Numerical Simulation and Validation of Droplet Deposition on Tomato Leaf Surface under Air-Assisted Spraying

Abstract

The interaction between the leaf and airflow directly influences droplet deposition on the leaf surface. This paper investigates the effect of this interaction on droplet deposition. A bidirectional fluid-structure coupling model was established using computational fluid dynamics (CFD) based on mechanical parameters and surface roughness of tomato leaves to simulate tomato leaf deposition under air-assisted spraying. Utilizing the model and considering air velocity, droplet size, and initial leaf inclination as experimental factors, a three-factor, three-level central composite design simulation and response surface analysis were conducted to examine the influence of each factor on the surface deposition amount of tomato leaves. The order of influence of each factor on the deposition amount is as follows: a quadratic regression model was established with the flow velocity having the greatest influence, followed by initial leaf inclination and then droplet size. The influence of each factor on the deposition distribution of the leaf surface was compared and studied separately. Airflow velocity significantly affected the deposition distribution of the leaf surface. Higher airflow velocities resulted in a lower proportion of deposition at the tip and a higher proportion at the base. The maximum relative errors of leaf deformation and deposition were 8.77% and 17.44%, respectively. The findings of this research can provide valuable insights for optimizing the working parameters of air-assisted atomizers.

1. Introduction

Air-assisted spraying technology uses high-speed airflow to transport droplets so that they can reach distant targets and deliver droplets to the surface and interior of crop canopy, effectively adhering to the front and back of leaves [1,2]. Effective coverage of different distances and crops can be achieved by adjusting airflow and spray parameters. However, the complex interactions between airflow, droplets, and crops are not fully understood and are critical to understanding droplet deposition on crops.

Most of the current studies on droplet–leaf interaction are based on static target leaves [3,4], while fewer studies have been conducted on dynamic leaf interaction with spray droplets. The leaves have different motion states under different airflow velocities [5], and the motion of the leaves in the air-fed spray state has a significant effect on the deposition of droplets on the leaves [6,7]. The effect of airflow on the motion state of the leaf will inevitably affect the deposition effect of droplets on the leaf; therefore, the study of the deposition characteristics of droplets on dynamic leaves deserves further research.

Computational fluid dynamics (CFD) is good at solving most flow problems and is now widely used in agricultural engineering [8]. At present, some scholars at home and abroad have combined experiments and CFD models to study the interactions among airflow, liquid droplets, and crops. Delele et al. [9] numerically simulated and analyzed the trajectory and deposition patterns of droplets sprayed by an air-assisted sprayer using a CFD model but did not consider crop interactions. Qiu et al. [10] and Cao et al. [11] simulated and investigated the deposition behavior of droplets on a dynamic leaf by using the CFD method, and the results show that leaf vibration can help droplet deposition to some extent. These studies provide an important theoretical basis for understanding droplet movement and attachment mechanisms under different conditions but do not consider the effect of airflow on droplet deposition. Endalew et al. [12] provided a new CFD integrated simulation method that directly incorporates the actual 3D architecture of the canopy into the CFD model to simulate branches and simulates leaves by creating porous media around the branches. This model was used to study pesticide deposition within the canopy and to improve the design and spraying parameters of sprayers. Salcedo et al. [13] also used the same method of incorporating the solid model of branches with porous media to simulate the spraying effects of air-assisted sprayers in orchards, and the model was validated for use in predicting the trajectory of spray droplets. Hong et al. [14] developed an integrated CFD model to study the deposition of pesticide spray droplets discharged from a sprayer in the canopy, on the ground, and through off-target drift in the air. The model simplified the canopy as a porous medium and used a Lagrangian particle transport model to track the movement of pesticide droplets. The use of a porous medium to simplify the leaf, while reducing the complexity of the numerical simulation, ignores the interaction of the airflow with the leaf. In addition to using porous media instead of leaves, some researchers have also used two-way fluid–solid coupling to study the deformation pattern of leaves under airflow [15,16] and the airflow distribution within the canopy [17], but they only focused on the bending deformation of the leaves under airflow and did not pay attention to its effect on droplet deposition. Therefore, further studies are needed to investigate the fog droplet deposition on the surface of dynamically deformed leaves.

