A method and system for multi-physical field coupling simulation and process parameter optimization of an ultrasonic-assisted zinc electrodeposition process

Abstract

This invention discloses a multiphysics coupling simulation and process parameter optimization method and system for ultrasonic-assisted zinc electrodeposition, belonging to the technical field of ultrasonic-assisted metal electrodeposition process modeling and process parameter optimization. The method includes: constructing a three-dimensional transient finite element model containing the electrolyte region, electrodes, inlet / outlet, and bottom ultrasonic transducer; defining the acoustic pressure field, acoustic particle velocity field, and Zn... 2+ H + The coupling relationship between ion mass transfer, charge conservation, electrode interface reaction, and zinc deposition thickness evolution was analyzed; operating parameters such as ultrasonic frequency, ultrasonic input power, and number of sound sources were set and transiently solved; based on mean absolute sound pressure, relative standard deviation of the sound field, and Zn... 2+ Supply status, H + The optimal process parameters were selected based on the distribution state and deposition thickness, and verified through electrochemical testing, deposition layer thickness, deposition quality, and current efficiency experiments. This invention reveals the influence of ultrasonic frequency, ultrasonic input power, number of sound sources, and current density on interfacial mass transfer and deposition behavior.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic-assisted metal electrodeposition process modeling and analysis and process parameter optimization technology, specifically involving a multi-physics field coupling simulation and process parameter optimization method and system for ultrasonic-assisted zinc electrodeposition process. Background Technology

[0002] Zinc electrodeposition is widely used in hydrometallurgy, metal recovery, anti-corrosion coatings, and the preparation of functional materials; during the zinc deposition process, Zn near the cathode... 2+ Supply, H + Consumption and hydrogen evolution side reactions together affect the thickness, uniformity, density and current efficiency of the deposited layer. When the interfacial mass transfer is insufficient or the concentration polarization is obvious, problems such as rough deposited layer, increased porosity, uneven local deposition and increased energy consumption are likely to occur.

[0003] Existing technologies include multi-physics coupling simulation methods for zinc electrodeposition based on transient finite element analysis, such as the method disclosed in CN122263544A. This method constructs a three-dimensional transient model containing the cathode, anode, and electrolyte regions, couples the ion mass transfer process with the electrode interface reaction process, and optimizes process parameters such as electrolyte flow rate, anode-cathode distance, zinc acid-to-acid ratio, and current density. Such methods can characterize the ion concentration field and deposition behavior inside the electrolyte to a certain extent, but they still have the following shortcomings: (1) The ultrasonic auxiliary effect is not considered. Ultrasonic waves can disturb the near-electrode diffusion layer and change the Zn through sound pressure oscillation, acoustic particle velocity, cavitation, microjets, and acoustic flow. 2+ and H + The spatial distribution of ultrasound input is not specified in the model, but the existing methods do not include an ultrasonic transducer or define the sound pressure field and acoustic particle velocity field, thus failing to characterize the coupling effect of ultrasonic input on interface mass transfer and deposition behavior; (2) There is a lack of ability to screen ultrasonic parameters. Ultrasonic frequency, ultrasonic input power and the number of ultrasonic sources are key operating parameters for ultrasonic-assisted electrodeposition, and stronger ultrasonic input does not necessarily lead to more favorable deposition conditions: excessive power, too many sound sources or inappropriate frequency may cause excessive local acoustic field gradient, H + Concentration disturbances are enhanced and interface response is uneven; existing simulation methods cannot explain the non-monotonic regulation between ultrasonic input and deposition improvement, and it is also difficult to determine the combination of ultrasonic parameters based on this; (3) There is a lack of acoustic evaluation indicators. It is difficult to judge the quality of ultrasonic parameters based solely on the appearance of the deposition layer or a single electrochemical curve, and it is also difficult to explain the effects of different ultrasonic frequencies, different ultrasonic powers and different ultrasonic source arrangements on Zn 2+ Supply and H + The differences between perturbations necessitate a method that can unify ultrasonic fields, ion migration, and interfacial reactions within the same finite element framework, and allows for the screening and experimental verification of process parameters such as ultrasonic frequency, ultrasonic input power, and the number of ultrasonic sources. Summary of the Invention

[0004] Technical problems solved: In the background art, it is difficult to simultaneously characterize the internal acoustic field distribution, ion concentration field evolution, and interfacial reaction competition relationship in the ultrasonic-assisted zinc electrodeposition process, and it is difficult to quantitatively evaluate the influence of ultrasonic parameters on deposition behavior. This invention provides a multi-physics field coupling simulation and process parameter optimization method and system for the ultrasonic-assisted zinc electrodeposition process. By establishing a three-dimensional transient finite element model that includes an ultrasonic transducer and couples the acoustic pressure field, acoustic particle velocity field and ion mass transfer, interfacial reaction, and deposition growth, quantitative analysis of the influence of process parameters such as ultrasonic frequency, ultrasonic input power, and number of ultrasonic sources is achieved, and the reliability of the simulation screening is verified by experiments.

