The Effect of Airflow-Assisted Parameters on Droplet Deposition on Soybean Leaves at the V7 Growth Stage

Abstract

In agricultural production, the underside of crop leaves and the middle-lower canopy are key areas where pests and diseases typically develop at early stages. Increasing droplet deposition in these critical regions is essential for improving pesticide efficacy and crop yield. This study aims to optimize airflow-assisted parameters to enhance spray operation quality. By extracting the physical characteristics of soybean leaves at the V7 growth stage and conducting theoretical analysis, the study explored the factors influencing leaf orientation and droplet deposition, as well as the coupling relationship between these two aspects. A one-way fluid–structure coupling model was established using COMSOL software 6.1 to simulate the interaction between airflow and soybean leaves. The simulation results showed that airflow caused 71.1% of upper leaves, 66.7% of middle leaves, and 43.3% of lower leaves to have a flipping angle greater than 10°, with most flipped leaves (61.9%) concentrated on the windward side. Using droplet deposition on the middle-lower canopy and the underside of leaves as evaluation indices, a numerical simulation orthogonal experiment was conducted. The results indicated that the optimal operational parameters were an initial airflow speed of 20 m/s, an outlet-to-canopy distance of 0.45 m, and a forward airflow deflection angle of 32°. This optimal parameter combination improved droplet deposition. Field experiments confirmed these results, showing that compared to the spraying without optimization, droplet deposition on the lower and middle canopy and the underside of the leaves increased by 2.1 times and 2.3 times, respectively.

1. Introduction

With the increasing demand for pest and disease control in agricultural production, the limitations of traditional spraying technologies in crop protection have become more apparent. Airflow-assisted spraying technology has gained attention due to its ability to improve pesticide deposition efficiency and reduce environmental impact [1]. Different crops exhibit variations in canopy structure, plant height, leaf orientation, and physicochemical characteristics. This study focuses on soybean, which is vulnerable to various pests and diseases during the V3 to V7 growth stages [2,3,4], including red spider mites, aphids, and powdery mildew, which typically affect the back of the leaves and the middle and lower canopy [5,6,7,8]. The leaf underside, with its dense stomata and thin cuticle, is highly susceptible to pathogen attack. During this period, soybean plants grow rapidly, and the canopy becomes dense. Continuous monitoring and controlling pests and diseases are essential to ensure effective protection. Effective deposition of pesticide droplets on the back of the leaves and in the middle and lower canopy is crucial to maintaining soybean yield and quality [9].

The density of the crop canopy is one of the main factors influencing droplet deposition [10,11], particularly for crops like soybeans. Existing studies have shown that spray modes combining flexible shielded openers (FSCO) with rotational air technology effectively reduce drift and improve droplet uniformity on soybean leaf surfaces [12]. Additionally, the combination of airflow-assisted and electrostatic spraying has been proven to enhance spray deposition on the upper canopy leaves of soybeans [13]. As an economically important crop, soybeans face more complex spray deposition issues due to their unique canopy structure and leaf orientation [14]. Sprayers with airflow assistance have become widely used for pest control in field crops. During application, researchers have found that airflow assistance reduces droplet drift and, by adjusting airflow intensity, helps separate the stems and leaves, widening the droplet transport path [15]. This improves droplet deposition in the middle and lower canopy and effectively controls pests on the underside of leaves [16]. Rocamora et al. [17] tested the relationship between airflow velocity, angle, and pesticide deposition during the later stages of crop growth, analyzing the deposition effect of airflow-assisted sprayers on lilies. Foque et al. [18] conducted spray tests using potted plants and confirmed that airflow influences droplet deposition. Duga et al. [19] tested wind-assisted orchard sprayers, finding that smaller canopy gaps lead to higher target deposition rates under airflow assistance.

In terms of optimizing parameters for airflow-assisted spraying, many researchers have utilized CFD models for numerical analysis to inform design improvements. Qiu et al. [20] developed a CFD model to simulate leaf vibration caused by droplets and verified its effect on droplet size distribution. Miao et al. [16] simulated pressure distribution and airflow velocity inside the guiding tube of an airflow-assisted sprayer, optimizing the pipe structure for better droplet transport to high-stemmed crops. Cui et al. [21] used a bidirectional fluid–structure interaction model to investigate the relationship between airflow and plant structure parameters in cotton crops. Most of the research has focused on airflow-assisted sprayers for orchards, while fewer studies have addressed leaf reorientation and parameter optimization for field crops under airflow-assisted spraying.

Existing studies have focused on improving spraying efficiency and reducing droplet drift in high-density plants, such as fruit trees and vegetables. However, research on the changes in leaf orientation and droplet deposition on the abaxial leaf surface and middle-lower canopy of field crops during airflow-assisted spraying is relatively limited. Therefore, this study aims to establish a mathematical model for leaf orientation angle and droplet deposition using a one-way fluid–structure interaction (FSI) and fluid–particle tracking simulation. Numerical simulations will be conducted to optimize the parameters of airflow-assisted spraying and investigate the effects of these parameters on leaf orientation and droplet deposition. The goal is to improve droplet deposition on the abaxial leaf surface and middle-lower canopy of soybean plants at the V7 growth stage, providing a practical solution for precision pest and disease control. This study also offers theoretical guidance for applying airflow-assisted spraying in field crop protection, enhancing the effective utilization of pesticides.

2. Materials and Methods

2.1. Material Phenotypic Characteristics and Physicochemical Properties

In mid-July 2024, soybean stem and leaf samples were collected from an experimental field in Kedong County, Heilongjiang Province, China. Sampling occurred at 5:00 P.M., with a humidity of 65% and a temperature of 28 °C, during the V7 growth stages of the soybean variety Longda 17 (Heihe City, Heilongjiang Province, China.). The soybean leaves exhibit high metabolic activity at this stage, with open stomata and lenticels facilitating the absorption and transport of pesticides and liquid fertilizers.

