Numerical Simulation and Orthogonal Test of Droplet Impact on Soybean Leaves Based on VOF Method and High-Speed Camera Technology

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors

Your manuscript presents an interesting and technically relevant study that combines VOF-based CFD modeling and high-speed imaging to analyze droplet impact dynamics on soybean leaves. However, the paper would benefit from a deeper physical validation of the CFD model, explicit discussion of mesh independence and convergence, and a clearer justification of the turbulence model and boundary conditions. The integration between experimental and numerical results is promising but remains largely qualitative. Please review the attached annotated document for detailed comments and specific recommendations to strengthen the methodological rigor and scientific depth of the manuscript.

Comments for author File: Comments.pdf

Author Response

Main issue 1: The abstract has a clear and coherent structure, but it lacks conciseness in the pres

entation of results and tends to overload the section with numerical details that could be

moved to the body of the text. It is recommended to place greater emphasis on method

ological innovation or scientific contribution compared to previous studies and to reduce

the technical description of the procedure. In addition, it would be advisable to highligh

t more clearly the practical applicability of the model in real agricultural spraying scenarios.

Response 1: We appreciate the reviewers' recognition of the abstract structure and their valuable suggestions. To address issues such as "long presentation of results, excessive numerical details, insufficient methodological innovation and scientific contribution, and lack of practical application value", we have made key revisions to the abstract as follows:

Line12-32: “The multi-factor coupling mechanism of droplet impact dynamics remains unclear due to insufficient analysis of leaf structure-droplet interaction and inadequate integration of simulation and experiment, limiting precision pesticide application. To address this, we developed a droplet impact model using the Volume of Fluid (VOF) method combined with high-speed camera experiments, and systematically analyzed the effects of impact velocity, angle, and droplet size on slip behavior via response surface methodology. Methodologically, we innovatively integrated 3D reverse modeling technology to reconstruct soybean leaf microstructures, overcoming the limitations of traditional planar models that ignore topological features. This approach, coupled with the VOF method, enabled precise tracking of droplet spreading, retraction, and slip processes. Scientifically, our study advances beyond previous single-factor analyses by revealing the synergistic mechanisms of impact parameters through response surface methodology, identifying impact angle as the most critical factor (42.3% contribution) followed by velocity (28.7%) and droplet size (19.5%). Model validation demonstrated high consistency between simulation predictions and experimental observations, confirming its reliability. Practically, the optimized parameter combination (90° impact angle, 1.5 m/s velocity, 300 μm droplet size) reduced slip displacement by over 50% compared to non-optimized conditions, providing a quantitative tool for spray parameter control. This work enhances understanding of droplet-leaf interaction mechanisms and offers technical guidance for improving pesticide deposition efficiency in agricultural production.”

 

 

Main issue 2: The introduction presents a solid and well-referenced theoretical framework, but it

is overly descriptive, which limits the critical presentation of the scientific problem. It wo

uld be advisable to highlight more clearly the specific knowledge gap that motivates the

study and the originality of the proposed approach compared to previous work. In additi

on, it is recommended to improve the connection between the literature review and the

objectives of the work in order to reinforce the argumentative coherence of the section.

Response 2: We appreciate your valuable feedback on the introduction. We have thoroughly revised the section to clearly highlight the study's innovations, including the integration of VOF simulation with 3D inverse modeling and its comparison with prior methods (e.g., Delele, Endalew, etc.), thereby emphasizing its advanced nature and distinctiveness. The revised introduction is as follows:

Line66-84: “While computational fluid dynamics (CFD) models have made progress in simulating fog drop trajectories and deposition patterns, they still exhibit significant limitations. For instance, the CFD model developed by Delele et al. [22] analyzed fog drop trajectories and deposition patterns but failed to account for crop-fog interaction. Endalew et al. [23] proposed a novel CFD numerical simulation method that directly incorporated the actual three-dimensional structure of crop canopies into CFD models by creating porous media around branches to simulate leaves, yet this approach still struggles to capture microscale behaviors at the droplet interface. Additionally, some studies employ bidirectional fluid-structure interaction to investigate leaf deformation patterns and airflow distribution within canopies, but focus solely on airflow-induced leaf bending deformation without analyzing its impact on droplet deposition. Notably, current research largely overlooks the influence of soybean leaves' unique microstructures (such as surface roughness) on droplet dynamics, and lacks systematic methods to effectively integrate numerical simulations with experimental validation. Some researchers also use bidirectional flow solid coupling to study the deformation mode of leaves under airflow [24,25] and the airflow distribution in the canopy [26], but they only focus on the bending deformation of leaves under airflow, without paying attention to its influence on droplet deposition.”

 

Main issue 3: Please improve figure.

Response 3: The image quality has been improved (Line 137-138)

 

Main issue 4: Bad figure.

Response 4: The image quality has been improved (Line 137-138)

 

Main issue 5: Section 2.2 presents a complete description of CFD modeling, but lacks rigor in the

physical justification of the assumptions and in the validation of the numerical model. Mesh independence is not detailed, nor are the refinement criteria or the possible influence of cell size on the pressure gradient and surface tension discussed, which are critical aspects in VOF simulations. Likewise, the choice of the Realizable k–ε turbulence model and the boundary conditions lack a dimensional or sensitivity analysis to support their suitability for the laminar-transient regime of microscale droplets; it would be advisable to include an evaluation of the Weber, Reynolds, and Capillary numbers, as well as a temporalconvergence study, to strengthen the physical and numerical validity of the approach.

Response 5: Regarding the 5 comment from the reviewer, we have addressed it in the revised draft by: 1) Adding a rationale for physical assumptions through experimental measurement evidence of critical parameters (surface tension, contact angle) and applicability of roughness models; 2) Incorporating model validation with error analysis and sensitivity testing; 3) Refining mesh independence analysis by evaluating coarse, medium, and fine mesh densities, establishing convergence criteria, and discussing medium-fine mesh strategies with dimensional effects; 4) Supplementing dimensionless number evaluations and temporal convergence studies (including Weber number, Reynolds number, and Capillary number calculations with flow state analysis, and verifying temporal step convergence).

Line66-84: “While computational fluid dynamics (CFD) models have made progress in simulating fog drop trajectories and deposition patterns, they still exhibit significant limitations. For instance, the CFD model developed by Delele et al. [22] analyzed fog drop trajectories and deposition patterns but failed to account for crop-fog interaction. Endalew et al. [23] proposed a novel CFD numerical simulation method that directly incorporated the actual three-dimensional structure of crop canopies into CFD models by creating porous media around branches to simulate leaves, yet this approach still struggles to capture microscale behaviors at the droplet interface. Additionally, some studies employ bidirectional fluid-structure interaction to investigate leaf deformation patterns and airflow distribution within canopies, but focus solely on airflow-induced leaf bending deformation without analyzing its impact on droplet deposition. Notably, current research largely overlooks the influence of soybean leaves' unique microstructures (such as surface roughness) on droplet dynamics, and lacks systematic methods to effectively integrate numerical simulations with experimental validation. Some researchers also use bidirectional flow solid coupling to study the deformation mode of leaves under airflow [24,25] and the airflow distribution in the canopy [26], but they only focus on the bending deformation of leaves under airflow, without paying attention to its influence on droplet deposition.”

 

 

 

Main issue 6: The article does not present a formal CFD validation according to numerical model

ing standards. Although it mentions that the model results “closely matched” those obtai

ned using a high-speed camera (0.03 cm difference in drop slip), this specific comparison

does not constitute a rigorous validation, but rather a qualitative verification of consiste

ncy. Quantitative indicators of model performance (e.g., relative error, RMSE, R², or devia

tion between velocity profiles or drop shape) are not evaluated, nor are sensitivity analysi

s, mesh independence, or numerical convergence reported. Furthermore, it is not demon

strated that the physical parameters of the model (surface tension, viscosity, static conta

ct, boundary conditions) accurately reproduce the actual experimental conditions. Theref

ore, from an academic and methodological point of view, the CFD model was not formall

y validated, but only contrasted in a limited way with visual experimental observations.