[0005] Technical solution: The present invention provides a method for multi-physics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process, comprising the following steps: Step 1: Construct a three-dimensional transient finite element model of the ultrasonic-assisted zinc electrodeposition process. The three-dimensional transient finite element model includes an electrolyte region, a cathode, an anode, an inlet, an outlet, and at least one ultrasonic transducer located at the bottom of the reaction tank. Step 2: Define the sound pressure field and acoustic particle velocity field in the three-dimensional transient finite element model, and establish the relationship between the sound pressure field, acoustic particle velocity field, and Zn in the electrolyte. 2+ and H + The coupling relationship between the ion mass transfer field, the electrode interface reaction field, and the zinc deposition layer growth field; Step 3: Set the operating parameters for the ultrasonic-assisted zinc electrodeposition process. The operating parameters include at least the ultrasonic frequency, ultrasonic input power, number of ultrasonic sources, acid-zinc ratio, electrolyte flow rate, current density, and deposition time. Step 4: Mesh the three-dimensional transient finite element model, with local refinement at the electrode surface, near the ultrasonic transducer, and in the inlet and outlet regions. Then, use the transient finite element method to calculate the sound pressure distribution, acoustic particle velocity distribution, and Zn under different operating parameters. 2+ Concentration field, H + Concentration field and zinc deposition thickness; Step 5: Post-process the calculation results based on mean absolute sound pressure, relative standard deviation of the sound field, and Zn. 2+ Supply status, H + The effects of distribution state and deposition thickness variations on operating parameters on ultrasonic-assisted zinc electrodeposition behavior were evaluated, and optimal process parameters were screened. Step 6: The preferred process parameters are experimentally verified through electrochemical testing, deposition layer thickness testing, deposition quality determination, and current efficiency calculation.

[0006] Preferably, the construction steps of the three-dimensional transient finite element model in step 1 are as follows: select a three-dimensional model and transient solution mode in the COMSOL Multiphysics simulation system; establish an electrolytic cell model with a reaction tank volume of 100 mL, wherein the electrolytic cell model includes an aluminum cathode located in the middle, lead-silver alloy anodes symmetrically arranged on both sides of the cathode, an electrolyte region located between parallel electrodes, and an inlet and an outlet; set one or more ultrasonic transducers at the bottom of the reaction cell; and use the electrolyte region, cathode, anode, and ultrasonic transducers as a unified computational domain to calculate the coupling response between the acoustic field, ion mass transfer, electrochemical reaction, and zinc deposition layer growth.

[0007] Preferably, in step 2, when defining the physical field, a three-level current distribution model is used to describe ion transport and interfacial reactions in the electrolyte, and an acoustic frequency domain model is used to describe the propagation of ultrasound in the electrolyte, specifically including: Step 21: Define Zn 2+ and H + Transient mass transfer equations in electrolytes, which simultaneously consider diffusion, migration and convection; Step 22: Define the electrolyte phase current density and the solid phase current density, and establish the charge conservation relationship; Step 23: Define the zinc ion reduction deposition reaction and hydrogen evolution side reaction at the cathode interface, and calculate the local reaction current density using the Butler-Volmer equation; Step 24: Define the ultrasonic sound pressure field and the sound particle velocity field, and calculate the sound field distribution under different ultrasonic frequencies, ultrasonic input power and the number of ultrasonic sound sources; Step 25: Compare the sound field distribution with Zn 2+ and H + The concentration field, local reaction current density at the interface, and the evolution of zinc deposition thickness were coupled and then processed.

[0008] Preferably, the governing equations for ion mass transfer, charge conservation, interfacial reaction, and zinc deposition thickness evolution in steps 21 to 23 are as follows: ; ; Furthermore, when there is no homogeneous charge generation or consumption within the electrolytic liquid phase, ; ; ; ; ; ; ; ; ; In the formula: C i N represents the concentration of component i; i R is the molar flux of component i; i For volumetric reaction source terms; i l Z is the electrolyte phase current density; F is the Faraday constant; z i D is the ionic charge number. i u is the diffusion coefficient; i For mobility; The liquid phase potential is u; the electrolyte velocity is i. s σ is the solid-state current density; s Solid-state conductivity; n is the solid-state potential; b i is the unit normal vector of the electrode-electrolyte interface; app i represents the applied current density; locm ν represents the local reaction current density at the m-th interface; i n is the stoichiometric coefficient; m Let δ be the number of electrons transferred in the m-th interfacial reaction; Zn M represents the zinc deposition thickness. Zn For the molar mass of zinc; i Zn n represents the local current density during zinc deposition. Zn ρ represents the number of electrons transferred in the zinc electrodeposition reaction. Zn The density of metallic zinc; i loc i is the local reaction current density at the electrode interface; i0 is the exchange current density; α a and α c η represents the charge transfer coefficients of the anode and cathode, respectively; η is the overpotential; R is the number of moles; T is the temperature; E eq ε is the equilibrium potential; exp(•) is an exponential function with the natural constant e as the base.

[0009] Preferably, the governing equations for the sound pressure field and the sound particle velocity field in step 24 are: ; ; ; ; ; ; In the formula: ρ is the fluid density; v is the fluid velocity; c is the speed of sound; p is the sound pressure; k ep t is the bulk modulus of the fluid medium; t is time; Pt For frequency domain sound pressure; q d It is a dipole source; ω is the angular frequency; Q m ε is a single-pole source; W is the average acoustic energy density; S is the acoustic power; and S is the cross-sectional area of ​​the ultrasonic probe.