The sampling method employed was the five-point sampling technique [22], during which the leaf angle within the sampling area was measured. The stem samples were taken by removing the branches and retaining only the main stem and branch sections. A total of fifty samples of soybean stems and leaves were collected. The samples were placed in resealable bags and refrigerated to prevent moisture loss and ensure measurement accuracy. The measurement locations of the geometric dimensions of the leaves and stems are shown in Figure 1a and Figure 1b. The soybean stems were all 820 mm in length; the geometric dimensions of the leaves and stems are shown in

Table 1. Structural parameters of soybean leaves.

Canopy	Leaf Length (mm)	Petiole Length (mm)	Leaf Width (mm)
Upper canopy	100	30	70
Middle canopy	85	25	60
Lower canopy	70	20	50

.

Due to natural competition, soybean plants exhibit a degree of randomness in the growth of their branches and leaves. However, the overall phenotypic characteristics of the plant follow a statistical pattern. During the V7 growth stages, the soybean plant generally takes a conical shape, with branches and leaves arranged in a spiral pattern along the stem. The horizontal angular displacement between adjacent branches is approximately 120°. The average plant height ranges from 800 mm to 900 mm, and the stem reaches its maximum diameter of 420 mm at a height of 350 mm, as shown in Figure 1c.

The leaf inclination angle in the sampling area was measured, revealing that the upper leaves had larger inclination angles while the lower leaves had smaller angles. The distribution of leaf inclination angles is shown in Figure 2. Leaves with inclination angles greater than 30° made up over 65% of the total, with average angles of 45° for upper canopy leaves, 35° for middle canopy leaves, and 25° for lower canopy leaves.

To ensure that the leaves and stems of the soybean plant are not broken or excessively bent by high-pressure airflow during auxiliary airflow spraying, it is crucial to determine the elastic moduli of the leaves accurately and stems. The WDW-S universal testing machine was used to measure the elastic modulus, employing the three-point bending method [23]. The determination of the leaf elastic modulus was divided into two parts: one for the leaf blade and another for the petiole. For the leaf blade, samples were selected with the midrib as the centerline, with the sample area measuring 25 mm in length and 10 mm in width at the root, middle, and tip of the leaf. For the petiole, samples were taken from the base and middle sections, each 10 mm long. For the stem, samples were taken from 100 mm, 200 mm, and 300 mm from the top of the plant, each with a length of 30 mm. The elastic modulus was calculated based on the deflection model for a supported beam in material mechanics [24] as follows:

$$E={\displaystyle \frac{{\mathit{PL}}^3}{48\omega I}}(1-v_{\mathrm{f}}^2).$$

(1)

In the equation, E represents the elastic modulus, Pa; P represents the externally applied load, N; L represents the span length, mm; ω represents the bending deflection, mm; and I represents the moment of inertia, mm⁴; v_f represents Poisson’s ratio.

The obtained parameters are presented in

Table 2. The calculated results for the elastic modulus.

Leaf Surface Elastic Modulus (MPa)	Petiole Elastic Modulus (MPa)	Stem Elastic Modulus (MPa)
47.5	2.5	1180

.

2.2. Force Analysis and Mathematical Model Development

2.2.1. Force Analysis of Soybean Plants Under Auxiliary Airflow

During the spraying operation, the forward motion of the sprayer generates an auxiliary airflow that creates aerodynamic loads on the soybean plant. This airflow causes bending deformation of the stem and disturbance of the leaves, thereby expanding the upper canopy channel and facilitating better droplet penetration into the middle and lower canopy. The spray and auxiliary airflow angles are adjusted synchronously during the operation, as shown in Figure 3.

The connection between the soybean stem and the ground is simplified as a cantilever beam model, as shown in Figure 4. When the auxiliary airflow acts on the soybean plant, the pressure exerted by the airflow can be approximated as a uniformly distributed load acting on the plant’s total windward surface area. Since the stem is fixedly connected to the leaf surface and petiole, the interaction between the stem and the leaf can also be modeled as a cantilever beam.

The resultant force of the concentrated load generated by the auxiliary airflow in the horizontal direction acts on the cantilever beam, producing the deformation equation as follows:

$${M\left(x\right)=F}_{\mathrm{p}}\times (x+L)\sin \alpha =- w″\left(x\right)\times \mathit{EI}$$

(2)

In the equation, M(x) represents the bending moment, N·m; F_p represents the externally applied load, N; x represents the coordinate of the deflection point on the x-axis mm; w(x) represents the deflection at point x, mm; and α represents the angle of the auxiliary airflow.

Ignoring the effect of travel speed on airflow velocity, the wind force load generated by the auxiliary airflow is given by [25]:

$$F_{\mathrm{p}}={\displaystyle \frac{1}{2}}{\rho }_1{v}_{\mathrm{a}}^{2}S\times \sin \alpha$$

(3)

In the equation, ρ₁ represents the air density, kg/m³; v_a represents the auxiliary airflow velocity, m/s; S represents the windward area of the soybean plant, mm².

Based on the airflow expansion law, the attenuation equation for the airflow velocity from the outlet to the front of the plant canopy is derived as follows [26]:

$$v_2=C_1{v}_1\sqrt{{\displaystyle \frac{b}{x_1}}}$$

(4)

In the equation, v₁ represents the airflow velocity at the outlet, m/s; v₂ represents the airflow velocity before entering the canopy, m/s; C₁ represents the attenuation coefficient; b represents the fan width, mm; x₁ represents the distance from the outlet to the canopy, mm.

As shown in Equation (4), the distance between the outlet and the canopy is a key factor influencing the airflow velocity before it reaches the canopy. The closer the auxiliary airflow is to the canopy, the smaller the velocity attenuation.