The three elements of airflow, droplet, and crop determine the effect of droplet deposition [18,19,20]. The purpose of this paper is to explore the effects of airflow velocity, droplet particle size, and initial leaf inclination angle of the leaf on droplet deposition and deposition distribution on the leaf surface in conjunction with bi-directional fluid–solid coupling as well as discrete term modeling.

2. Materials and Methods

2.1. Determination of Tomato Leaf Parameters

2.1.1. Leaf Size

Tomato leaves were collected from the greenhouse at Jiangsu University, specifically using the Provence variety. In order to eliminate differences in leaf age of leaves at different heights, the tomato plant canopy was divided into upper, middle, and lower layers. Ten leaves were randomly selected from each layer as samples. A straightedge was used to measure the length and width of the leaves as well as the length of the petiole. Additionally, a vernier caliper was employed to measure the average thickness of the leaves and the average diameter of the petiole. Leaf contours were traced using graph paper. The samples were then placed in self-sealing bags to prevent water loss, which could affect the accuracy of the mechanical parameter measurements, and promptly transferred to the laboratory for further analysis.

2.1.2. Measurement of Mechanical Properties of Tomato Leaves

The physical properties of real leaves are quite complex [21,22]. In this study, the material properties of tomato leaves and petioles were simplified and treated as isotropic elastic materials. For computational fluid dynamics (CFD) simulations, materials must have parameters such as modulus of elasticity, density, and Poisson’s ratio. For tomato leaves and petioles, Poisson’s ratios could be 0.32 and 0.34, respectively, in accordance with what was described by [23,24]. A total of 30 samples were used in this study, with 15 samples designated for the elasticity modulus test and the remaining 15 for the density test.

The modulus of elasticity was measured by the three-point bending method using a physical property analyzer (TA-XT.Plus, Stable Micro Systems Co., Godalming, UK). The parameters of the physical property analyzer were set as follows: probe P5 (radius of curvature 5 mm). The test mode was compression; the pre-test speed and mid-test speed were 0.1 mm; the post-test speed was 5 mm; the sampling frequency was 400 Hz; and the spacing between the supporting vertical walls was 15 mm according to the Chinese national standard GB/T34171-2017 [25]. A section of the petiole with a length of 20 mm was intercepted, and along the direction of the main veins of the leaf surface, a section of the leaf surface in the middle of the leaf surface with a length of 20 mm and a width of 10 mm was intercepted. The petiole specimen or the leaf specimen was placed on a support frame, and the mid-point deflection and load increment values were collected as the probe moved vertically downward. The stress-displacement curves were obtained with the help of a physical property analyzer, and the petiole elastic modulus was obtained by using Equation (1); the leaf elastic modulus was obtained by using Equation (2) [16]. The measurement process is shown in Figure 1.

$$E_p={\displaystyle \frac{L^3}{48I_1}}\left({\displaystyle \frac{\Delta F}{\Delta \delta }}\right)$$

(1)

$$\begin{array}{c}{E}_l={\displaystyle \frac{L^3}{48I_2}}\left({\displaystyle \frac{\Delta F}{\Delta \delta }}\right)\left(1-{\mu }^2\right)\end{array}$$

(2)

where ΔF represents the load increment, N; Δδ represents the center deflection increment, mm; L is the horizontal support span, mm; I₁ and I₂ are the moment of inertia of the petiole and leaf samples, mm⁴; and μ is Poisson’s ratio.

Statistical analysis of the results showed that the average modulus of elasticity of the petiole was 148.6 MPa, with a 95% confidence interval of [131.9, 165.3] MPa. The average modulus of elasticity of the leaf was 45.3 MPa, with a 95% confidence interval of [31.9, 59.7] MPa. The densities of the tomato petiole and leaf, determined using the conventional weighing method, were 1019.6 kg·m⁻³ and 575.9 kg·m⁻³, respectively.