[0010] Preferably, the electrolyte flow rate, inlet velocity, and dimensionless mass transfer parameters in step 3 satisfy the following relationship: ; ; ; ; ; ; In the formula: Q is the volumetric flow rate; U in A represents the average inlet velocity. in d is the inlet cross-sectional area; in D is the inlet pipe diameter. h Re is the hydraulic diameter; Re is the Reynolds number; S c S is the Schmitt number; h L is the Sherwood number; c D is the mass transfer characteristic length; i ρ is the diffusion coefficient of component i in the electrolyte; μ is the dynamic viscosity; and ρ is the electrolyte density.

[0011] Preferably, in step 5, the average absolute sound pressure level is used to evaluate the overall intensity of the sound field, and the relative standard deviation of the sound field is used to evaluate the spatial uniformity of the sound field. The relative standard deviation of the sound field is: ; In the formula: s is the relative standard deviation of the sound field; P i is the sound pressure amplitude at the i-th node; is the average sound pressure amplitude; P is the average absolute sound pressure; i is the node number; n is the total number of nodes.

[0012] Preferably, the operating parameters in step 3 include: ultrasonic frequency of 25-40kHz, ultrasonic input power of 5-30W, number of ultrasonic sound sources of 1-5, and current density of 300-600A•m. -2 The acid-zinc ratio was 3.0, and the simulated deposition time was 6 hours.

[0013] Preferably, the electrochemical tests in step 6 include cyclic voltammetry, nucleation overpotential testing, Tafel curve testing, and cathodic polarization curve testing; the experimental verification uses an experimental system constructed with a constant temperature water bath, a constant current power supply, a peristaltic pump, an acrylic electrolytic cell, two lead-silver alloy anodes and an aluminum cathode, with ultrasonic input power of 10W, 20W and 30W and 300A•m. -2 and 600A•m -2 The current density was compared, and the deposition time for each group was 1.5 hours.

[0014] This invention also discloses a multiphysics coupling simulation and process parameter optimization system for ultrasonic-assisted zinc electrodeposition using the above method, comprising: The model building module is used to build a three-dimensional transient finite element model of the ultrasonic-assisted zinc electrodeposition process. The three-dimensional transient finite element model includes an electrolyte region, a cathode, an anode, an inlet, an outlet, and at least one ultrasonic transducer disposed at the bottom of the reaction tank. The physics field definition module is used to define the sound pressure field and acoustic particle velocity field in the three-dimensional transient finite element model, and to establish the relationship between the sound pressure field, acoustic particle velocity field and Zn in the electrolyte. 2+ and H + The coupling relationship between the ion mass transfer field, the electrode interface reaction field, and the zinc deposition layer growth field; A parameter setting module is used to set operating parameters; the operating parameters include at least ultrasonic frequency, ultrasonic input power, and the number of ultrasonic sound sources. The mesh generation and solution module is used to generate a mesh for the three-dimensional transient finite element model. Local mesh refinement is applied to the electrode surface, near the ultrasonic transducer, and inlet and outlet regions, while a relatively coarse mesh is used in the electrolyte bulk region. The transient finite element solution method is then used to calculate the sound pressure distribution, acoustic particle velocity distribution, and Zn content under different operating parameters. 2+ Concentration field, H + Concentration field and zinc deposition thickness; The post-processing evaluation module is used to evaluate the sound field based on mean absolute sound pressure level, relative standard deviation of sound field, and Zn. 2+ Supply status, H + The effects of distribution patterns and deposition thickness variations on operating parameters on ultrasonic-assisted zinc electrodeposition behavior were evaluated, and optimal process parameters were screened.

[0015] Compared with the prior art, this invention application has the following outstanding substantive features and significant progress: 1. This invention incorporates the ultrasonic transducer, acoustic pressure field, and acoustic particle velocity field into the same three-dimensional transient finite element framework, and establishes the coupling relationship between the acoustic field and ion mass transfer, charge conservation, interfacial reaction, and zinc deposition thickness evolution. It can intuitively display the acoustic pressure distribution, acoustic particle velocity distribution, and ion concentration field distribution inside the electrolyte that are difficult to observe experimentally. 2. This invention simultaneously examines the overall sound field intensity, spatial uniformity of the sound field, and Zn. 2+ Supply status and H + The distribution state, which does not use ultrasonic power or sound pressure peak as the sole evaluation criterion, can reflect the non-monotonic correspondence between ultrasonic input enhancement and deposition improvement, which helps to avoid misjudging local strong sound fields as favorable process conditions. 3. This invention verifies the simulation screening results with experimental results such as electrochemical testing, deposition layer thickness, deposition quality, and current efficiency, which can reduce a large number of trial and error experiments and provide a basis for the design of ultrasonic-assisted zinc electrodeposition process. 4. This invention can screen for Zn within the range of parameters studied. 2+ Transportation, H + The combination of disturbance control and zinc layer growth in ultrasound-assisted electrodeposition technology has engineering application value. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method for multi-physics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition according to the present invention; Figure 2 A schematic diagram of the three-dimensional transient finite element model and mesh generation for ultrasound-assisted zinc electrodeposition; Figure 3 Zn at different ultrasonic frequencies 2+ and H + Concentration field distribution comparison chart; Figure 4 Comparison of concentration field and acoustic field response under different ultrasonic input powers; Figure 5 A comparison of the concentration field and sound field response under different numbers of ultrasonic sources; Figure 6 Comparison of concentration field and zinc deposition thickness under different current densities; Figure 7 This is a comparison chart of the mechanism of ultrasound-assisted zinc electrodeposition and experimental verification results.