Based on the above analysis, the deflection equation for stem curvature and the angular displacement expression at the stem’s end interface can be expressed as follows:

$$\left\{\begin{array}{l}{y}_1={\displaystyle \frac{{\rho }_1{v}_{\mathrm{a}}^{2}S\times \sin \alpha }{12E_1{I}_{1}S}}(3L-x)\\ {\theta }_1={\displaystyle \frac{{\rho }_1{v}_{\mathrm{a}}^{2}S\times \sin \alpha }{4E_1{I}_{1}S}}\times L^2\end{array}\right.$$

(5)

In the equation, E₁ represents the elastic modulus of the soybean stem, MPa; I₁ represents the moment of inertia of the soybean stem, mm⁴.

2.2.2. Force Analysis of Soybean Leaves Under the Influence of Auxiliary Airflow

When considering the leaf as the research object, two cases are defined based on the relationship between the direction of the auxiliary airflow and the leaf’s orientation: the windward and leeward directions. The connection between the leaf petiole and the stem can be treated as a fixed connection, with the contact area considered a fixed plane. The simplified mechanical models for both cases are shown in Figure 5.

Ignoring the influence of vehicle speed on airflow velocity, the wind load exerted by the auxiliary airflow on the leaf can be expressed as:

$$F_{\mathrm{p}1}={\displaystyle \frac{1}{2}}{\rho }_1{v}_{\mathrm{a}}^2\sin \alpha \times S_1\times \cos \beta .$$

(6)

In the equation, F_p1 represents the wind force load on the leaf, N; β represents the leaf tilt angle,°; S₁ represents the leaf’s windward area, mm².

After the auxiliary airflow enters the canopy, the wind pressure it generates decreases due to the resistance imposed by the canopy structure, leading to further attenuation of the airflow velocity. The resistance coefficient of the crop canopy is typically considered constant [27], independent of variations in canopy position and airflow velocity. It is generally related to leaf area density, with values typically ranging from 0.5 to 1.0. Therefore, the mathematical model for the airflow velocity after entering the canopy is [28]:

$${\mathit{lnv}}_3{=\mathit{lnv}}_2{-d}_{\mathrm{c}}{C}_{\mathrm{d}}{L}_{\mathrm{ad}}$$

(7)

In the equation, v₃ represents the velocity of the auxiliary airflow within the canopy, m/s; C_d represents the resistance coefficient of the canopy; L_ad represents the leaf area density, m²/m³; d_c represents the canopy depth, mm.

The uniformly distributed load generated by the auxiliary airflow and the bending moment applied to the leaf surface induce bending deformation in the soybean leaf. To investigate the bending deflection curve of the leaf surface, the bending moment and uniformly distributed load applied to the leaf were calculated separately. When only the bending moment acts on the leaf, the deflection curve equation and the expression for the rotation angle at the free end section are as follows:

$$\left\{\begin{array}{l}{y}_2={\displaystyle \frac{{\rho }_1{v}_{\mathrm{a}}^2\sin \alpha \times S_1\times \cos {\beta (x+L}_2)\times x^2}{4E_2{I}_2}}\\ {\theta }_2={\displaystyle \frac{{\rho }_1{v}_{\mathrm{a}}^2\sin \alpha \times S_1\times \cos \beta \times 2L_2^3}{2E_2{I}_2}}\end{array}\right..$$

(8)

In the equation, E₂ represents the elastic modulus of the soybean leaf surface, MPa; I₂ represents the moment of inertia of the soybean leaf, mm⁴.

When the leaf is subjected solely to a uniformly distributed load, it moves upward and flips. Additionally, under the influence of the airflow, both sides of the leaf bend inward to overcome the resistance of the leaf veins. The deflection curve equation and the expression for the angular displacement are as follows:

$$\left\{\begin{array}{l}{y}_3={\displaystyle \frac{{\rho }_1{v}_{\mathrm{a}}^2\mathrm{s}\mathrm{i}\mathrm{n}\alpha \times S_1\times \mathrm{c}\mathrm{o}\mathrm{s}\beta \times x^2}{48E_3{I}_3{L}_1}}{(x}^2-4L_{1}x+6L_1^2)\\ {\theta }_3={\displaystyle \frac{{\rho }_1{v}_{\mathrm{a}}^2\mathrm{s}\mathrm{i}\mathrm{n}\alpha \times S_1\times \mathrm{c}\mathrm{o}\mathrm{s}\beta \times L_1^2}{12E_3{I}_3}}\end{array}\right.$$

(9)

In the equation, E₃ represents the elastic modulus of the soybean petiole, MPa; I₃ represents the moment of inertia of the soybean petiole, mm⁴.

By superimposing the expressions obtained for both cases, the deflection curve equation and end-section rotation angle of the soybean leaf under the combined effects of both bending moment and uniformly distributed load due to the auxiliary airflow are as follows:

$$\left\{\begin{array}{l}{y}_4{=y}_2+y_3={\displaystyle \frac{1}{2}}{\rho }_1{v}_{\mathrm{a}}^2\mathrm{s}\mathrm{i}\mathrm{n}\alpha \times S_1\times \mathrm{c}\mathrm{o}\mathrm{s}\beta \times x^2({\displaystyle \frac{{\mathit{xL}}_2+L_2^2}{2E_2{I}_2}}+{\displaystyle \frac{x^2{-4L}_{1}x+6L_1^2}{24E_3{I}_3{L}_1}})\\ {\theta }_4{=\theta }_2{+\theta }_3={\displaystyle \frac{1}{2}}{\rho }_1{v}_{\mathrm{a}}^2\mathrm{s}\mathrm{i}\mathrm{n}\alpha \times S_1\times \mathrm{c}\mathrm{o}\mathrm{s}\beta \times x^2({\displaystyle \frac{2L_2^3}{E_2{I}_2}}+{\displaystyle \frac{L_1^2}{6E_3{I}_3}})\end{array}\right..$$

(10)

During the action of the auxiliary airflow, the rotation angle of the leaf tip around point A under the influence of auxiliary airflow is as follows:

$${\theta }_t=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left[{\displaystyle \frac{L_1{+L}_2}{{(L}_1{+L}_2)\mathrm{t}\mathrm{a}\mathrm{n}{\beta +h}_1}}\right]+\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left[{\displaystyle \frac{L_1{+L}_2}{{(L}_1{+L}_2)\mathrm{t}\mathrm{a}\mathrm{n}{(\beta +\theta }_4{)+h}_1}}\right].$$

(11)

In the equation, h₁ represents the height of the petiole at the point of attachment to the stem, mm.