2.1.3. Surface Roughness Measurement of Tomato Leaf

Considering the effect of leaf surface properties on deposition [26], the leaf surface roughness was calculated and measured using a super depth of field 3D microscope (Keyence VHX-900F, Keyence Co., Osaka, Japan) [27]. The surface roughness was defined as the arithmetic mean of the absolute value of the surface height deviation as shown in Equation (3) and the measurement procedure is shown in Figure 2. The measured result was 21.74 µm.

$$R_a={\displaystyle \frac{1}{N}}{\displaystyle \sum }_i{\displaystyle \sum }_j\left|Z_{\left(i,j\right)}-Z_{ave}\right|$$

(3)

where $Z_{\left(i,j\right)}$ is the distance between each point and the mean plane, µm; $Z_{ave}$ is the height of the mean plane, µm; and $N$ is the number of measurement points

2.2. Geometric Modeling and Simulation Parameters

2.2.1. Geometric Modeling

According to the average values of the sample statistics, the dimensions of the leaf model are as follows: the leaf surface is 64.8 mm long, 36.8 mm wide, and 0.3 mm thick; the petiole is 22.6 mm long and 2.0 mm in diameter; and the area of the leaf is 1732.3 mm². Therefore, the leaf size parameters remain constant during the analysis. The geometric model is shown in Figure 3, featuring a spray surface of 50 × 100 mm located 5 mm from the velocity inlet and an airflow field of 200 × 200 × 300 mm. The modeling was performed using SolidWorks 2020, followed by meshing and coupled solving in ANSYS 2020R2 (ANSYS Inc., Canonsburg, PA, USA).

Reasonable simplification of the model helps to improve mesh quality and computational accuracy. The tomato leaf consists of two parts: the petiole and the leaf surface. The primary simplifications of the leaf model involve removing the continuous serrated bumps along the leaf edge and the veins covering the leaf, as it has been found in previous studies that these small structures have a small effect on the flow field but may degrade the quality of the mesh, making the results unscientific and increasing the computational cost [16]. The mesh division is shown in Figure 4. The number of meshes in the solid and fluid domains of the leaf are 31,036 and 459,146, respectively, with maximum mesh skewness below 0.6 and average orthogonality above 0.8.

2.2.2. Simulation Parameter Setting

In the leaf solid domain, the front end of the petiole is set as a fixed support, while the rest of the leaf surfaces are set as coupling interfaces. The right side of the fluid domain is the velocity inlet, while the other five surfaces are pressure outlets. The spray surface is used as the incidence source for the droplets, and the incidence mode is set as surface. Droplet fragmentation and aggregation are considered [28]. The coupling surface, i.e., the discrete-phase boundary conditions on the leaf surface, are all set as wall-film, which consists of four states, viscous, rebound, diffusion, and splash, covering various scenarios of droplet impact on the leaf surface. The velocity inlet, pressure outlet, and wall discrete-phase boundary conditions are set to escape. Since the volume fraction of droplets in the flow field is less than 1%, it is assumed that the discrete phase in the simulation process satisfies the Lagrangian discrete-phase model.

The solution methods are pressure-based and transient, and the analytical model is standard K-epsilon [15]. The outlet pressure is set to 0 to simulate the atmospheric pressure around the tomato leaves in a real environment. A sequential solution approach is used to solve the fluid and solid domains iteratively. In each iteration, the Fluent module first calculates the effect of the airflow on droplet motion and the forces exerted on the tomato leaves. Then, the transient structural module calculates the deformation of the tomato leaves based on these forces. The deformation of the tomato leaves, in turn, affects the airflow and the trajectory of the droplets. The system coupling module repeats the iterations until the calculations converge.

In the system coupling module, the coupling time step is set to 0.001 s, the minimum number of iteration steps is set to 1, the maximum number of iteration steps is set to 5, and the simulation computation time is set to 1 s. A 32 GB RAM computer equipped with an Intel i5-12400F processor and ANSYS 2020R2 software is used for the simulation. The bidirectional fluid–solid coupling simulation is very time-consuming, taking more than 24 h for a single simulation. After computation, the transient structure module provides the maximum deformation (spatial displacement at the same location on the leaf) at the end of the petiole, the center of the leaf, and the tip of the leaf. The mass of droplets deposited on the leaf surface is obtained in Fluent, and leaf surface deposition is calculated as the ratio of the mass of droplets deposited to the surface area of the windward side of the leaf.