[0017] Reference numerals: 10, reactor body; 20, baffle assembly; 21, baffle; 30, stirring assembly; 31, stirring shaft; 32, stirring blade; 40, ultrasonic action assembly; 41, ultrasonic generator; 42, ultrasonic transmitter; 50, ultrasonic-stirring coupling simulation and flow field evaluation module. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following description is provided in conjunction with the appendix. Figures 1-7 The technical solutions of the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0019] like Figure 1 As shown, the present invention provides a method for multi-physics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process, the method comprising the following steps.

[0020] A three-dimensional transient finite element model of the ultrasonic-assisted zinc electrodeposition process was constructed in the COMSOL Multiphysics simulation platform. For example... Figure 2 As shown, the three-dimensional transient finite element model includes an electrolyte region, parallel electrode plates, an inlet, an outlet, and two ultrasonic transducers located at the bottom of the electrolytic cell; the cathode is an aluminum plate located in the middle, and the anode is a lead-silver alloy electrode symmetrically distributed on both sides of the cathode; the electrolytic cell volume is 100 mL. This three-dimensional transient finite element model is used to uniformly describe sound field propagation, fluid inlet disturbance, ion mass transfer, electrode interface reaction, and deposition layer growth. An acidic zinc sulfate electrolyte system is selected, and Zn is defined as... 2+ and H + The initial concentration, electrolyte physical properties, electrode material properties, and cathode and anode boundary conditions.

[0021] The three-dimensional geometric model of this invention is based on the actual spatial relationship between the electrolytic cell, electrodes, and ultrasonic transducers: a current path is formed between the cathode and the anode, the inlet and outlet are used to describe electrolyte replenishment and flow renewal, and the bottom transducer area is used to apply the ultrasonic boundary; by placing the above geometric objects in the same computational domain, a clear spatial correspondence can be formed between the acoustic field disturbance area and the electrochemical reaction interface, avoiding the separate evaluation of ultrasonic effects from the electrode surface.

[0022] Define the sound pressure field and acoustic particle velocity field in the three-dimensional transient finite element model, and establish the relationship between the sound pressure field, acoustic particle velocity field, and Zn in the electrolyte. 2+ and H + The coupling relationship between the ion mass transfer field, the electrode interface reaction field, and the zinc deposition layer growth field is investigated. When defining the physical fields, a three-level current distribution model is used to describe ion transport and interfacial reactions in the electrolyte, and an acoustic frequency domain model is used to describe the propagation of ultrasound in the electrolyte. Zn is defined. 2+ and H +The transient mass transfer equation in the electrolyte simultaneously considers diffusion, migration, and convection. Electrolyte phase current density and solid phase current density are defined, and a charge conservation relationship is established. The zinc ion reduction deposition reaction and hydrogen evolution side reaction at the cathode interface are defined, and the Butler-Volmer equation is used to calculate the local reaction current density. The governing equations for ion mass transfer, charge conservation, interfacial reactions, and the evolution of zinc deposition thickness during zinc electrodeposition are as follows: ; ; Furthermore, when there is no homogeneous charge generation or consumption within the electrolytic liquid phase, ; ; ; ; ; ; ; ; ; In the formula: C i N represents the concentration of component i; i R is the molar flux of component i; i For volumetric reaction source terms; i l Z is the electrolyte phase current density; F is the Faraday constant; z i D is the ionic charge number. i u is the diffusion coefficient; i For mobility; The liquid phase potential is u; the electrolyte velocity is i. s σ is the solid-state current density; s Solid-state conductivity; n is the solid-state potential; b i is the unit normal vector of the electrode-electrolyte interface; app i represents the applied current density; locm ν represents the local reaction current density at the m-th interface; i n is the stoichiometric coefficient; m Let δ be the number of electrons transferred in the m-th interfacial reaction; Zn M represents the zinc deposition thickness. Zn For the molar mass of zinc; i Zn n represents the local current density during zinc deposition. Zn ρ represents the number of electrons transferred in the zinc electrodeposition reaction. Zn The density of metallic zinc; i loci is the local reaction current density at the electrode interface; i0 is the exchange current density; α a and α c η represents the charge transfer coefficients of the anode and cathode, respectively; η is the overpotential; R is the number of moles; T is the temperature; E eq ε is the equilibrium potential; exp(•) is an exponential function with the natural constant e as the base.