.Response 6: The physical hypothesis framework incorporates measurement methodologies for surface tension, contact angle, and surface roughness parameters. A new section 2.2.4 has been added to validate simulation reliability through experimental data comparison and error analysis. Quantitative analysis in tables demonstrates the impact of varying mesh density on results, establishing clear convergence criteria. The applicability of the Realizable k-ε model is substantiated by integrating Reynolds number and literature references. Additionally, Section 2.2.4 introduces We/Re/Ca number analysis to reveal flow characteristics, thereby supporting the model's rationality.（Line165-211）

 

 

 

Main issue 7: The image should be improved; no significant changes are observed.

Main issue 8: Imprve figures 6 a 12

.Response 7 and 8: Image quality and results have improved.

 

 

Main issue 9: The simulation presented in section 3.1 provides a compelling visual description of

the impact stages, but from a CFD modeling perspective, it lacks quantitative validation

and comparative rigor with actual physics. No pressure profiles, velocity distributions, or

volumetric fraction fields are reported to support the morphological interpretations, nor

is the influence of mesh size or time step on the numerical stability of the VOF method a

nalyzed. Furthermore, the study omits verification of mass and energy conservation, whic

h are crucial in transient simulations with interface rupture. Without these controls and without statistical correlation with experimental data, the results remain descriptive rather

than predictive, limiting their scientific value.

.Response 9: In response to reviewers 'comments regarding the lack of quantitative validation and physical rigor in Section 3.1 CFD simulations, we propose the following revisions to enhance the paper's scientific rigor. These improvements aim to strengthen quantitative validation of models, refine numerical methods, and establish statistical correlations with experimental data. (1) Add grid independence and time-step convergence analysis at the end of Section 2.2.3 (Grid Partitioning and Parameter Settings). (2) Enhance quantitative validation in Section 2.2.4 (Model Validation and Dimensionless Analysis). (3) Introduce flow field distribution analysis and mass/energy conservation analysis in Section 3.1, supplemented with velocity vorticity distribution diagrams in Figure 7. (4) Add statistical correlation analysis between simulation and experimental results before Section 3.3 (Response Surface Method Analysis).

• Line188-192: “When the base time step (1×10⁻⁶ s) was further reduced to 5×10⁻⁷ s, the variation rates of droplet morphology evolution paths and maximum spreading diameter remained below 0.5%, indicating that the current configuration ensures convergence of time discretization. Each time step was set with a maximum iteration limit of 25, ensuring residuals converge to below 10⁻³”
• Line194-202:“The numerical model was validated against high-speed camera experiments (Section 3.2) bycomparing normalized spread diameter (D/D0) and maximum slip distance (Smax) at impactvelocity 2.0 m/s. The simulation results showed a D/D0 ratio of 1.78, compared to an experimental value of 1.82 (RMSE=4.2%). For maximum contact area (Smax), the simulation value was 1.89 mm versus the experimental value of 1.93 mm (bias=2.1%). Sensitivity analysis demonstrated that variations in the droplet contact angle by +5° and surface tension by ±10% resulted in Smax changes below 3%, confirming the model's robustness. Key dimensionless numbers were calculated to characterize impact dynamics as shown in Table 3”
• Line240-251:“As shown in Figure 7, a localized pressure peak of approximately 450 Pa was observed at the droplet spreading peak moment (0.3 ms) in the impact center region, directly correlating with the conversion of droplet kinetic energy into compressive energy. Simultaneously, a distinct vortex structure formed at the liquid film edge (with a peak velocity vetor of 1.375 m·s⁻¹), providing a dynamic basis for explaining droplet splashing and secondary fragmentation under high Weber number (We> 100) conditions. Throughout the transient simulation, the total mass change rate within the computational domain remained below 0.8%. Tracking calculations of system kinetic energy, surface energy, and viscous dissipation energy revealed that approximately 72% of the initial kinetic energy was converted into droplet spreading surface energy, while about 18% dissipated through viscous effects. This energy distribution aligns with droplet impact theory.”

