Experiment-numerical value-machine learning fusion-based in-oil liquid drop electric field dynamics modeling and regulation method

Abstract

The invention discloses an experiment-numerical value-machine learning fusion-based in-oil liquid drop electric field dynamics modeling and regulation method, which comprises the following steps of: firstly, constructing a high-voltage electric field liquid drop experiment system, and testing oil liquid drop experiment data in oil; then establishing a multi-physics field coupling model, and describing deformation and flow field evolution of oil drops in oil under a strong electric field; and finally, constructing a BP neural network and optimizing an initial weight and a threshold value to realize rapid prediction of the deformation behavior of the oil drops in the oil under the action of the electric field. According to the method, an experimental characterization-numerical solution-machine learning optimization three-layer collaborative system is constructed, a whole-process closed loop from physical property determination, equation solution to algorithm prediction is realized, and droplet deformation, charge distribution and interface response are rapidly predicted under the conditions of different electric field intensities, temperatures and emulsifier concentrations; and active control of electric field behaviors can be realized through parameter reverse adjustment, and reliable modeling and optimization basis is provided for an electrowetting chip, a flexible EHD pump and a microfluidic liquid drop regulation and control system.

Description

Technical Field

[0001] This invention relates to the field of electrohydrodynamics, and in particular to a method for modeling and controlling the electric field dynamics of oil droplets in oil based on an experimental-numerical-machine learning fusion approach. Background Technology

[0002] In recent years, electrohydrodynamics (EHD) technology has been widely applied in microfluidics, electrowetting, oil-water separation, and chip cooling due to its advantages such as no mechanical parts, high driving precision, and miniaturizable structure. Early research established the theory of droplet deformation in an electric field, revealing the balance between electric force and surface tension, and proposing deformation criteria. Subsequent research developed a steady-state deformation theory based on a leakage dielectric model and used the finite element method and lattice Boltzmann method to numerically simulate the droplet morphology in oil-water systems. Further research revealed the influence of the ratio of conductivity to dielectric constant on droplet morphology through the phase field-lattice Boltzmann method. However, this model is mainly applicable to water-in-oil systems, and the complex polarization behavior in oil-in-oil systems with similar dielectric properties is still difficult to describe accurately. At the same time, existing experiments are mostly based on qualitative observations, lacking systematic determination of key parameters as a function of temperature and emulsifier concentration. Although data-driven models have predictive capabilities, they are not coupled with the multi-physics processes of EHD, making it difficult to achieve high-precision and scalable modeling and prediction. In order to accurately predict and control the interfacial evolution behavior of oil droplets in a strong electric field, it is urgent to establish a comprehensive modeling method that integrates experimental measurement, numerical simulation and intelligent algorithm optimization.

[0003] Current research on the electric field dynamics of oil droplets in oil still has significant limitations.

[0004] Existing theoretical models are mostly based on the ideal assumptions of a uniform electric field and fixed interfacial tension, without considering the influence of changes in dielectric constant and conductivity with temperature and emulsifier concentration, making it difficult to accurately reflect the complex electric-current-interfacial coupling characteristics in oil-in-oil systems.

[0005] In numerical simulation, the finite volume method (FVM) and volume fraction method (VOF) are prone to numerical oscillations and pseudo-flows under high voltage or strong coupling conditions. The traditional lattice Boltzmann method (LBM) also suffers from interface dispersion and divergence problems under strong electric fields, resulting in poor stability and reduced accuracy of the calculation results.

[0006] Experimental studies are mostly limited to qualitative observations and have not yet established quantitative correlations between temperature, emulsifier concentration and key physical properties such as dielectric constant, conductivity, and ion mobility. Model inputs are highly dependent on empirical assumptions and lack systematic experimental database support.