[0023] The above equations allow for the simultaneous solution of the ion concentration field, electrolyte potential, solid-phase potential, local reaction current density, and zinc layer thickness, thus characterizing the competitive relationship between the main reaction and the hydrogen evolution side reaction. The ion mass transfer model uses Zn... 2+ and H + Main object to be solved: Zn 2+ H is used to characterize the source of materials for the cathode deposition reaction. + It is used to characterize the impact of hydrogen evolution side reactions on the interfacial environment; considering diffusion, migration and convection terms, it can describe the changes in ion distribution under the combined effects of inlet flow, concentration gradient and potential gradient; coupling the interfacial flux with the local reaction current density can make the deposition thickness change consistent with the cathode surface reaction rate.

[0024] Define the ultrasonic sound pressure field and the acoustic particle velocity field, and calculate the sound field distribution under different ultrasonic frequencies, ultrasonic input power, and the number of ultrasonic sources; then compare the sound field distribution with Zn. 2+ and H + The concentration field, local interface reaction current density, and zinc deposition thickness evolution results were coupled and post-processed. To simplify the model, it was assumed that the ultrasonic propagation velocity was much higher than the average electrolyte flow velocity, the background fluid was approximately stationary, the ultrasonic propagation process was approximately adiabatic, and only the linear propagation behavior of small-amplitude sound waves was considered. The governing equations for the sound pressure field and the acoustic particle velocity field are: ; ; ; ; ; ; In the formula: ρ is the fluid density; v is the fluid velocity; c is the speed of sound; p is the sound pressure; k ep t is the bulk modulus of the fluid medium; t is time; P t For frequency domain sound pressure; q d It is a dipole source; ω is the angular frequency; Q m ε is a single-pole source; W is the average acoustic energy density; S is the acoustic power; and S is the cross-sectional area of ​​the ultrasonic probe.

[0025] Simultaneously, the average absolute sound pressure level is used to evaluate the overall intensity of the sound field, and the relative standard deviation of the sound field is used to evaluate the spatial uniformity of the sound field. The relative standard deviation of the sound field is: ; In the formula: s is the relative standard deviation of the sound field; P i Let be the sound pressure amplitude at the i-th node; be the average sound pressure amplitude; P be the mean absolute sound pressure; i be the node number; and n be the total number of nodes. The mean absolute sound pressure is used to evaluate the overall intensity of the sound field, while the relative standard deviation is used to evaluate the spatial fluctuations and uniformity of the sound field. The sound pressure distribution reflects the propagation and superposition of ultrasonic energy in the electrolyte, and the acoustic particle velocity reflects the ability of ultrasound to disturb the local mass transfer boundary layer. By using the mean absolute sound pressure and the relative standard deviation, it can be determined whether a certain combination of ultrasonic parameters only produces strong disturbances locally or can form a relatively stable mass transfer improvement effect near the electrodes.

[0026] The operating parameters for the ultrasonic-assisted zinc electrodeposition process are set, including at least the ultrasonic frequency, ultrasonic input power, number of ultrasonic sources, acid-zinc ratio, electrolyte flow rate, current density, and deposition time; the electrolyte flow rate, inlet velocity, and dimensionless mass transfer parameters satisfy the following relationship: ; ; ; ; ; ; In the formula: Q is the volumetric flow rate; U in A represents the average inlet velocity. in d is the inlet cross-sectional area; in D is the inlet pipe diameter. h Re is the hydraulic diameter; Re is the Reynolds number; S c S is the Schmitt number; h L is the Sherwood number; c D is the mass transfer characteristic length; i ρ is the diffusion coefficient of component i in the electrolyte; μ is the dynamic viscosity; and ρ is the electrolyte density.

[0027] In this embodiment, the physical property parameters are: inlet pipe diameter d in =1.00×10 -2 m; electrolyte density ρ = 1.20 × 10⁻⁶ m 3 kg•m -3 Dynamic viscosity μ = 1.20 × 10⁻⁶ -3 Pa•s;Zn 2+ Diffusion coefficient D i=7.0×10 -10 m 2 •s -1 Mass transfer characteristic length L c =0.10m.

[0028] Operating parameters include: ultrasonic frequency of 25-40kHz, ultrasonic input power of 5-30W, number of ultrasonic sound sources of 1-5, and current density of 300-600A•m. -2 The acid-to-zinc ratio was 3.0, and the simulated deposition time was 6 hours. These parameters were used to define the electrolyte renewal conditions and to ensure that the flow boundary and mass transfer boundary corresponded, thus providing a basis for evaluating Zn under the combined effects of ultrasound and flow. 2+ Transportation capacity provides the foundation.

[0029] To balance local field gradient resolution and computational efficiency, local mesh refinement is applied to the electrode surface, near the ultrasonic transducer, and inlet and outlet regions, while a relatively coarse mesh is used in the bulk electrolyte region (e.g., ...). Figure 2 (As shown); near the electrode surface there are variations in reaction current density, concentration gradient and deposition thickness, near the transducer there are acoustic pressure and acoustic particle velocity gradients, and near the inlet and outlet there are variations in flow boundaries. Therefore, a denser grid is used in the above regions; the field variables in the main electrolyte region change relatively gently, so a coarser grid can be used to reduce the computational load.

[0030] The transient finite element method was used to calculate the sound pressure distribution, acoustic particle velocity distribution, and Zn under different operating parameters. 2+ Concentration field, H + Concentration field and zinc deposition thickness; the simulated deposition time was set to 6 hours, and calculations were performed in groups based on ultrasonic frequency, input power, number of sound sources, and current density. The output sound pressure distribution, acoustic particle velocity distribution, and Zn concentration field were calculated. 2+ Concentration field, H + Concentration field and zinc deposition thickness distribution, combined with Figures 3-6 Perform the analysis.