2.3. Experimental Validation

The velocity of sprayer-assisted airflow in the greenhouse reaching the tomato canopy at different distances was measured using an impeller-type anemometer (Kestrel 5500, Nielsen-Kellerman Co., Boothwyn, PA, USA), and, according to the principle of terminal velocity [29], the terminal velocity of the airflow from the wind-delivered sprayer was 2 m·s⁻¹, the range of the airflow velocities was taken to be 2~6 m·s⁻¹, the initial leaf inclination angle of the leaves range is 15~75°, droplet size is taken as 100~200 µm, and each factor is uniformly selected at five levels within the range of values taken, as shown in

Table 1. Simulated factors and levels.

Levels	Considerations
	Airflow Velocity (m·s−1)	Droplet Size (µm)	Initial Leaf Inclination Angle (°)
1	2	100	15
2	3	125	30
3	4	150	45
4	5	175	60
5	6	200	75

.

2.3.1. Verification of Leaf Deformation

A high-speed camera (I-speed TR, Olympus Co., Shinjuku, Tokyo, Japan) was used to monitor the displacement of the tomato petiole end, leaf surface form center, and leaf tip to verify the accuracy of the CFD model [30]. As shown in Figure 5, the experiment was conducted indoors to avoid the effect of natural wind. To provide auxiliary airflow, a centrifugal fan (YWL 2E-150, Hangda Electric Co., Taizhou, China) was selected, and a transformer was used to adjust the wind speed. The tomato leaves were fixed on an adjustable bracket, and the center of the airflow outlet of the blower duct was at the same height as the center of the tomato leaf shape. By adjusting the angle between the bracket and the horizontal plane, the leaf tilt angle can be adjusted. The optical axis of the camera was perpendicular to the reference plane and the motion plane in order to film and record the dynamic deformation process of the tomato leaf. Prior to the validation test, three tomato leaves of similar size to the model were selected. In order to obtain accurate deformation data, small balls of sticky foam were used and stuck to the end of the petiole, the shaped center of the leaf, and the tip of each leaf. The video was recorded three times for each leaf during the trial. At the end of the test, the maximum deformation at the petiole end, leaf form center, and leaf tip were measured using Tracker 6 [31], and the average value was taken as the final deformation value.

Monitoring points were positioned at the petiole end, leaf centroid, and tip of the simulated leaf to capture data on petiole and leaf deformation across various parameters, which is illustrated in Figure 6. In the experimental study, it was found that the accuracy of defoliation was affected by the rapid water loss and severe wilting of the leaves during the blowing process of the auxiliary airflow, the number of tests was reduced to ensure the validity of the validation, and five sets of parameter tests were selected to ensure that all parameters were included in the test. Validation test arrangement and results are detailed in

Table 2. Simulation error statistics of leaf deflection.

No.	Initial Leaf Inclination Angle (°)	Airflow Velocity (m·s−1)	Petiole Tip (mm)	Leaf Centroid (mm)	Leaf Tip (mm)	Error Extremum (%)
			Verification /Simulation	Verification /Simulation	Verification /Simulation
1	15	2	2.59/2.65	46.34/48.56	81.79/87.34	6.79
2	30	5	9.67/10.02	70.84/75.41	119.29/129.53	7.95
3	45	6	12.44/12.89	62.26/64.89	113.33/123.27	8.77
4	60	3	6.63/6.28	52.79/50.37	96.46/93.49	4.80
5	75	4	7.62/7.46	89.38/84.49	48.03/46.17	5.12

, with the maximum error recorded at 8.77%. This discrepancy may be attributed to the absence of consideration for leaf veins, but this error is acceptable [15]. Analysis of the dynamic deformation characteristics of tomato leaves in the coupled simulation revealed significant bending deformation at the junction of the petiole and leaf surface. According to the results of Section 2.1.2, it can be seen that the elastic modulus of the leaf is smaller than the elastic modulus of the petiole, and the connection between the leaf and the petiole belongs to the stress concentration area, while the leaf is the area on the leaf that is mainly affected by the airflow, so the deformation easily occurs at the connection between the leaf and the petiole. This observation aligns with the deformation patterns observed in actual tests.