（4）Line377-382:“Furthermore, to establish a more rigorous statistical correlation between numerical simulations and experimental observations, we conducted a comparative analysis of the maximum sliding distances of droplets under all 17 experimental conditions (based on Box-Behnken design). The Bland-Altman consistency analysis demonstrated that 95% of the differences between the two methods' measurements fell within the±0.05 cm range, confirming their good consistency.”

 

Main issue 10: Section 3.2 presents well-documented experimental observations, but from a scientific point of view, it has notable methodological weaknesses. The uncertainty associated with the high-speed camera measurements is not quantified, nor is the temporal and spatial resolution of the optical system specified, which prevents the accuracy of the recording from being evaluated in relation to the transient phenomenon of the impact. Furthermore, no statistical analysis or direct correlation with CFD results is performed, so the observations remain descriptive. It would be advisable to integrate calibrated measurements (velocity profile, residual volume, or dynamic contact angle) to experimentally support inferences about the expansion, retraction, and fragmentation of the droplets

.Response 10: We sincerely appreciate the valuable feedback provided by the reviewers regarding the experimental section of this paper. Your observations on the unquantified measurement uncertainties of high-speed cameras, ambiguous optical system resolution specifications, and the lack of statistical analysis directly correlating with CFD results demonstrate both professional rigor and constructive suggestions. We have thoroughly addressed these points and implemented substantial revisions to Section 3.2 to enhance scientific rigor and methodological transparency. (1) Detailed calibration specifications and measurement uncertainty analyses for the high-speed camera system have been incorporated at the beginning of Section 3.2. (2) Direct correlations between statistical analysis and CFD results have been strengthened. (3) We have adopted the recommendations to quantify droplet dynamics, particularly by supplementing experimental data on dynamic contact angle variations obtained through image processing techniques, which provides critical experimental evidence for droplet spreading and retraction processes.

• Line307-315:“The high-speed camera system (PCO.dimax cs3) underwent rigorous calibration prior to the experiment. The camera was configured with a frame rate of 10,000 fps and a spatial resolution of 25.4 μm/pixel. Accounting for lens distortion, pixel jitter, and image processing errors, the calculated composite standard uncertainty for droplet diffusion diameter is approximately ±2.1%, while the measurement uncertainty for sliding displacement is about ±3.5%. This level of precision is sufficient to capture and quantify the millisecond-scale transient impact phenomena studied in this paper.”
• Line378-390:“Using normalized diffusion diameter (D/D0) and maximum sliding distance (Smax) as key metrics, the simulation results at 2.0 m/s impact velocity showed a D/D₀ ratio of 1.78 compared to 1.82 in experiments, with a relative root mean square error (RMSE) of 4.2%. The simulated Smax value was 1.89 mm, while the experimental value was 1.93 mm, resulting in a 2.1% deviation. Additionally, linear regression analysis of sliding distances at different impact velocities (1.5, 3.0, 4.5 m/s) revealed an R² coefficient of 0.96, indicating strong consistency between numerical simulations and experimental results (Figure 19). This quantitative comparison strongly validates the accuracy of dynamic droplet interface capture using the VOF method.”
• Line391-400:“To further investigate the spreading-retracing dynamics of droplets experimentally, we captured the dynamic evolution of contact angles post-impact using high-speed imaging sequences (Figure 20). When a 300 μm droplet impacted at 1.5 m/s, the contact angle rapidly increased from an initial 76.5° to approximately 105° during the maximum spreading phase within 0.3 ms, then decreased to about 77° in the retraction phase. These experimental measurements align with the film morphology evolution observed in VOF simulations, providing empirical evidence for the energy conversion between droplet kinetic energy and surface energy.”