[0031] Post-processing not only outputs single-field variable contour plots, but also the sound field distribution and Zn 2+ Concentration, H + Corresponding analysis of concentration and zinc deposition thickness: If the sound field intensity increases under a certain parameter condition but H + The perturbation is synchronously enhanced, and Zn 2+ If the supply to the cathode interface is not effectively improved, it will not be considered a preferred condition; if Zn under certain parameter conditions... 2+ Supply, H + If a good balance is maintained between disturbance control and deposition thickness growth, then this condition will be considered as a candidate process condition for subsequent experimental verification.

[0032] The experimental system was constructed using a constant temperature water bath, a constant current power supply, a peristaltic pump, an acrylic electrolytic cell, two lead-silver alloy anodes, and an aluminum cathode. Ultrasonic powers of 10W, 20W, and 30W and a current of 300 A•m were selected. -2 and 600A•m -2 Current densities were compared, with each group having a deposition time of 1.5 hours. The simulated trends were verified using cyclic voltammetry, nucleation overpotential, Tafel curves, cathodic polarization curves, zinc layer thickness, deposition quality, and current efficiency. Experimental verification was not a replacement for simulation but rather a means to examine trends selected from simulations: cyclic voltammetry and nucleation overpotential reflect nucleation and reduction behavior; Tafel curves and cathodic polarization curves characterize reaction kinetics and polarization features; and zinc layer thickness, deposition quality, and current efficiency validate the deposition results.

[0033] This invention also discloses a multi-physics coupling simulation and process parameter optimization system for ultrasonic-assisted zinc electrodeposition using the above-mentioned method, including a model construction module, a physics field definition module, a parameter setting module, a mesh generation and solution module, and a post-processing evaluation module. The model construction module is used to construct a three-dimensional transient finite element model of the ultrasonic-assisted zinc electrodeposition process. The three-dimensional transient finite element model includes an electrolyte region, a cathode, an anode, an inlet, an outlet, and at least one ultrasonic transducer disposed at the bottom of the reaction tank. The physics field definition module is used to define the acoustic pressure field and acoustic particle velocity field in the three-dimensional transient finite element model, and to establish the relationship between the acoustic pressure field, acoustic particle velocity field, and Zn in the electrolyte. 2+ and H + The coupling relationship between the ion mass transfer field, the electrode interface reaction field, and the zinc deposition layer growth field is described. The parameter setting module is used to set operating parameters, which include at least the ultrasonic frequency, ultrasonic input power, and the number of ultrasonic sources. The mesh generation and solution module is used to mesh the three-dimensional transient finite element model, locally refining the mesh on the electrode surface, near the ultrasonic transducer, and in the inlet and outlet regions, while using a relatively coarse mesh in the electrolyte bulk region. The transient finite element solution method is then used to calculate the sound pressure distribution, acoustic particle velocity distribution, and Zn under different operating parameters. 2+ Concentration field, H + Concentration field and zinc deposition thickness; the post-processing evaluation module is used to evaluate the concentration field, relative standard deviation of the sound field, and Zn concentration based on the mean absolute sound pressure level, Zn relative standard deviation, and Zn deposition thickness. 2+ Supply status, H + The effects of distribution patterns and deposition thickness variations on operational parameters on ultrasonic-assisted zinc electrodeposition behavior are evaluated, and optimal process parameters are screened. The system described above can also be stored as a computer program in a computer-readable storage medium, which, when executed by a processor, implements the method.

[0034] Specifically, the method provided by the present invention is illustrated by comparing and illustrating the following Examples 1-4 and Comparative Examples 1-4.

[0035] Example 1: In the COMSOL Multiphysics simulation platform, a three-dimensional model is selected to establish an ultrasonic-assisted zinc electrodeposition model. The three-dimensional transient finite element model includes the electrolyte region, an aluminum cathode located in the middle, lead-silver alloy anodes symmetrically distributed on both sides of the cathode, an inlet, an outlet, and two ultrasonic transducers located at the bottom of the electrolytic cell. An acidic zinc sulfate electrolyte system is selected, and Zn is defined... 2+ and H + The initial concentration, electrolyte properties, electrode material properties, and cathode and anode boundary conditions were determined. The ultrasonic frequency was set to 25 kHz, the input power to 5 W, the number of sound sources to 2, and the current density to 300 A•m. -2 The acid-zinc ratio was set to 3.0, and the simulated deposition time was set to 6 hours. Zn was extracted after the solution was obtained. 2+ Concentration field, H + Concentration field, sound pressure distribution, and acoustic particle velocity distribution were used as a benchmark example for frequency screening.

[0036] Comparative Example 1: The difference from Example 1 is that, while maintaining consistent model geometry, electrode materials, zinc acid-to-electrolyte ratio, input power, number of sound sources, current density, and simulated deposition time, the ultrasonic frequency was adjusted to 40 kHz. By comparing Example 1 and Comparative Example 1, the effect of ultrasonic frequency variation on the internal sound field distribution of the electrolyte and Zn... 2+ Transport to the cathode interface and H + The effect of concentration perturbation can be used to determine whether the improvement effect of interfacial mass transfer is synchronously enhanced under different frequency conditions.