Through the force analysis of soybean stems and leaves, it was found that under the influence of the uniformly distributed load generated by the wind, the deflection curve trajectory and angular displacement at the leaf tip, excluding intrinsic physical and chemical parameters, depend solely on the initial airflow velocity, outlet-to-canopy distance, and airflow forward deflection angle. Therefore, the key factors influencing leaf orientation and improving droplet deposition in the middle and lower canopy are the initial airflow velocity, outlet-to-canopy distance, and airflow forward deflection angle.

In this study, leaf orientation changes are influenced by various factors, with initial airflow velocity, outlet-to-canopy distance, and airflow forward deflection angle being the primary contributors. The airflow affects leaf orientation and exerts force on the stem, causing it to bend. These factors influence the leaf orientation and play a crucial role in droplet deposition. Through an analysis of the forces acting on the soybean stem and leaves, we found that under uniformly distributed loads (induced by wind), the deflection curve of the leaf and stem, as well as the angle of the end section, are related to airflow velocity as follows: airflow velocity directly impacts droplet transport efficiency and deposition quantity, with higher airflow velocities helping to effectively deliver droplets to the back of the leaves and the middle-lower canopy. The relationship with airflow angle is as follows: the forward deflection angle of the airflow affects its impact force and droplet distribution. Proper angle settings can optimize droplet deposition on plant surfaces. The relationship with nozzle height is as follows: the distance between the nozzle and canopy determines the flight time of the droplets in the air, and an optimal height can reduce droplet evaporation and drift, thus improving deposition.

2.3. Leaf Surface Droplet Deposition: Numerical Modeling and Analysis

2.3.1. Single-Factor Simulation Experiments on Factors Affecting Leaf Orientation

This study conducted single-factor simulation experiments to analyze the effects of various factors on leaf orientation, such as auxiliary the initial airflow velocity, outlet-to-canopy distance, and airflow forward deflection angle. The goal was to determine the adjustment ranges for each factor. COMSOL Multiphysics 6.1 (COMSOL Inc., Stockholm, Sweden) was used for the one-way fluid–structure coupling simulations of airflow and leaf interaction. The fluid state was determined to be turbulent based on the Reynolds number, and a 2D computational domain of 1800 mm × 1200 mm was constructed based on soybean plant height and inter-plant spacing. Air was set as the fluid material, and the realizable k-ε turbulence model was chosen for the fluid calculation. The Navier–Stokes equations were used for the governing equations, and the auxiliary airflow attenuation equation (Equation (4)) was incorporated into the model.

A cross-sectional model of the leaf surface was established based on the phenotypic characteristics of the leaf, with a thickness of 3 mm. The center of the leaf section was modeled as a cone with a base diameter corresponding to the petiole diameter, and fixed constraints were applied. Mathematical models for the stem and leaf sections were incorporated using Equation (5) and Equation (11), respectively. Boundary conditions were set, with the upper right corner as the inlet for the auxiliary airflow and the leaf surface and other boundaries as walls.

Based on theoretical analysis, actual operating conditions, and fan power, the initial auxiliary airflow velocity was set between 5 m/s and 25 m/s [29,30,31]. The initial velocity at the inlet was adjusted to simulate different initial airflow velocities within the computational domain.

The optimal spray direction angle for horizontal target spraying was 20° and 30° [32]. Since the leaf orientation change is related to the auxiliary airflow angle through a trigonometric function and is synchronized with the spray angle, the experimental factor range was expanded from 10° to 50°. The inlet shape corresponding to different angles was modeled based on the nozzle structure.

Due to the hydraulic system’s consistent control over the airflow system and spray bar height, the airflow outlet height was adjusted to prevent the airflow from being too close to the canopy, which could cause leaf breakage. The effect of height changes on droplet uniformity was also considered. The range of auxiliary airflow distance to the canopy was set to 0.3 m to 0.7 m [33,34].

Single-factor simulation experiments examined the effects of initial airflow velocity, outlet-to-canopy distance, and airflow forward deflection angle. Tracking points were added at the edges of the leaf section to determine the trajectory of the leaf surface orientation by tracking the position of these points. The leaf-reorientation angle was used as the evaluation metric. The output model is as follows:

$$\delta =\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}({\displaystyle \frac{2y_{\mathrm{b}}{-2y}_{\mathrm{a}}}{2x_{\mathrm{b}}{+W}_1-2x_{\mathrm{a}}}}).$$

(12)

In the equation, $\delta$ represents the flip angle of the leaf cross-section. (x_a, y_a) represents the coordinate of the tracking point on the leaf edge before reorientation, and (x_b, y_b) is the coordinate on the leaf edge after reorientation.

Five levels for the simulation factors were defined within the specified parameter ranges, as shown in

Table 3. The factors and levels for simulation.

Level	Initial Airflow Velocity (m/s)	Outlet-to-Canopy Distance (m)	Airflow Forward Deflection Angle (deg)
1	5.0	0.3	10
2	10.0	0.4	20
3	15.0	0.5	30
4	20.0	0.6	40
5	25.0	0.7	50

. Single-factor fluid–structure coupling simulations were conducted, with each simulation experiment repeated three times.