2.3.2. Leaf Surface Deposition Validation

As shown in Figure 7, the leaves were fixed using an adjustable angle mount, tomato leaves of similar size to the model were selected before each experiment, and their area was measured using ImageJ 1.53t [32]. The leaves were located 1 m from the nozzle. The droplet size was achieved by adjusting the spray pressure of the nozzle (Hypro VP110-01, Pentair Co., Golden Valley, MN, USA). The particle size spectrum of the droplets produced by the nozzle was measured in a laboratory environment using a laser particle size analyzer (DP-02, Omec Co., Zhuhai, China) at a location chosen to be 50 cm from the nozzle. The selected spray parameters are listed in

Table 3. Spray parameter.

Spray Pressure (MPa)	Flow Rate (L·min−1)	VDM (μm)
0.1	0.26	169.70
0.2	0.33	144.28
0.3	0.40	126.86
0.4	0.46	117.48
0.5	0.52	111.23

. Since the flow rate of the nozzle varied at different spray pressures, it was necessary to ensure the consistency of the spray volume by controlling the spray time. The test design is shown in

Table 4. Leaf surface deposition verification test scheme.

No.	Air Velocity (m·s−1)	Spray Pressure (MPa)	Initial Leaf Inclination Angle (°)	Spray Time (s)
1	2	0.5	45	1.5
2	3	0.4	30	1.2
3	4	0.3	15	1
4	5	0.2	60	0.9
5	6	0.1	75	0.8

, and the rationale for the selection of test parameters is consistent with the leaf deformation validation test, with a spray time at 0.3 MPa. The fluorescent dye rhodamine B was added to the spray solution at a concentration of 0.25 g·L⁻¹ and was placed in a self-sealing bag with dimensions of 12 cm × 18 cm after the surface of the leaves was naturally air-dried for 2 h. Subsequently, 10 mL of deionized water was added to wash all the rhodamine B on the surface of the leaves into the bag, and 3 mL of the eluent was taken to determine the concentration of rhodamine B with a UV-visible spectrophotometer (UV-9100c, LabTech Co., Beijing, China) [33], which had an absorption wavelength of 554 nm.

The simulation is shown in Figure 8. As indicated in

Table 5. Simulation error statistics of leaf surface deposition.

No.	Sedimentation (μL·cm−2)		Inaccuracies/%
	Verification	Simulation
1	4.50	4.02	11.94
2	3.84	3.57	7.56
3	3.30	2.81	17.44
4	2.11	1.79	17.88
5	1.71	1.52	12.50

, the maximum relative error between the simulation and validation tests across the five groups of test parameter combinations is 17.88%. Coupled with the results of the leaf deformation validation test, this demonstrates that the tomato leaf fluid–solid coupling simulation model developed in this study can effectively replicate the deformation process of tomato leaves under airflow and the deposition process of droplets. This capability lends support to the understanding of deposition laws.

2.4. CFD Analysis Methods

2.4.1. Deposition Volume Analysis

Using the constructed fluid–solid coupling model of tomato leaf deposition, the experimental analysis of tomato leaf surface droplet deposition law under airflow was carried out by considering three factors, namely, airflow velocity v, initial leaf inclination angle β, and droplet size d. The results are summarized as follows. Therefore, a central composite test program was designed to explore the effects of each factor on the droplet deposition characteristics on the surface of a single leaf. The spray surface flow rate was taken as 0.000362 kg·s⁻¹ (measured with a liquid collection device according to the deposition verification arrangement), the spray nozzle was VP110-01, and the spray flow rate was 0.3 MPa. Keeping the spray flow rate fixed, air velocity, droplet particle size, and initial inclination angle of the crop leaf were taken as test factors, and the amount of leaf surface deposition was taken as an indicator.

The simulation parameters are shown in

Table 6. Experimental scheme and results of droplet deposition.

