the more diluted dispersion. There were few differences in deposition on sugar beet between any of the spray solutions because, in contrast to the other species, the leaf surface of this species is relatively easy to wet. It has been shown that deposition on easy-to-wet surfaces is independent of the nature of the spray solution with the drop sizes (VMD - 1 1 0 - 130 pm) used in these studies.'

2(e)).

4 DISCUSSION

The five further plant species were selected as a wider

range of examples with which to test the mathemat- ical model for predicting spray deposition derived previous1y.l

With the exception of soybean, where the leaf hairs, rather than the true leaf surface, are the initial points of contact with approaching spray drops, and broad bean and mustard, where slight run-off may have occurred at high 'Triton X-100' concentrations, the observed spray depositions on these further leaf targets were in good agreement with those predicted by the mathematical model using dynamic surface tensions (Table 2) measured by the MBPM at a nitrogen flow rate of 6.4 ml min-l (cf. observed and predicted spray depositions in Figs 2(a)-(d)).

This was also confirmed statistically, where the value for the weighted sum of squares of the analysis had a reasonably low value of 4.8 (Table 4). The calculated morphology factors, slope of the regression, total residual sums of squares for the original data set and for the new data combined with the original data are also compared in this table. There were no major changes to the estimated MT values or the percentages of variance explained between those in the original and in the second combined data analyses, showing that the model accom- modated the new data without any need for modification, confirming its robustness. There was a slight increase in the regression coefficient from 6.8 to 7.5.

The plants tested so far have fallen into one of three categories. First, those with leaf surfaces that had low contact angles (< 70") with water, and were thus easy to wet, showed either no change or slight decrease in spray deposition with change in solution composition. The amounts of spray that were caught were determined by their morphologies, and extents of overlap, in the way that they were grown and treated in these trials.

Secondly, those with leaf surfaces that had high contact angles (1 15-1 30") with water and were thus difficult to wet. The response surfaces of deposition on the leaves of these plants were systematically curved with increases in deposition with increase in both the acetone and 'Triton X-100' contents. The ultimate levels of deposition, the plateaux, were achieved at either an acetone concentration of approximately 350 ml litre-l or a 'Triton X-100' concentration of 0.5 g litre-' or at lower levels of both when they were in combination. Thus the presence of either 'Triton X-100' in a 500 ml litre-' solution of acetone in water or of acetone in a 0.5 g litre-' solution of 'Triton X-100' in water brought about no further increase in spray deposition. The heights of the plateaux, as with the easy-to-wet leaf surfaces, were determined by the morphology/extent of overlap of the plant leaves as used in these tests. The upright surface of the two-leaf stage of wheat has, from the plants tested to date, provided the lowest plateau, though it could be predicted that rice plants at a similar growth stage would give an even lower plateau, and the more horizontal expanded trifoliate for pea provided the highest plateau. Thus, of the plants tested, pea leaves are those most

140 B. T. Grayson, S. E. Pack, D . Edwards, J. D. Webb

subject to increases in spray deposition with reduction in surface tension of the spray solution. Under the spraying conditions (drop sizes 110-130 pm, drop velocities - 1-2 m SS') of these tests the plateaux of these difficult- to-wet species are achieved with solutions of dynamic surface tensions less than - 42 mN msl at the nitrogen flow rate (6.4 ml min-l) used in the MBPM apparatus employed in this study.

A third category, those with extensively hairy leaves and represented by soybean in this work, has also been identified. In this case contact angles of small drops placed on the hairy leaf surface are large and low spray deposition of water would be expected. In practice, this does not occur and moderate spray deposition with water was observed which was increased to some extent by reduction of surface tension by either 'Triton X-100' or acetone (Fig. l(e)). The increases with aqueous surfactant solutions are not well predicted by the mathematical model because, presumably, the hairs 'catch' the spray drops in a manner different from their deposition on a less hairy surface and may preferentially attract the smaller size fraction of spray drops. The influence of hairs on leaf surfaces in catching and retaining water drops of different sizes and by different types of leaf hairs has been extensively discussed by Hartley and Graham-Bryce3 and Hull, Davis and Stolzenberg* and the complications would, clearly, be beyond the scope of the model in eqn (1).

In addition to the categories identified to date there will also be an intermediate category for smooth leaves between the easy- and difficult-to-wet species where contact angles with water drops would be between 70" and 110".

In the second part of this work, using dilutions of normal types of formulations, the correlations between observed depositions and those predicted by eqn (1) were good for green foxtail, pea and maize with correlation coefficients ( r ) of 0.985, 0.988 and 0.935 respectively, and also sugar beet, where there were no differences between formulations, but poorer for wheat (r = 0.886). In this particular test the wheat plants were used at the expanding first leaf stage, rather than the two-leaf stage used previously and the morphology factor (0.3 1) may have been an over-estimate for this growth stage. If a morphology factor of half this value (0.15) had been used in eqn (l), the correlation coefficient would have increased to 0.94.

The observed depositions on green foxtail were all slightly larger than predicted and, in this case, the morphology factor, also taken from the previous work, may have been a slight under-estimate. Clearly, mor-

phology of the plant will be a sensitive parameter for spray deposition. In the original work the spray depositions were measured on plants grown on different occasions throughout the year and the morphology factor was a mean value over those plants. In this diluted formulation work, the plants were grown and used on the same occasion to obtain the replicated data and so there would be little variation in the morphology and the factors for wheat and green foxtail were not coincident with the mean values obtained over a year.

One interesting consequence of the variation in spray deposition with formulation dilution with EC and SL formulations on difficult-to-wet targets is that any biological response curve will be a function both of change in the concentration of the active ingredient and of change in spray deposition. This would not be present on easy-to-wet species or with screening solutions containing high amounts of acetone which wet difficult- to-wet leaves more easily. This would also be absent with SC and WP formulations whose depositions would not be influenced by concentration, since the dynamic surface tensions of their dilutions are high and remain relatively unaffected owing to the presence of only small amounts of surfactants. The biological effect/dose response curves should, therefore, be different for these situations. This implies that selectivity factors between easy- and difficult- to-wet species would change as testing progresses from acetone/aqueous surfactant solutions to dispersions of commercial-type formulations. A decision on whether to include an adjuvant such as a surfactant or an emulsi- fiable oil, which will reduce spray solution surface tensions in a formulation testing programme, may depend on whether this is likely to be a desirable feature.

ACKNOWLEDGEMENTS

We are grateful to Mr Darren Batten for technical assistance.

REFERENCES

1. Grayson, B. T., Pestic. Sci., 33 (1991) 281-304. 2. Adam, N. K., In Contact Angle, Wettability and Adhesion,

Chapter 2. Ado. in Chem. Series No. 43, ed. R. F. Gould. American Chemical Society, Washington, DC, 1964.

3. Hartley, G. S. & Graham-Bryce, I . J., Physical Principles of Pesticide Behaviour, Chapter 8 . Academic Press, London, 1980.

4. Hull, H. M., Davis, D. G. & Stolzenberg, G. E . , Adjuvants for Herbicides, Chapter 3 . Weed Science Society of America, Champaign, IL, 1979.