2.3.2. Multi-Factor Simulation Test for Droplet Deposition

This study evaluated the effectiveness of plant protection operations using droplet deposition on the middle and lower canopy and the abaxial leaf surface of soybeans as key indicators. The coupling relationship between leaf orientation and droplet deposition during airflow-assisted spraying was investigated to optimize spray performance.

A 3D model of the soybean plant was constructed based on the collected plant samples, as shown in Figure 6a. The plant spacing was 200 mm with a row spacing of 650 mm, and the model included 25 plants. The airflow inlet model was designed based on the structure of the airflow-assisted sprayer outlet, with a spray diffusion zone constructed in front of the inlet. The droplet fluid inlet, which served as the injection source for the droplet simulation, had a spacing of 500 mm, a particle density of 1000 kg/m³, a particle size of 0.22 mm, and a surface tension of 0.0729 N/m. The injection flow rate was 1.36 L/min, and the injection pressure was 0.4 MPa. A machine travel speed of 2.2 m/s was applied in the dynamic mesh module, as shown in Figure 6b.

After importing the plant model, the turbulence physical field, solid mechanics physical field, and fluid flow particle tracking physical field were added. The drag force condition was applied within the fluid physical field, and the Hadamard–Rybczynski drag law was selected. The bottom surface of the computational domain was set as the outlet. The mathematical models for the turbulence and solid mechanics physical fields were the same as those used in the leaf fluid–structure coupling simulations. Additionally, Equation (7) was added to the airflow velocity attenuation model (Equation (4)) to represent the velocity decay after the airflow enters the canopy. In the solid mechanics physical field, the connection between the plant roots and the petiole was fixed, and both the leaves and the stem were treated as linearly elastic materials. The mathematical leaf and stem orientation models were implemented using Equations (5) and (10).

In the fluid flow particle tracking physical field, a particle counter was placed on the leaf surface to count the particles for each simulation, tracking droplet deposition at various canopy locations. The mesh was structured to enhance the convergence of the numerical simulation. The mesh size was gradually refined from 10 mm to 1 mm. To assess the grid independence and the consistency of the flow field, the accuracy of droplet collection by the leaf was used as the key indicator. A final mesh size of 1 mm was chosen for optimal computational accuracy. Turbulence simulation results were first used as initial conditions for the solid mechanics physical field for multi-physics coupling. The results of the fluid–structure coupling simulation were then used as input conditions for the fluid flow particle tracking physical field, enabling transient droplet deposition numerical simulations.

2.4. Field Experiment

2.4.1. Experimental Conditions

To validate the accuracy of the simulation results, the improvement in droplet deposition was investigated using the optimized operational parameters derived from the simulations. Field comparison tests were conducted with conventional and wind-assisted sprayers, which feature adjustable airflow angles. The carrier machine used for the trials was a CFJ2204 tractor, (Jiangsu Changfa Agricultural Equipment Co., Ltd, Changzhou, China) and the field tests were conducted with the air-assisted sprayer (3WF-1200 model, Manufacturer: Harbin Huayi Technology Service Co., Ltd., Harbin, China) developed by the research team. The sprayer is equipped with a mechanism that synchronizes the adjustment of both the spray boom angle and the auxiliary airflow angle. This mechanism allows for adjusting the airflow’s inclination relative to the canopy height via a hydraulic cylinder. The airflow speed is adjusted by varying the fan speed using a hydraulic motor, and the auxiliary airflow velocity is precisely measured using a portable anemometer (BENETECH GM8901+, Shenzhen Benetech Technology Co., Ltd., Shenzhen, Guangdong, China), as shown in Figure 7a. XR11003-VP flat fan nozzles (CFJ2204 Tractor, Jiangsu Changfa Agricultural Equipment Co., Ltd., Changzhou, Jiangsu, China. TeeJet Technologies Co., Ltd., Springfield, IL, USA) were used, with water as the spraying medium (surface tension: 72 mN/m). The spray pressure was maintained within the 0.4 ± 0.05 MPa range, while the fan pressure was fixed within 1 ± 0.1 MPa.

The experiments were conducted in the test field of Kedong County, Heilongjiang Province, China. Meteorological conditions, such as temperature, humidity, and wind speed, influence the effectiveness of spraying. To enhance the generalizability of the study’s results, field trials were conducted from 3:00 to 5:00 p.m., when temperatures are higher and evaporation rates are faster. During this period, the ambient temperature was 32.2 °C, with a relative humidity of 65% and a northern wind direction. The maximum wind speed recorded was 5.6 m/s. A photograph of the experimental site is shown in Figure 7b.

2.4.2. Experimental Procedures and Methods

Based on the analysis of simulation experiments and the requirements of practical agricultural production, droplet deposition tests were conducted on the dorsal surface of soybean leaves and the middle and lower canopy layers during the V7 growth stages. To minimize experimental errors, the sampling distance for each trial was set to 5 m, with the length of each sampling area fixed at 10 m. The deposition effect was investigated by attaching water-sensitive paper (Sygenta brand) to the soybean leaves using paperclips and staplers on the front and back sides of the plant’s upper (Figure 8a), middle, and lower leaves (Figure 8b) [35].

The experimental plot measured 200 m in length and 45 m in width, with the spraying equipment having a working width of 15 m. The spraying machine was operated against the wind during the experiment to ensure consistent trial conditions. Three operational conditions were tested: no auxiliary airflow, an airflow angle of 0°, and operation with optimized parameters based on simulation results. For each condition, the average forward speed of the spraying equipment was set at 2.2 m/s. Each trial was repeated three times, and the average droplet deposition on the front and back sides of leaves from all canopy layers was recorded. The field experimental layout is shown in Figure 9.