No.	Air Velocity (m·s−1)	Droplet Size (µm)	Initial Leaf Inclination Angle (°)
1	5	175	30
2	5	175	60
3	5	125	30
4	4	150	75
5	3	125	30
6	4	150	45
7	4	100	45
8	3	125	60
9	4	150	45
10	6	150	45
11	4	150	45
12	4	150	45
13	3	175	30
14	4	150	15
15	3	175	60
16	4	200	45
17	5	125	60
18	4	150	45
19	2	150	45
20	4	150	45

, with 20 groups, of which 15 are factor groups and 5 are nulls for estimation errors. Analysis of variance (ANOVA) was conducted using the Design-Expert^® 8.0 software (Stat-Ease Inc., Minneapolis, MN, USA) to examine simulation experiment results, and statistical significance was evaluated at p < 0.05.

2.4.2. Sediment Distribution Analysis

As shown in Figure 9, the leaf was divided equally into A, B, and C, three regions according to its length, and Fluent was utilized to derive the deposition data on the leaf surface, calculate the deposition amount of each part separately, and calculate the deposition percentage of each part by using the formula [25].

$$D_i={\displaystyle \frac{d_{ri}}{{\displaystyle \sum _1^n}{d}_{ri}}}\times 100\%$$

(4)

where D_i is the deposition percentage of each fraction and d_ri is the deposition amount of each fraction, μL·cm⁻².

In order to study the effect of each factor on the distribution of droplet deposition on the leaf surface, the parameters were selected as shown in

Table 7. Parameter selection.

No.	Air Velocity (m·s−1)	Droplet Size (µm)	Initial Leaf Inclination Angle (°)
1	2	150	45
2	3	150	45
3	4	150	45
4	5	150	45
5	6	150	45
6	4	100	45
7	4	125	45
8	4	175	45
9	4	200	45
10	4	150	15
11	4	150	30
12	4	150	60
13	4	150	75

.

3. Results and Discussion

3.1. ANOVA Results

The analysis of variance (ANOVA) for leaf surface deposition Dr is shown in

Table 8. Variance analysis of leaf surface deposition.

Variation Source	Sum of Square	Degree of Freedom	F Value	p Value
Model	6.730	9	354.940	<0.001 **
v	5.750	1	2727.180	<0.001 **
d	0.098	1	46.330	<0.001 **
β	0.668	1	317.080	<0.001 **
vd	0.002	1	1.000	0.340
vβ	0.019	1	9.020	0.013 *
dβ	0.003	1	0.148	0.708
v2	0.121	1	57.510	<0.001 **
d2	0.032	1	15.090	0.003 *
β2	0.015	1	7.120	0.024 *
Residual	0.021	10
Lack of fit	0.015	5	2.320	0.189
Pure error	0.006	5
Total value	6.750	19

Note: ** indicates highly significant (p < 0.01); * indicates significant (0.01 < p ≤ 0.05).

. The regression model was significant (p < 0.0001), and the lack of fit term was not significant (p = 0.189), indicating that the regression was valid. In general, the use of quadratic independent variables in ANOVA leads to complexity in the relationship between observations and effects. However, it is important to note that the use of quadratic independent variables in this study was necessary because it has a significant impact on the reliability of the regression analysis.

The effects on the amount of droplet deposition were as follows: v, d, β, and v² were highly significant; vβ, d², and β² were significant; and vd and dβ were not significant. Based on the sum of squares, the order of significance of the effect of each factor on the amount of surface deposition on tomato leaves was airflow velocity v > initial leaf inclination angle of the leaf β > droplet size d. The analysis showed that airflow parameters, spray parameters, and the growth characteristics of tomato leaves play equally important roles. Therefore, when using air-assisted spraying, different airflow parameters and spray parameters should be applied according to the growth characteristics of leaves to optimize the effect of plant protection operations.

$$\begin{array}{l}{D}_{\mathrm{r}}=2.80-0.60v+7.81\times {10}^{-2}d-2.04\times {10}^{-1}\beta +4.88\times {10}^{-2}v\beta +6.94\times {10}^{-2}{v}^2-3.56\\ \times {10}^{-2}{d}^2+2.44\times {10}^{-2}{\beta }^2\end{array}$$

(5)

Figure 10 illustrates the response surface depicting the influence of the interaction between airflow velocity and initial leaf inclination angle on the amount of deposition on the leaf surface when the droplet particle size is situated at the center level (d = 150 μm). From the figure, it can be seen that the amount of deposition decreases with the increase in airflow velocity as well as initial leaf inclination angle. Meanwhile, the correlation analysis shows that the Pearson coefficient of v is −0.911 with p < 0.01, which indicates that the airflow velocity is highly significant and negatively affects the amount of deposition. The correlation test of β with p = 0.177 > 0.05 indicates that there is no significant linear relationship between the initial inclination of the leaf and the amount of deposition.