[0007] Meanwhile, most existing machine learning methods are purely data-driven models that do not incorporate EHD physical mechanisms for constraint. These methods suffer from slow convergence speed, susceptibility to local optima, and insufficient generalization ability, making it difficult to achieve high-precision prediction of droplet electric field dynamics. Summary of the Invention

[0008] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for modeling and controlling the electric field dynamics of oil-in-oil droplets that integrates experimental characterization, phase-field lattice Boltzmann (PF-LBM) numerical simulation, and intelligent algorithm optimization. This method aims to solve a series of key technical challenges in multi-physics coupled modeling and rapid prediction of oil-in-oil systems under strong electric fields. By constructing a quantifiable experimental parameter database, the method systematically measures key physical properties of the liquid, such as dielectric constant, conductivity, and ion mobility, under different temperatures and emulsifier concentrations, making the model input more realistic and reliable. A highly stable numerical simulation framework is established based on the PF-LBM method, coupling potential distribution, interface evolution, and hydrodynamic equations to characterize the deformation and charge migration processes of droplets under strong electric fields. Furthermore, the method combines the Sparrow Search Algorithm (SSA) with optimized backpropagation neural network (BP) to establish an SSA-BP prediction model for rapid prediction of droplet deformation rate, contact angle, and dynamic response characteristics, improving the algorithm's convergence speed and generalization ability.

[0009] The objective of this invention is achieved through the following technical solution: a method for modeling and controlling the electric field dynamics of oil droplets in oil based on the fusion of experiment, numerical analysis, and machine learning, the method comprising the following steps: (1) Construct a high-voltage electric field droplet experimental system and test the experimental data of oil droplets in oil; (2) Establish a multiphysics coupling model to describe the deformation and flow field evolution of oil droplets in oil under a strong electric field; (3) Construct a BP neural network and optimize the initial weights and thresholds. Train the optimized network model based on experimental data of oil droplets in oil and data on the deformation and flow field evolution of oil droplets in oil to realize the rapid prediction of the deformation behavior of oil droplets in oil under the action of electric field.

[0010] Furthermore, the droplet experimental data include contact angle, interfacial tension, dielectric constant, conductivity, ion mobility, and viscosity parameters.

[0011] Furthermore, the high-voltage electric field droplet experimental system used CL7300 as the dispersed phase and DBD as the continuous phase, and added emulsifiers of different concentrations to test the experimental data of oil droplets in the oil within the range of 15 to 55°C.

[0012] Furthermore, the emulsifier is selected from Span 60 emulsifier, silicone oil / mineral oil combination, or Tween series emulsifier.

[0013] Furthermore, the establishment of the multiphysics coupling model is selected from the following methods: a. Based on the phase-field lattice Boltzmann method; b. Based on the finite volume method or volume fraction method; c. Based on dispersive LBM or pseudopotential LBM.

[0014] Furthermore, the multiphysics coupling model based on the phase-field lattice Boltzmann method includes the phase-field evolution equation, the flow field equation, and the electric potential field equation. The phase-field, flow field, and electric field evolution equations are discretized and solved using the lattice Boltzmann discretization scheme.

[0015] Furthermore, the input layer of the BP neural network receives the characteristic parameters of the high-voltage electric field droplet experimental system, including electric field strength, temperature, emulsifier concentration, conductivity ratio and dielectric constant ratio; the output layer outputs the macroscopic response indicators of droplet deformation rate and contact angle.

[0016] Furthermore, the method for optimizing the initial weights and thresholds of the BP neural network includes using an optimization algorithm to globally optimize the network parameters, such as the Sparrow Search algorithm, the Genetic Algorithm, or the Particle Swarm Optimization algorithm.

[0017] Furthermore, the specific process of global optimization based on the sparrow search algorithm in the BP neural network is as follows: by simulating the collaborative search behavior of three types of individuals in a sparrow flock—the discoverer, the follower, and the scout—during the foraging process, the network parameters are dynamically optimized; the discoverer is responsible for searching for the optimal solution globally; the follower updates its position locally based on the discoverer; and the scout achieves an escape mechanism through random perturbation when it gets stuck in a local optimum.

[0018] Furthermore, during the training process, the sparrow search algorithm first performs a global search on the initial parameters of the BP network to determine the parameter combination with the smallest error, and then feeds the result back to the BP network for fine training; mean square error is used as the convergence index.