3. Results and Discussion

3.1. Analysis of the Results of the Single-Factor Simulation Experiment on Leaf Orientation

Figure 10 illustrates the process of a single-factor simulation. The analysis reveals the relationship between initial airflow velocity, airflow forward deflection angle range, and the outlet-to-canopy distance. As the airflow velocity, angle, and distance increase, the windward leaf elevation angle increases, and the tendency for the leaf to fold inward along the midrib also intensifies. This leads to a higher likelihood of effective droplet deposition on the back of the leaf. Additionally, for lateral leaves, the bending of the stem and the downward pressure exerted on the leaf surface from the wind increase the chance of droplet deposition on the leaf’s underside.

Scatter plots were created to represent the relationship between the leaf angle of rotation for the top and middle leaves and the three key factors: initial airflow velocity, airflow forward deflection angle, and outlet-to-canopy distance. Polynomial fitting equations were applied to these plots, as shown in Figure 11. The red curve represents the fitted rotation angle for the top leaf, while the green curve represents the fitted rotation angle for the middle leaf.

The results of the single-factor simulations indicate that the initial airflow velocity, the airflow forward deflection angle range, and the outlet-to-canopy distance affect the leaf-reorientation angle. The study found that when the initial airflow velocity exceeds 20 m/s, the change in the leaf-reorientation angle becomes less pronounced. Furthermore, excessively large angles may lead to the tearing or breakage of the leaves. Thus, the maximum initial airflow velocity is set at 20 m/s.

When the airflow forward deflection angle exceeds 40°, the increase in leaf-reorientation angle for the upper and middle canopy leaves slows down. Additionally, compared to an outlet-to-canopy distance of 0.4 m, the distance of 0.3 m results in a smaller increase in the leaf-reorientation angle of the top leaves, and the distance of 0.3 m may reduce droplet uniformity [36].

Based on the above analysis, to further investigate the interaction effects of these three factors on droplet deposition, the following parameter ranges were determined for the multi-factor simulation experiment: initial airflow velocity range of 15–20 m/s, airflow forward deflection angle range of 20–40°, and outlet-to-canopy distance range of 0.4–0.6 m.

3.2. Consistency Check of the Fluid–Structure Interaction (FSI) Model for the Plant Population

In the leaf orientation simulation model, changes in airflow-assisted parameters have a relatively isolated and direct effect on leaf orientation. However, since the leaf orientation model established in this study is coupled with the droplet deposition model for the plant population, it is necessary to perform a consistency check for the changes in leaf orientation between the two models. Figure 12 shows the leaf orientation under the fluid–structure interaction simulation for the plant population, using the following parameters: initial airflow velocity of 20 m/s, outlet-to-canopy distance of 0.4 m, and airflow forward deflection angle of 30°.

Analysis of the figure shows that the airflow most influences the upper canopy leaves. In contrast, the middle and lower canopy leaves exhibit more variability due to the higher density of plant models in the computational domain and the differences in leaf orientation and airflow attenuation. As a result, some leaves experience smaller flip angles, negative flip angles, or no orientation change. Statistical analysis of data from three repeated experiments within the initial airflow velocity of 20 m/s reveals that 71.1% of upper canopy leaves have a flip angle greater than 10°, 66.7% of middle canopy leaves, and 43.3% of lower canopy leaves. Most leaves with a flip angle greater than 10° are concentrated on the windward side, accounting for 61.9% of the total leaf count, while those with negative flip angles are primarily found on the leeward side, making up 26.6% of the total leaf count.

Figure 13 shows the average flip angles of the leaves at different positions within the canopy, as predicted by the two models. The error rate between the leaf orientation model and the plant population model is 7.8 ± 0.7%, with the error rate for the flip angle of leaves in the middle of the canopy being 5.3 ± 0.5%. These results indicate that the airflow effectively reorientates the leaves within the computational domain of the plant population model, and the two models demonstrate strong consistency in their performance.

The differences between the two models primarily arise from variations in the airflow distribution within individual plants and plant groups. In the individual plant model, the airflow can effectively cover the leaf surfaces, promoting droplet deposition and uniform pesticide distribution. However, in the plant group model, airflow encounters obstructions due to mutual shielding between plants and the complex structure of the canopy, which hinders airflow transmission and prevents some leaves from receiving adequate airflow. This uneven distribution weakens the impact of airflow on leaf orientation, leading to residual errors. Therefore, when developing the plant group model, it is essential to account for the characteristics of plant groups by introducing a canopy attenuation coefficient to optimize airflow distribution and improve spray performance.

Due to the attenuation of airflow and the denser upper and middle canopy, the leaf angle of the lower leaves is smaller. The factors influencing leaf posture change are complex. The main factors affecting leaf posture variation are the airflow’s magnitude, direction, and height [37,38]. During the airflow-assisted spraying, the airflow influences the leaves and loads the plant stems, causing them to bend. These factors influence both leaf reorientation and droplet deposition. Given these complexities, it is necessary to incorporate fluid flow and particle tracking simulations in the deformed plant canopy to understand better droplet deposition after the canopy changes [39,40].

3.3. Droplet Deposition Simulation Results, Parameter Optimization, and Discussion

Figure 14 illustrates the transient process of leaf orientation and droplet deposition simulation. The changes in leaf orientation as the airflow moves from low to high velocity occur in five stages: static lift, vertical oscillation, horizontal oscillation, torsional vibration, and leaf stabilization. In the stabilized state, both sides of the leaf bend inward under the influence of the airflow, overcoming the resistance of the leaf veins. In contrast, the leaf tip flips upward, overcoming the elasticity of the petiole, which increases droplet deposition on the abaxial surface of the leaf. By using auxiliary airflow to rotate and disturb the plant’s stems and leaves, the droplet transport pathways within the canopy are expanded, leading to an improved droplet deposition rate in the middle and lower canopy targets. The figure shows four groups with varying airflow velocity and deflection angle. Droplet deposition shifts as airflow velocity and angle increase, with more forward droplet movement in higher velocity and angle groups.