3.2. Effect of Factors on the Distribution of Deposits on the Surface of the Leaf

3.2.1. Effect of Airflow Velocity on the Leaf Surface Deposition Distribution

As shown in Table 7, the initial leaf tilt angle of 45°, droplet size of 150 µm, and different airflow velocities are used as simulation parameters to compare the amount and percentage of deposition in different regions of the leaf under different scenarios. According to

Table 9. The amount of deposition in each area of leaf under different airflow velocities.

Air Velocity (m·s−1)	Sedimentation (μL·cm−2)
	A	B	C
2	4.45	4.87	4.36
3	4.23	2.79	2.43
4	3.95	2.09	1.72
5	3.03	1.54	1.22
6	2.59	1.28	1.01

, the deposition amounts in different regions of the leaf can be observed. The increase in air velocity reduces the leaf’s windward area, so the amount of leaf surface deposition gradually decreases. Specifically, at an airflow speed of 2 m·s⁻¹, the deposition amounts in different regions are relatively uniform. However, when the airflow speed exceeds 2 m·s⁻¹, the deposition proportions change across different regions. Combining the data from Table 9 and Figure 11, it can be observed that as airflow speed increases, the deposition amount in Region A first increases and then decreases, while the deposition amounts in Regions B and C gradually decrease. The deposition percentage in Region A shows a gradually increasing trend, whereas Regions B and C exhibit a gradually decreasing trend. The one-way ANOVA shows that the effect of airflow velocity on the deposition percentage in each region is significant (p < 0.05), but the trend of the deposition distribution gradually flattens out with the increase in airflow velocity. The change of airflow velocity not only affects the inclination angle of the leaf but also affects the airflow field around the leaf. In order to explain this deposition pattern, the pressure distribution on the surface of the leaf under different airflow velocities is illustrated, as shown in Figure 12.

The data are analyzed in conjunction with Table 9 and Figure 12. When the auxiliary air velocity is 2 m·s⁻¹, the pressure distribution on the windward side shows a trend of being high in the center area and decreasing gradually to the surrounding area, and the pressure distribution on the leaf surface is relatively uniform, in which case the deposition of each area on the leaf surface is relatively consistent, but the deposition percentage in the center area is higher. This shows that when the auxiliary airflow speed is low, the influence of the airflow on the movement of the droplets is relatively small, and the deposition on the leaf surface is relatively uniform. However, when the auxiliary airflow velocity exceeds 2 m·s⁻¹, the situation on the leaf surface starts to change. The higher-pressure region starts to shift to the leaf base division, resulting in a change in the pressure distribution on the leaf surface, which affects the deposition of droplets, with less distribution of deposited mass at the lower pressure. This phenomenon illustrates the close relationship between the pressure distribution and the deposition distribution, and the influence of the airflow velocity on the deposition on the leaf surface is not only reflected in the change of the deposition mass but also in the change of the deposition location. In addition, the formation of this deposition pattern is also affected by the vibration of the leaf itself. At higher air velocity, the tip part of the leaf vibrates more, making it difficult to deposit droplets on the leaf surface.

3.2.2. Effect of Droplet Particle Size on Leaf Surface Deposition Distribution

As shown in Table 7, the initial leaf tilt angle of 45°, airflow velocity of 4 m·s⁻¹, and different droplet sizes are used as simulation parameters to compare the amount and percentage of deposition in different areas of the leaf for different cases. The following conclusions can be drawn from the data in

Table 10. The deposition amount in each area of the leaf under different droplet sizes.