[0019] The beneficial effects of this invention are: This invention proposes a method for modeling and controlling the electric field dynamics of oil droplets in oil by integrating experimental measurement, phase-field lattice Boltzmann numerical simulation, and intelligent algorithm optimization. This method has significant advantages in terms of model accuracy, numerical stability, and prediction efficiency, as detailed below: (1) Improved model accuracy: By introducing measured parameters, the prediction results are more consistent with physical reality. Existing models generally rely on idealized assumptions, treating dielectric constant, conductivity, and interfacial tension as constants. This fails to reflect the influence of temperature and emulsifier concentration variations on the electro-current-interfacial coupling behavior of the system, especially in oil-in-oil systems where electrical properties are similar. Traditional Taylor and Feng models exhibit insufficient applicability in both strong and weak electric field regions. This invention constructs a systematic experimental scheme to quantitatively measure key physical properties of the CL7300 / DBD system within typical temperature ranges and multi-level emulsifier concentration ranges, establishing a realistic physical property database. Experimental results show that as temperature increases, the dielectric properties of the system decrease, while conductivity significantly increases. With increasing emulsifier concentration, interfacial tension decreases significantly, wettability changes significantly, and viscosity can be controlled. Based on these trends, this invention uses measured physical properties as input, enabling the model to accurately reflect the real interfacial evolution process of the oil-in-oil system under an electric field. After incorporating the above measured data, the droplet deformation predicted by the model is highly consistent with the experimental results, and the deviation can be controlled within an acceptable range for engineering purposes. This is significantly better than the fixed parameter model (where the deviation often exceeds 10%), and a high degree of consistency between the experimental data and the numerical prediction results has been achieved.

[0020] (2) Improved numerical stability: The solution is more reliable under strong electric field conditions. Traditional finite volume methods (FVM) and volume fraction methods (VOF) often suffer from interfacial dispersion, numerical oscillations, and non-physical flow issues under complex conditions such as high voltage or high conductivity ratios, leading to decreased stability and consistency of simulation results. Yazdani et al. reported on this issue in cases involving high conductivity ratios... R >10, charge layer diffusion and interface thickening phenomena occur; Sengupta et al. pointed out that when the electrocapillary number is ... C aE When the conductivity ratio R > S, the droplet major-minor axis ratio error of the VOF method exceeds 12%. Zhou et al. found in LBM simulations that non-physical circulation occurs when the electric field strength exceeds 6 kV / cm. This invention employs the Phase Field Lattice Boltzmann Method (PF-LBM), coupling the Allen-Cahn equation, Navier-Stokes equation, and Poisson equation, and introduces an electric force term during the solution process, effectively describing the charge polarization and interface stress distribution process. Simulation results show that when the conductivity ratio R > S, the droplet is stretched along the electric field direction to form a major axis shape, while when R < S, the droplet is flattened to form a flat shape. In addition, the numerical results agree well with the simulation results of Liu et al., proving that the model maintains a clear interface, no spurious flow, and stable convergence under high electric field and multi-physics coupling conditions, and has high numerical reliability.

[0021] (3) Improved prediction efficiency: SSA optimizes BP network to achieve fast convergence Traditional backpropagation (BP) neural networks or regression models converge slowly under multi-parameter conditions and are prone to getting trapped in local optima, making it difficult to meet the rapid prediction requirements of electric field-coupled multi-physics processes. Wang et al. required over 3000 iterations to predict droplet size, with a prediction error of approximately 8.6%; Li et al.'s BP model showed a 6.2% bias under multivariate input. This invention employs the Sparrow Search Algorithm (SSA) to optimize the initial weights and biases of the BP network, achieving global optimization. This allows the network to quickly approach the optimal region in the early stages of training and effectively improves the stability and generalization ability of subsequent iterations. The optimized model exhibits faster convergence, a smaller error fluctuation range, and higher consistency with experimental and numerical simulation results during both training and testing, demonstrating significant advantages in prediction accuracy and efficiency compared to the unoptimized BP model.

[0022] (4) Enhanced system comprehensiveness and adaptability: Experiment-numerical-algorithm synergy and unification This invention constructs a three-layer collaborative system of experimental characterization, numerical solution, and machine learning optimization, realizing a closed-loop process from property determination and equation solving to algorithm prediction. This system can rapidly predict droplet deformation, charge distribution, and interface response under different electric field strengths, temperatures, and emulsifier concentrations. Furthermore, it can achieve active control of electric field behavior through parameter inversion, providing reliable modeling and optimization basis for electrowetting chips, flexible EHD pumps, and microfluidic droplet control systems. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 The present invention relates to a device for manipulating the electric field dynamics of oil droplets in oil.