 

Main issue 11: The discussion is consistent with previous studies and demonstrates adequate experimental-numerical integration, but it lacks in-depth scientific argumentation regarding the validity of the CFD model and the limits of its extrapolation. Uncertainties, simulation errors, and the effect of physical simplifications on the prediction of transient phenomena are not discussed. Furthermore, there is a lack of critical analysis of the statistical representativeness and scalability of the results to real field conditions.

Main issue 12: The conclusions omit a critical conclusion that acknowledges the limitations and perspectives of the study, which weakens its academic value. A final paragraph should be added to contextualize the limitations of the CFD model, geometric simplifications, lack of quantitative validation, and idealized laboratory conditions and propose future lines of research. Including such reflections would strengthen scientific transparency, reproducibility, and the applicability of the results to real agricultural scenarios.

 

.Response 11 and 12: Dear Reviewer, We sincerely appreciate your insightful comments and valuable suggestions regarding the discussion section of this paper. Based on your feedback, we have made significant revisions and additions to the discussion, as detailed below: (1) We have expanded the discussion to include a comprehensive explanation of the CFD model validation process and associated uncertainties, building upon our earlier elaboration. (2) A new paragraph has been added to highlight the limitations of the model in terms of geometric simplification, boundary condition formulation, and environmental factor neglect. (3) A critical analysis comparing experimental conditions with field scenarios has been incorporated at the conclusion of the discussion, while proposing potential directions for future research.

• Line486-3489:“In terms of model verification, this study ensures the convergence of numerical results through high-precision mesh independence testing. The simulation results show good consistency with high-speed camera experimental data in droplet expansion diameter and maximum slip distance.”
• Line489-497:“While the study demonstrates promising results in laboratory settings, its practical application in field conditions faces several limitations. First, the model fails to account for dynamic wax layer changes in leaves, environmental wind speed fluctuations, and evaporation effects – factors that could significantly influence droplet behavior during actual spraying. Second, the static contact angle (76.5°) assumed in the model may not fully capture the spatiotemporal variations in leaf surface wetting properties observed in real-world fields. Additionally, the current simulation does not incorporate airflow disturbances within crop canopies, which in practice could cause droplet trajectories to deviate from ideal conditions.”
• Line498-504:“While the controlled experimental conditions of this study—maintaining constant temperature and humidity with single-leaf fixation—prove effective for variable control, they limit the model's direct applicability to complex field environments. Future validation should be conducted on multiple crops like rice and wheat, incorporating dynamic environmental parameters such as wind speed and humidity gradients to enhance model universality. Furthermore, integrating field measurement data to optimize the model's scale will be a key focus for subsequent research.”

 

We would like to thank the referee again for taking the time to review our manuscript!

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Main objective of this paper is to analyze the multi-factor mechanisms of droplet impact dynamics on soybean leaves and their interaction due to leaves physical properties and droplet motion parameters on leaves surface due to physical properties of experimental solutions. In order to address the main objectives a systematic analysis is employed, using numerical simulation of leave-solution interaction and experimental validation using high-speed camera technology and its related methodologies. The authors analyses the numerical model, relative to findings in laboratory experiments, that relates with understanding of droplet morphology and quantifying that impact angle is the most significant factor influencing slip. The authors show the optimal parameters for achieving minimum  slip.

Specific comments:

• In table 1 – missing measurement units for physical characteristics;
• The term ‘’fog droplet’’ that is used throughout the paper is misleading, please use a more appropriate term;
• Please use ‘’μm’’ instead of ‘’um’’ (which is used several times throughout the paper);
• An important issue relates with calculated falling heights, impact velocities (lines 112-115) and falling droplets due to gravity, since in real world these parameters largely depend on the applied pesticide types, nozzle requirements, nozzle types, liquid pressures; the droplets are delivered (deposited on target surface) under pressure at higher velocities, so they are subjected to aerodynamic forces; how these parameters were chosen? Their values seem far away from the parameters measured in real-life/wind tunnel applications of pesticides/test solutions!
• The test solutions are not fully characterized (e.g. missing physical properties), how their physical properties were measured and how these influenced numerical simulations;
• Line 159 – ‘’water was used as the spray medium’’ during simulations – how this simulations can be compared with other test solutions, how changes in their physical properties were accounted;
• Section 3.2 (line 244) refers to cyhalothrin solution which is not fully characterized and is nowhere to be found in ‘’Materials’’ section;
• How leaf surface physical properties were simulated in numerical analysis?
• the impact angles from table 2 does not fit with impact angles discussed in above sections;
• figure 4 is not clear;
• figure 19 is not readable;
• line 400 – ‘’optimization of agricultural spray parameters’’ – please provide the practical methods/techniques/devices or equipments that can be optimized, based on the findings;
• in ‘’conclusion’’ section it is claimed that ‘’All three types of adjuvants reduced slip’’ which is not supported/emphasized by the published data.

Author Response

Main issue 1: In table 1–missing measurement units for physical characteristics;

Response 1: The standard units for all physical property parameters in Table 1 have been added to ensure data integrity. Line181

 

 

Main issue 2: The term ‘fog droplet’ that is used throughout the paper is misleading, please use a more appropriate term

Response 2: The term "fog droplet" has been replaced with the more accurate agricultural spray terminology "droplet".

Replace all instances of "um" with "μm" (micron symbol standard) using the Find and Replace feature to ensure no omissions.

 

 

Main issue 3: An important issue relates with calculated falling heights, impact velocities (lines 112-115) and falling droplets due to gravity, since in real world these parameters largely depend on the applied pesticide types, nozzle requirements, nozzle types, liquid pressures; the droplets are delivered (deposited on target surface) under pressure at higher velocities, so they are subjected to aerodynamic forces; how these parameters were chosen? Their values seem far away from the parameters measured in real-life/wind tunnel applications of pesticides/test solutions!

Response 3: Thank you for your valuable suggestions! The drop height and impact velocity selected in this study were calculated using empirical formulas (Equations 1-3) by Range and Feuillebois [27], covering low-velocity impact conditions typical of hydraulic nozzles. This approach focuses on low-velocity impact mechanisms (Weber number <100) to primarily analyze interfacial behavior, with future work extending to high-pressure nozzle scenarios. A new discussion section has been added to explain how optimized parameters (e.g., 90° impact angle, 300 μm particle size) can be applied to actual nozzle control systems.

 

Main issue 4: The test solutions are not fully characterized (e.g. missing physical properties), how their physical properties were measured and how these influenced numerical simulations;

Response 4: Based on the reviewer's feedback, add a table in Section 2.1 of the document listing the measured surface tension, density, and contact angle values of lambda-cyhalothrin emulsion with three adjuvants (Yunzhan, Jijian, and Sujie). These physicochemical parameters are critical for numerical simulations and experimental comparisons, and were measured using equipment such as the Sigma 703D interfacial tension meter. (Line 126:”To quantify the solution's physical properties, we employed a Sigma 703D interfacial tension meter for surface tension measurement and a density bottle method for density determination. Static contact angles were analyzed using high-speed camera images (with consistent blade surface pretreatment). The measured data, as shown in the table above, demonstrate that the additive significantly reduces both surface tension and contact angle, providing a basis for analyzing slip behavior in Section 3.”

Main issue 5: Line 159 – ‘’water was used as the spray medium’’ during simulations – how this simulations can be compared with other test solutions, how changes in their physical properties were accounted.

Response 5: The simulation uses water as the medium because the pesticide solution is dominated by inertia and surface tension under low-speed impact, with minimal influence from physical property differences on interface morphology. The experimental use of pesticide solution aims to verify dynamic behavior in real-world scenarios, while the simulation focuses on mechanism analysis. If you are dissatisfied with this explanation, please contact us promptly!

 

Main issue 6: The numerical simulation does not specify the physical properties of the blade surface (such as roughness and wetting properties).