[0037] Example 2: Based on the three-dimensional transient finite element model described in Example 1, the ultrasonic input power is set to 10W, the ultrasonic frequency is still set to 25kHz, the number of sound sources is still set to 2, and the current density is still set to 300A•m. -2 The acid-zinc ratio was still set at 3.0, and the simulated deposition time was still set at 6 hours. This example was used to evaluate the acoustic field enhancement and Zn under moderate ultrasonic input conditions. 2+ Supply Improvement and H + The coordination relationship between disturbance control is determined. The output concentration field and sound field results are then compared with those under lower or higher power conditions.

[0038] Comparative Example 2: The difference from Example 2 is that, while maintaining the same ultrasonic frequency, number of sound sources, current density, zinc acid-to-acid ratio, and simulated deposition time, the ultrasonic input power was adjusted to 30W. By comparing Example 2 and Comparative Example 2, the local sound field intensity, sound field uniformity, and Zn content were analyzed after increasing the power. 2+ Redistribution and H +Changes in disturbances should be considered to avoid using power increases alone as the basis for judging process optimization.

[0039] Example 3: Based on the parameters described in Example 2, two bottom ultrasonic sources were used as the sound field input method, maintaining an ultrasonic frequency of 25kHz, an input power of 10W, and a current density of 300A•m. -2 The acid-zinc ratio was 3.0, and the simulated deposition time was 6 hours. This example was used to evaluate the relationship between acoustic wave superposition, acoustic field uniformity, and ion concentration field response under a dual-source arrangement, and in conjunction with Zn... 2+ and H + Concentration distribution is used to determine the effect of dual sound sources on the mass transfer environment at the cathode interface.

[0040] Comparative Example 3: The difference from Example 3 is that, while maintaining the same ultrasonic frequency, input power, current density, acid-zinc ratio, and simulated deposition time, the number of ultrasonic sources was adjusted to five. By comparing Example 3 and Comparative Example 3, the sound field superposition method, local high sound pressure regions, and H-values ​​were analyzed after increasing the number of sound sources. + Concentration perturbation and Zn 2+ The change in the supply path was investigated to determine whether increasing the number of sound sources could actually improve the deposition interface environment.

[0041] Example 4: Based on the ultrasonic frequency, input power, and dual sound source conditions described in Example 2, the current density is set to 600 A•m. -2 The acid-zinc ratio was still set to 3.0, and the simulated deposition time was still set to 6 hours. This example was used to evaluate the effect of increasing the current density on zinc deposition thickness, reaction driving force, and concentration field stability under preferred ultrasonic-assisted conditions. After the solution was obtained, Zn 2+ Concentration field, H + Corresponding analysis was performed on the concentration field and zinc deposition thickness distribution.

[0042] Comparative Example 4: The difference from Example 4 is that, while maintaining the same ultrasonic frequency, input power, number of sound sources, acid-zinc ratio, and simulated deposition time, the current density was adjusted to 300 A•m. -2 By comparing Example 4 and Comparative Example 4, the effects of current density variation on zinc layer growth trend, ion consumption rate, and interface concentration distribution were determined, thereby evaluating the feasibility of increasing current density under the ultrasonic-assisted conditions.

[0043] Examples 1-4 and Comparative Examples 1-4 all employ the same multiphysics coupling solution process: first, three-dimensional geometry and material properties are established; then, equations for acoustic field, ion mass transfer, charge conservation, and interface reaction are set; followed by mesh generation, transient solution, and result post-processing. Only the key parameters to be examined are changed between different examples, while other conditions remain consistent. This reduces the interference of non-target variables on the interpretation of results, allowing the effects of ultrasonic frequency, ultrasonic power, number of ultrasonic sources, and current density to be identified separately.

[0044] Specific process parameters for Examples 1-4 and Comparative Examples 1-4: Example 1: frequency 25kHz, power 5W, number of sound sources 2, current density 300A•m -2 Comparative Example 1: Frequency 40kHz, Power 5W, Number of Sound Sources 2, Current Density 300A•m -2 Example 2 uses a frequency of 25kHz, a power of 10W, two sound sources, and a current density of 300A•m. -2 Comparative Example 2 has a frequency of 25kHz, a power of 30W, two sound sources, and a current density of 300 A•m. -2 Example 3 uses a frequency of 25kHz, a power of 10W, two sound sources, and a current density of 300A•m. -2 Comparative Example 3: Frequency 25kHz, Power 10W, Number of Sound Sources 5, Current Density 300A•m -2 Example 4 uses a frequency of 25kHz, a power of 10W, two sound sources, and a current density of 600A•m. -2 Comparative Example 4: Frequency 25kHz, Power 10W, Number of Sound Sources 2, Current Density 300A•m -2 .

[0045] Examples 1-4 and Comparative Examples 1-4 were all constructed based on the same three-dimensional model for ultrasonic-assisted zinc electrodeposition. The main differences lie in the variations of process parameters such as ultrasonic frequency, input power, number of ultrasonic sources, and current density. The ion concentration distribution, sound field distribution, deposition thickness, and experimental verification results under different parameter conditions are as follows: Figures 3-7 As shown.