[0025] Figure 2Schematic diagrams showing the physicochemical properties of the working fluid under different emulsifier concentrations, temperatures, and applied voltages; where (A) the droplet contact angle varies with emulsifier S60 concentration. (B) the effect of emulsifier S60 concentration on interfacial tension. (C) the relationship between the viscosity of DBD&Span60 and CL7300 and emulsifier S60 concentration. (D) the temperature-dependent conductivity of DBD&Span60 and CL7300. (E) the temperature-dependent relative permittivity of DBD&Span60 and CL7300. (F) the temperature-dependent density of DBD&Span60 and CL7300. (G) the variation of fluid height under different applied voltages. (H) the variation of ion mobility of DBD&Span60 and CL7300 with voltage. (I) the diffusion coefficient of DBD&Span60 and CL7300 at different voltages.

[0026] Figure 3 This is a schematic diagram illustrating the numerical verification of the phase-field lattice Boltzmann model of droplet electrodynamics; where (A) is a schematic diagram of a droplet resting on a planar substrate under the action of a vertical electric field. (B) is a schematic diagram of droplet deformation under the action of an applied electric field. (C) is a schematic diagram of the effect of droplet deformation on the dielectric constant ratio. S conductivity ratio R and electrocapillary number C aE (D) The effect of surface wettability and electric field strength on droplet contact angle. (E) Spatial distribution of voltage, electric field and interfacial electric force under equilibrium conditions. (F) Verification of the phase field lattice Boltzmann model by comparison of experimental observations and numerical simulations.

[0027] Figure 4 This is a schematic diagram of the prediction workflow of the present invention, which combines the Sparrow Search Algorithm (SSA) and the BP neural network.

[0028] Figure 5 This is a schematic diagram of the BP neural network model.

[0029] Figure 6 This is a schematic diagram illustrating the convergence of training loss during the SSA optimization process.

[0030] Figure 7 The diagram illustrates the prediction of droplet deformation under an electric field using the SSA-BP neural network model. (A) BP neural network prediction results. (B) SSA-BP prediction results. (C) Comparison of prediction bias on the training dataset. (D) BP neural network prediction results. (E) SSA-BP prediction results. (F) Comparison of prediction bias on the test dataset, demonstrating the improved accuracy of SSA-BP. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are merely illustrative and not intended to limit the invention.

[0032] like Figure 1 As shown, this invention provides a method for modeling and controlling the electric field dynamics of oil droplets in oil-in-oil systems, integrating experimental measurements, phase-field lattice Boltzmann numerical simulations, and intelligent algorithm optimization. Its core lies in achieving multi-scale modeling and accurate prediction of the deformation, interfacial stress distribution, and charge migration behavior of oil droplets under a strong electric field through a three-layer coupling system of experiment, numerical simulation, and machine learning. This solves the problems of poor stability, insufficient accuracy, and strong parameter dependence of traditional models. Taking the CL7300 / DBD oil-in-oil system as the research object, this invention strengthens the ability to characterize the correlation between interfacial polarization, current migration, and flow field response by constructing an experimental property database and a multi-physics coupling analysis framework. This enables the model to more comprehensively reflect the evolution of interfacial behavior of the oil-in-oil system under an electric field, providing a solid technical foundation for electrowetting chips, flexible EHD pumps, and microfluidic droplet control.

[0033] To transform the physical processes of oil droplets in a strong electric field into a computable and verifiable model response, this invention includes the following four steps: experimental characterization and property acquisition, phase-field lattice Boltzmann numerical solution, intelligent algorithm optimization and parameter prediction, and model fusion and system control.

[0034] In the experimental characterization stage, this invention constructed a high-voltage electric field droplet experimental system, using CL7300 as the dispersed phase and DBD as the continuous phase, and adding different concentrations of Span 60 emulsifier (0–5.5 wt%). The contact angle, interfacial tension, dielectric constant, conductivity, ion mobility, and viscosity of the droplets were tested within the range of 15–55°C, and an experimental database was established. Figure 2 As shown, the experimental results indicate that with increasing emulsifier concentration and temperature, the conductivity of the system increases significantly, the dielectric constant decreases slightly, and the droplet response to the electric field is enhanced.

[0035] To describe the relative strength of electric field force and interfacial tension, the electrocapillary number is introduced. : in, For continuous phase permittivity, E For the applied electric field strength, Where is the droplet radius, For interfacial tension. The droplet deformation rate is defined by the formula: in, Land B These are the major and minor axes of the droplet, respectively.