Based on theoretical analysis and the results of the single-factor experiments, the ranges of the factors were determined. A three-factor, three-level orthogonal experimental design was then employed to simulate further the droplet deposition effect under the influence of auxiliary airflow. A leaf particle counter quantified the droplet deposition at the upper, middle, and lower canopy leaf positions. The factors and levels of the orthogonal experiment are shown in

Table 4. Factors and levels for droplet deposition simulation.

Level	Initial Airflow Velocity (m/s)	Outlet-to-Canopy Distance (m)	Airflow Forward Deflection Angle (deg)
−1	15.0	0.4	20
0	17.5	0.5	30
1	20.0	0.6	40

.

Based on the simulation results in the upwind computational domain, the variance results and significance test analysis are presented in

Table 5. Multivariable variance analysis results.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F-Value	p-Value	Significance Level
Model	313.95	9	34.88	15.50	0.0008	**
A	80.65	1	80.65	35.83	0.0006	**
B	56.18	1	56.18	24.96	0.0016	*
C	16.82	1	16.82	7.47	0.0292	*
AB	26.01	1	26.01	11.55	0.0115	*
AC	0.49	1	0.49	0.22	0.6550
BC	0.090	1	0.090	0.040	0.8472
A2	29.12	1	29.12	12.94	0.0088	**
B2	10.51	1	10.51	4.67	0.0675
C2	82.63	1	82.63	36.71	0.0005	**
Lack of fit	3.80	3	1.27	0.42	0.7463
Error	11.95	4	2.99
Total sum	329.71	16

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

. In the table, A, B, and C represent the auxiliary initial airflow velocity, outlet-to-canopy distance, and airflow forward deflection angle. The variance analysis indicates that all three factors affect droplet deposition. The regression model has a p-value of 0.0008, suggesting a high significance level for the droplet drift rate model. Additionally, the lack of fit terms, with a value of 0.7463, is not significant, indicating that the model fits the data well.

By eliminating the non-significant terms, the regression model for droplet deposition density is obtained:

$$Y=30.86+3.18A-2.65+1.45C-2.25\mathit{AB}-2.63A^2-4.43C^2$$

(13)

To avoid getting trapped in local optima during the global search for the optimal solution, the multi-island genetic algorithm (MIGA) was employed to optimize the auxiliary airflow parameters for spraying. Based on the previous response surface analysis and the actual spraying conditions, the mathematical optimization model was determined as follows:

$$\left\{\begin{array}{l}\mathit{maxf}\left(Y\right)\\ \mathrm{s}.t.\left\{\begin{array}{l}15\le A\le 20\\ 0.4\le B\le 0.6\\ 20\le C\le 40\end{array}\right.\end{array}\right.$$

(14)

The maximum droplet deposition was set as the optimization objective. By solving the objective function, the optimal parameter combination was determined to be: auxiliary airflow initial velocity of 21.74 m/s, outlet-to-canopy distance of 0.458 m, and forward deflection angle of 32.36°. These values were rounded to practical levels to facilitate subsequent field experiments and parameter adjustments.

Figure 15 shows the average droplet deposition quantities on the upper, middle, and lower canopy leaf positions (both front and back) for conventional spraying, conventional airflow-assisted spraying, and optimized airflow-assisted spraying. The numerical simulation results indicate that, compared to conventional spraying without airflow assistance, the droplet drift was reduced by 38.43% under the influence of auxiliary airflow. When comparing the optimal parameter combination with conventional airflow-assisted spraying, the droplet deposition at the middle and lower canopy and on the abaxial leaf surface increased by 2.04 and 1.92 times, respectively. Compared to conventional spraying without airflow, droplet deposition at the middle and lower canopy and on the abaxial leaf surface increased by 3.8 and 4.2 times, respectively.

This study’s simulation results indicate that adjusting airflow-assisted spraying parameters can improve droplet deposition. This finding is consistent with the results of Zhong et al. (2020) [41], who also observed that increasing airflow intensity and adjusting airflow angles can enhance droplet deposition through numerical simulations. Specifically, the angle and strength of the airflow played a key role in the airflow field within the spraying area. The airflow effectively prevented droplet drift and precisely delivered droplets to the crop leaf surfaces, thereby reducing drift caused by external factors such as natural wind and improving deposition efficiency.

Previously, Dai et al. (2023) [42] found that the distance between the airflow outlet and the canopy is an important factor influencing droplet deposition. When the airflow outlet is closer to the crop canopy, the airflow can more effectively deliver droplets to the leaf surfaces, reducing droplet drift and dispersion, which enhances spray deposition efficiency. In contrast, when the distance between the outlet and the canopy is too large, the airflow delivery efficiency decreases, and droplets are more susceptible to natural wind, leading to a reduction in deposition. Our study also confirmed this phenomenon, as we observed higher droplet deposition when the airflow outlet was positioned closer to the canopy.

Furthermore, Sun et al. (2021) [43] further highlighted that an appropriate spray angle could effectively enhance droplet deposition. Although this improvement diminishes as the canopy penetration increases, the average droplet deposition and penetration rate within the canopy are still enhanced. Our results are consistent with this, suggesting that adjusting the synchronization angle between the airflow and spray can improve droplet deposition within the canopy. These findings support the practical application of optimizing airflow-assisted spraying parameters for pesticide application and crop protection. Figure 15 shows the average droplet deposition quantities on the upper, middle, and lower canopy leaf positions (both front and back) for conventional spraying, conventional airflow-assisted spraying.

3.4. Field Comparison Test Results

The auxiliary airflow parameters were optimized based on droplet deposition simulations. After the airflow-assisted spraying (Figure 16a), the water-sensitive paper on the dorsal surface of the leaves changed color (Figure 16b).