Droplet Size (µm)	Sedimentation (μL·cm−2)
	A	B	C
100	3.90	2.02	1.60
125	3.94	2.07	1.67
150	3.95	2.09	1.72
175	3.98	2.23	1.79
200	4.09	2.43	1.91

and Figure 13: First, the deposition amount in each region shows an increasing trend with the increase in the droplet particle size. This shows that the droplet size has a certain influence on the amount of deposition on the leaf surface, mainly because the droplet size influences the droplet volume, and the increase in droplet volume makes the effect of inertia and gravity more pronounced. Therefore, the droplets are less prone to drift and are more likely to be deposited on the leaf surface. Second, in terms of the deposition percentage for each region, the deposition percentage for region A shows a gradual decrease with increasing droplet size, while the deposition percentage for regions B and C shows a gradual increase. In conjunction with Figure 12c, at 4 m·s⁻¹, the pressure on the leaf surface decreases from region A to region C, indicating that the velocity of the airflow on the leaf surface increases from region A to region C. The increase in droplet particle size reduces the drift of the droplets, which is more effective for higher-velocity regions B and C. However, in terms of significance, the droplet size is significant for regions A and B (p < 0.05) but not for region C (p = 0.459 > 0.05).

3.2.3. Effect of Initial Lobe Inclination on Sediment Distribution

As shown in Table 7, a droplet size of 150 µm, an airflow velocity of 4 m·s⁻¹, and different initial leaf inclinations are used as simulation parameters to compare the amount and percentage of deposition in different regions of the leaf for different scenarios. The data in

Table 11. The amount of sediment in each area of the leaf under different initial leaf inclination angles.

Initial Leaf Inclination Angle (°)	Sedimentation (μL·cm−2)
	A	B	C
15	4.68	2.37	2.09
30	4.44	2.14	1.79
45	3.95	2.09	1.72
60	3.33	2.07	1.71
75	3.05	2.06	1.70

and Figure 14 allow the following conclusions to be drawn: first, the change in the initial leaf inclination angle mainly affects the windward area of the leaf. At an airflow velocity of 4 m·s⁻¹, the windward area of the leaf gradually decreases with the increase in the initial leaf inclination angle. Consequently, the amount of deposition in each area decreases. Secondly, as shown in Table 11, in terms of the deposition percentage of each region, the deposition percentage of region A gradually decreases with the increase in the initial leaf inclination angle, while the deposition percentage of region B and region C gradually increases. As shown in Figure 15, under the condition of constant airflow velocity, the change in the initial leaf inclination angle not only affects the windward area but also affects the pressure distribution on the leaf surface, which may be the main reason for the change in the deposition percentage in each region. Through one-way ANOVA, it was learned that the effect of the initial leaf inclination angle on the deposition percentage of each region was significant (p < 0.05), but when the initial leaf inclination angle was greater than 60°, the change in the deposition percentage of each region was gradually flattened, which may be due to the fact that the initial leaf inclination angle has a smaller effect on the change in the leaf inclination angle.

4. Conclusions

In this study, a CFD model of the surface deposition law of tomato leaves under the action of auxiliary airflow was established by combining two-way fluid–solid coupling and the discrete term particle tracking method. Through the experimental validation of leaf deformation and surface deposition, it was found that the maximum relative errors between the simulation and validation tests were 8.77% and 17.44%, respectively, which could effectively simulate the deformation process of tomato leaves and the deposition process of droplets under the action of airflow. In the case of the same sprayer flow rate, air velocity, droplet size, and initial leaf inclination angle have a significant effect on the amount of leaf surface deposition, of which air velocity has the greatest effect, followed by the initial leaf inclination angle; droplet size has the least effect. The air velocity and initial leaf inclination angle have a significant effect on the percentage of deposition on each region of the leaf surface, which may be due to the pressure distribution on the leaf surface. The droplet size is significant for regions A and B and not significant for region C. The effect of air velocity and initial leaf inclination angle on the percentage deposition on each region of the leaf surface is significant. Different airflow parameters, spraying parameters, and crop growth parameters affect the deposition percentage in different regions of the leaf surface. Therefore, the sprayer operating parameters can be adjusted to target the pest and disease areas on the surface of tomato leaves to improve the efficiency of pesticide utilization.