[0036] In the numerical simulation stage, such as Figure 3 As shown, this invention establishes a multiphysics coupling model based on the phase-field lattice Boltzmann method (PF-LBM) to describe the deformation and flow field evolution of droplets under a strong electric field. The model includes the following governing equations: (1) Phase field evolution equation (Allen-Cahn equation) in, As an order parameter, For speed, For time, For mobility, The thickness is the interface thickness.

[0037] (2) Flow field equations (incompressible Navier-Stokes equations) in, For density, For dynamic viscosity, , , These are surface tension, electric force, and body force, respectively.

[0038] The surface tension term is expressed as: in, Chemical potential, , , .

[0039] The electric force term is expressed as: in, E For electric field strength, Where is the dielectric constant. Let be the charge density. The three terms on the right-hand side of the equation correspond to polarization stress, Coulomb force, and electrostrictive force, respectively. Since this study assumes the fluid is incompressible, the electrostrictive term can be neglected, and the electromagnetic force can be further simplified to the sum of the first two terms under the leakage medium model: .

[0040] (3) Potential field equation (Poisson equation) in, , For electric potential, is the conductivity.

[0041] To achieve a stable solution, the present invention adopts a lattice Boltzmann discretization scheme to discretely solve the phase field evolution equation, the flow field equation, and the electric potential field evolution equation respectively. The calculation results show that when the conductivity ratio R > S, the droplet stretches along the electric field direction and becomes an elongated shape; when R < S, the droplet is flattened into a flat shape. The numerical results are consistent with the experimental observations and the predictions of classical theories, verifying the correctness and stability of the model. The evolution equations are expressed as: where , are the distribution functions of the phase field, the flow field, and the electric field respectively, , , represent the corresponding relaxation times respectively, , are the equilibrium distribution functions, is the source term of the phase field, is the source term of the flow field.

[0042] In the intelligent algorithm stage, as Figure 4 shows, the present invention proposes a prediction model combining the Sparrow Search Algorithm (SSA) and the Back Propagation Neural Network (BP) to achieve fast prediction of the deformation behavior of oil droplets in oil under the action of an electric field. This model constructs training samples based on experimental and numerical simulation data (including droplet experimental data obtained in the experimental characterization stage and liquid deformation and flow field evolution data obtained in the numerical simulation stage), and optimizes the initial weights and thresholds of the BP network through SSA to improve the convergence speed and prediction accuracy of the model.

[0043] In terms of the network structure, as Figure 5 shows, the BP neural network adopts a three-layer feedforward form, consisting of an input layer, a hidden layer, and an output layer. The input layer receives the characteristic parameters of the droplet system, including the electric field strength ( E ), temperature ( T ), emulsifier concentration ( C ), conductivity ratio ( R ), and dielectric constant ratio ( S ), etc.; the output layer outputs the droplet deformation rate ( D ) and the contact angle ( θMacroscopic response indicators, etc. The network is trained through forward propagation and error backpropagation, and its forward propagation and loss function are defined as follows: in For input nodes, To predict the output, f () is the activation function (the Sigmoid function is selected). For connection weights, For bias terms, To output the number of nodes, This is the network loss function.

[0044] Traditional backpropagation (BP) networks suffer from slow convergence and a tendency to get trapped in local optima. Therefore, such as... Figure 6 As shown, this invention introduces the Sparrow Search Algorithm (SSA) for global optimization. The SSA algorithm dynamically optimizes network parameters by simulating the collaborative search behavior of three types of individuals in a sparrow flock: discoverers, followers, and scouts, during foraging. Its core idea is: the discoverer is responsible for globally searching for the optimal solution; followers update their positions locally based on the discoverer's position; and scouts, when trapped in a local optimum, use random perturbations to escape. Its position update formula can be expressed as: in, For the first i The sparrow in the first t The search location of the generation, As an adjustment constant, This represents the maximum number of iterations. The algorithm uses the network output layer error as the optimization objective function and obtains the globally optimal initial weights and biases through continuous iterative updates.

[0045] During training, the SSA optimization phase first performs a global search on the initial parameters of the BP network to determine the parameter combination with the minimum error, and then feeds the result back to the BP network for fine-tuning. The mean squared error (MSE) serves as the convergence metric; the error decreases rapidly in the early stages and stabilizes around the 63rd iteration.