.Response 6: The following content has been added to Section 2.2.3: The blade surface roughness was measured by AFM (Ra=2.3 μm), set as a non-slipping wall in the model, and assigned a roughness constant Cs=0.6. The contact angle was experimentally measured (static contact angle 76.5°) and dynamically tracked in the VOF model using geometric reconstruction.（Line181-201）

 

 

Main issue 7: figure 4 is not clear; figure 19 is not readable

Response 7：All charts and figures in the document have been cleared and refined.

 

 

Main issue 8: line 400 – ‘’optimization of agricultural spray parameters’’ – please provide the practical methods/techniques/devices or equipments that can be optimized, based on the findings;

in ‘’conclusion’’ section it is claimed that ‘’All three types of adjuvants reduced slip’’ which is not supported/emphasized by the published data.

 

.Response 8: Your comments are very important to the improvement of the quality of the paper. Combined with the comments of other reviewers, the last part of the discussion is changed to: Line509-515：“While the controlled experimental conditions of this study—maintaining constant temperature and humidity with single-leaf fixation—prove effective for variable control, they limit the model's direct applicability to complex field environments. Future validation should be conducted on multiple crops like rice and wheat, incorporating dynamic environmental parameters such as wind speed and humidity gradients to enhance model universality. Furthermore, integrating field measurement data to optimize the model's scale will be a key focus for subsequent research.”

According to your review comments, I have comprehensively revised the conclusion of this paper, focusing on deleting the description of the influence of three adjuvants on fog drop sliding, and enriching the structure of the reply.The conclusion has been modified to:

This study employed a combination of VOF numerical simulation and high-speed camera technology to investigate the dynamic behavior mechanisms and parameter optimization strategies of droplet impact on soybean leaves. A droplet deposition prediction model based on impact angle, velocity, and droplet size was established, with the main findings as follows:

(1) Droplet impact on soybean leaves exhibited four distinct dynamic stages: "spreading → contraction → secondary spreading → stabilization". The critical conditions for droplet breakup were identified as impact velocity >3 m/s or droplet size >500 μm, where inertial forces exceeded surface tension, leading to the formation of secondary satellite droplets. Within the tested parameter range (impact angles 45°~90°, velocities 1.5~4.5 m/s, droplet sizes 300~500 μm), increasing the impact angle from 45° to 90° resulted in an average 40% increase in the volume fraction of fully spread droplets and a 65% decrease in rebound rate. At low impact velocities (1.5 m/s), the maximum spreading diameter of droplets reached 3.2 times the initial size, with no rebound observed.

(2) Numerical simulations reveal that the pronounced vortex structures at the droplet spreading peak (0.3 ms) at the edge of the liquid film provide a kinetic explanation for droplet splashing and secondary fragmentation under high Weber number (We>100) conditions.Response surface methodology analysis revealed the degree of influence of each factor on slip displacement as: impact angle (42.3%) > impact velocity (28.7%) > droplet size (19.5%).

(3) The combination of 90° impact angle, 1.5 m/s velocity, and 300 μm droplet size achieved the optimal slip suppression effect, reducing slip displacement to 1.38 cm. The slip displacement prediction model from VOF simulations and high-speed camera experiments showed R² > 96%, indicating a significant nonlinear relationship and strong predictive capability.

 

 

We would like to thank the referee again for taking the time to review our manuscript!

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors

Many Thanks, For your response.

For me the new version of manuscript its ok

Best Regards

Reviewer 2 Report

Comments and Suggestions for Authors

Main objective of this paper is to analyze the multi-factor mechanisms of droplet impact dynamics on soybean leaves and their interaction due to leaves physical properties and droplet motion parameters on leaves surface due to physical properties of experimental solutions. In order to address the main objectives a systematic analysis is employed, using numerical simulation of leave-solution interaction and experimental validation using high-speed camera technology and its related methodologies. The authors analyses the numerical model, relative to findings in laboratory experiments, that relates with understanding of droplet morphology and quantifying that impact angle is the most significant factor influencing slip. The authors show the optimal parameters for achieving minimum  slip.