After the spraying operation, the water-sensitive paper was dried and sealed in bags, with information such as the experimental group, leaf position, and test time recorded on the bag. Figure 17 shows the color change on the water-sensitive paper at different positions during the comparison test.

The droplets on the collected water-sensitive paper were identified and analyzed using the OpenCV computer vision module in Python (version 4.5.3). After removing anomalous data from three experimental sets, the results are presented in Figure 18. Compared to conventional airflow-assisted spraying, the optimal parameter combination increased droplet deposition on the lower canopy and abaxial leaf surfaces by 2.1 and 2.3 times, respectively. Compared to conventional spraying without airflow assistance, droplet deposition on the lower canopy and abaxial leaf surface increased by 4.2 and 5.6 times, respectively.

Comparison results indicate that the droplet deposition on the upper and middle canopy front leaves in conventional spraying operations is similar to that of optimized airflow-assisted spraying on the target. However, there is a difference in droplet deposition on the abaxial leaf surface. This suggests that using the optimal parameter combination for spraying can effectively enhance droplet deposition on soybean plants’ lower and middle canopy and the abaxial leaf surface.

The discrepancy between the simulated and field trial results is as follows: the error rate for droplet deposition on the upper canopy leaves is 13%, on the lower canopy is 8.3%, and on the abaxial leaf surface is 5.1%. The primary reason for these discrepancies is the influence of natural wind speed (5.6 m/s) on the droplets during the trial [44,45]. Additionally, the sunny afternoon conditions increased the exposure of the upper canopy leaves as the leaf angles increased [46,47]. In contrast, the natural wind affected the lower canopy leaves less, resulting in higher consistency between the simulation and field results, particularly for droplet deposition on the abaxial leaf surface, which had a lower error rate.

In conventional spraying, the droplets deposited on the leaves exhibited irregular deformation. This phenomenon is attributed to the high natural wind speed [48,49], which causes plant stems and leaves to oscillate, leading to changing angles between the droplets and the target at deposition [50]. As a result, the droplets could not stabilize on the target, leading to tailing [51]. In contrast, the optimized airflow-assisted spraying operation produced fewer tailing droplets on the water-sensitive paper. The airflow curtain reduced the effect of irregular natural winds on plant stems and leaves while decreasing the angle between the droplets and the target, reducing the effect force during deposition. Furthermore, the optimal forward spray angle enhanced the droplets’ penetration ability, increasing droplet deposition on the lower and middle canopy leaves [52].

In the field experiments conducted in this study, adjustments to the initial airflow velocity, angle, and outlet height improved droplet deposition on the underside of leaves and the middle and lower canopy layers. These parameters have also been emphasized in studies on orchard airflow-assisted spraying, where they are considered key factors for optimizing spray coverage and minimizing waste [53,54,55]. Although some key differences exist between orchard spraying and field crop spraying [56,57], the results regarding high-speed airflow to assist droplets in reaching targets are similar to our findings [58].

This study focused solely on spraying operations during the V7 growth stage of soybean, where airflow-assisted spraying demonstrated clear advantages in droplet deposition in the middle and lower canopy. However, different crops exhibit differences in canopy structure, plant height, leaf orientation, and physicochemical properties [59,60], necessitating adjustments to the airflow-assisted spraying parameters. For crops with taller stalks, such as corn, or crops with higher planting density, such as wheat, spraying efficacy may be influenced by canopy structure, leading to incomplete canopy penetration or uneven deposition. Therefore, a comprehensive analysis of factors such as canopy structure, environmental conditions, climate variability, and growth stages is essential to develop optimized parameter adjustment strategies for different crops, which can be used to develop intelligent spraying systems further. By incorporating real-time data feedback, sensor monitoring, and database support, the practicality and accuracy of this method can be improved.

While the field experiments in this study were conducted at fixed locations and times, which introduced certain limitations in environmental variability, introducing real-time environmental data, conducting cross-scenario experiments, and increasing model flexibility could improve the model’s adaptability to varying environmental conditions.

Moreover, while airflow-assisted spraying technology offers clear advantages in increasing spraying efficiency and environmental protection, its high operational and equipment costs may limit its use on small-scale farms [61,62]. The high initial investment and operational costs may burden smallholders economically. In some cases, airflow-assisted spraying may not provide the expected outcomes, as factors such as the crop growth cycle, canopy structure, and environmental conditions can affect the spraying efficacy. Under high wind conditions, incorrect airflow direction may result in drift, increasing the risk of environmental contamination [63,64]. Therefore, more precise airflow control strategies are necessary to mitigate these issues. Nevertheless, airflow-assisted spraying technology holds economic promise for large-scale farms. Improving spraying efficiency and crop protection effectiveness can reduce pesticide use and production costs, ultimately enhancing farmers’ economic returns.

4. Conclusions

This study uses a combination of simulation and field validation methods to investigate the effect of airflow-assisted spraying on droplet deposition and leaf orientation in soybean crops during the V7 growth stage. Compared to conventional non-airflow-assisted spraying and traditional airflow-assisted spraying methods, the results indicate that optimized airflow-assisted spraying improved droplet deposition, especially on the abaxial leaf surface and the lower and middle layers of the canopy. The study highlights the importance of optimizing spraying parameters (such as airflow velocity, outlet-to-canopy distance, and airflow deflection angle) to enhance spraying efficiency and coverage. Using simulation models to predict droplet behavior also provides a new direction for precision agriculture, particularly large-scale field applications.

This research contributes to developing more efficient spraying technologies for soybean cultivation and provides valuable insights for future field operations. Future studies could explore the long-term effects of airflow-assisted spraying on plant health, pesticide efficacy, and environmental sustainability. Furthermore, investigating its application in crops with different canopy structures could expand the scope and applicability of airflow-assisted spraying technology.