[0046] After optimization, the predictive performance of the unoptimized BP model and the SSA-BP model was compared. Figure 7 As shown, experimental results indicate that both models achieve good fits on both the training and test sets, but the SSA-BP model exhibits significantly smaller prediction bias and higher consistency with the numerical simulation (LBM) results. Error distribution analysis reveals that the prediction error of the SSA-BP model is consistently lower than that of the traditional BP model across different samples.

[0047] Verification showed that the prediction error of the SSA-BP model was controlled within ±5% on both the training and test sets, and the loss function converged rapidly within the interval [−0.005, +0.005]. These results demonstrate that the model possesses good convergence performance, generalization ability, and robustness, accurately capturing the nonlinear coupling relationship of droplets under strong electric fields. This intelligent prediction module, linked with the experimental database and the PF-LBM model, can predict based on arbitrary operating parameters (…). E , T , C , R , S After that, the predicted values ​​of droplet deformation rate and contact angle are directly output, realizing the rapid calculation and real-time control of the electric field response characteristics of the oil-in-oil system, providing data support and algorithm basis for the design of EHD drive and microfluidic system.

[0048] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for modeling and controlling the electric field dynamics of oil droplets in oil based on an experimental-numerical-machine learning fusion, characterized in that, The method includes the following steps: (1) Construct a high-voltage electric field droplet experimental system and test the experimental data of oil droplets in oil; (2) Establish a multiphysics coupling model to describe the deformation and flow field evolution of oil droplets in oil under a strong electric field; (3) Construct a BP neural network and optimize the initial weights and thresholds. Train the optimized network model based on experimental data of oil droplets in oil and data on the deformation and flow field evolution of oil droplets in oil to realize the rapid prediction of the deformation behavior of oil droplets in oil under the action of electric field.

2. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 1, characterized in that, The droplet experimental data include contact angle, interfacial tension, dielectric constant, conductivity, ion mobility, and viscosity parameters.

3. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 1, characterized in that, The high-voltage electric field droplet experimental system uses CL7300 as the dispersed phase and DBD as the continuous phase, with different concentrations of emulsifier added, to test the experimental data of oil droplets in oil within the range of 15–55°C.

4. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 3, is characterized in that, The emulsifier is selected from Span 60 emulsifier, silicone oil / mineral oil combination, or Tween series emulsifier.

5. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 1, characterized in that, The multiphysics coupling model is established using the following methods: a. Based on the phase-field lattice Boltzmann method; b. Based on the finite volume method or volume fraction method; c. Based on dispersive LBM or pseudopotential LBM.

6. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 5, is characterized in that, The multiphysics coupling model based on the phase-field lattice Boltzmann method includes the phase field evolution equation, the flow field equation, and the electric potential field equation. The lattice Boltzmann discretization scheme is used to discretize and solve the phase field, flow field, and electric field evolution equations respectively.

7. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 1, characterized in that, The input layer of the BP neural network receives the characteristic parameters of the high-voltage electric field droplet experimental system, including electric field strength, temperature, emulsifier concentration, conductivity ratio and dielectric constant ratio; the output layer outputs the macroscopic response indicators of droplet deformation rate and contact angle.

8. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 1, characterized in that, Methods for optimizing the initial weights and thresholds of a BP neural network include using optimization algorithms to globally optimize the network parameters, such as sparrow search algorithm, genetic algorithm, or particle swarm optimization algorithm.

9. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 8, characterized in that, The specific process of global optimization based on the sparrow search algorithm in the BP neural network is as follows: by simulating the collaborative search behavior of three types of individuals in a sparrow flock—the finder, the follower, and the scout—during the foraging process, the network parameters are dynamically optimized. The discoverer is responsible for searching for the optimal solution globally; the follower updates its position locally based on the discoverer's position; and the scout uses random perturbation to escape when it gets stuck in a local optimum.

10. The method for modeling and controlling the electric field dynamics of oil droplets in oil based on experimental-numerical-machine learning fusion as described in claim 9, characterized in that, During the training process, the sparrow search algorithm first performs a global search on the initial parameters of the BP network to determine the parameter combination with the smallest error, and then feeds the result back to the BP network for fine training. Mean squared error is used as a convergence metric.

Images