[0046] Figure 3 The concentration distribution of Zn²⁺ and H⁺ at different ultrasonic frequencies is shown in the graph. Figure 3 This technique illustrates the effect of frequency variation on the ion concentration field. Under the same input power, number of sound sources, and current density, changes in ultrasonic frequency alter the propagation and attenuation characteristics of sound waves in the electrolyte, thereby affecting the concentration boundary layer near the cathode. Simultaneous observation of Zn... 2+ and H + The distribution of Zn can be used to determine whether a certain frequency truly improves the Zn required for the main reaction. 2+The supply, or whether the hydrogen evolution side reaction-related ion response is enhanced due to local perturbation; this analytical method transforms frequency screening from a simple comparison of sound pressure intensity to a comprehensive comparison of the sound field and the mass transfer state of the reaction interface. For example... Figure 3 As shown, under the conditions of 5W input power, 100mL electrolytic cell volume, 3.0 acid-zinc ratio, and dual sound sources, changing the ultrasonic frequency will synchronously affect Zn. 2+ and H + While higher frequencies may produce a stronger local acoustic response in a concentration field, they do not necessarily improve the near-cathode Zn concentration. 2+ The supply indicates that simply increasing the frequency or pursuing the peak sound pressure level cannot achieve a better interface mass transfer environment.

[0047] Figure 4 A comparison of concentration response and sound field response under different ultrasonic powers; Figure 4 This is used to illustrate the impact of input power variations on multiphysics coupling results. Increased input power generally enhances the acoustic response, but a stronger acoustic field can cause localized sound pressure concentration, increasing the difference in disturbance levels between different regions within the electrolyte. For zinc electrodeposition, a stronger acoustic field is not necessarily better; rather, it requires a suitable acoustic field for Zn... 2+ Feeding to the cathode, H + A balance must be struck between concentration disturbance control and interfacial reaction stability; therefore, in power screening, both concentration distribution and sound field uniformity are considered to avoid misjudging excessively strong local sound fields as optimal process conditions. Figure 4 As shown, when the power increases from 5W to 30W, the overall sound field intensity increases, but Zn 2+ The concentration response exhibits a non-monotonic change; moderate ultrasonic input can improve Zn 2+ Redistribution, while maintaining a relatively stable H + The sound field should be optimized to avoid excessive concentration of high-value areas and excessive spatial gradients under high-power conditions.

[0048] Figure 5 A comparison of concentration response and sound field response under different numbers of ultrasonic sources; Figure 5 This technique illustrates the impact of varying the number of sound sources on sound field superposition and concentration response. Changing the number of sound sources alters the direction of sound wave propagation, the superposition region, and the location of the high sound pressure region within the electrolyte. An appropriate number of sound sources can expand the effective perturbation range, improving mass transfer conditions near the cathode. However, excessive numbers of sound sources may lead to uneven sound field distribution and H... + Increased disturbance; by comparing the concentration field and sound field distribution under dual-source and multi-source conditions, it is possible to determine whether increasing the number of sound sources has practical significance for deposition optimization. For example... Figure 5 As shown, changes in the number of sound sources alter the superposition of sound waves and the sound field distribution within the electrolyte; when the number of sound sources is excessive, although local Zn 2+The redistribution has been enhanced, but H + The perturbation and local sound field superposition enhancement are also more obvious; dual sound sources can achieve more in Zn 2+ Supply, H + Achieving a more stable balance between disturbance control and sound field stability.

[0049] Figure 6 A comparison of concentration response and zinc deposition thickness at different current densities; Figure 6 To illustrate the effect of current density variation on deposition thickness and ion distribution, after the ultrasonic parameters are determined, the current density determines the driving force of the cathode interface reaction and Zn. 2+ Consumption rate, if the current density is increased, Zn 2+ Insufficient supply may lead to increased concentration polarization; if ultrasound assistance can maintain relatively stable ion transport, higher current density can promote zinc deposition layer growth; the deposition thickness distribution and Zn 2 + H + The correspondence between concentration fields is used to evaluate whether the increase in current density is within an acceptable process window. For example... Figure 6 As shown, under optimal ultrasonic frequency, ultrasonic input power, and dual acoustic sources, increasing the current density can enhance the driving force of the deposition reaction and promote the growth of the zinc deposition layer. However, it is also necessary to pay attention to H. + Related side reaction competition and interfacial concentration perturbations; therefore, current density screening should consider the increase in zinc deposition thickness and Zn 2+ Supply and H + Distribution stability is used as a common evaluation criterion.

[0050] As the above analysis shows, the method described in this invention does not simply list the effects of ultrasonic parameters on zinc electrodeposition results, but rather establishes a complete chain of "parameter input—sound field distribution—ion concentration field—interfacial reaction—deposition thickness—experimental verification." This chain can explain why certain enhanced ultrasonic input conditions may not necessarily have the best deposition effect, and also explains why a moderate combination of ultrasonic power, a reasonable number of sound sources, and an appropriate current density is more conducive to forming stable deposition behavior.

[0051] As can be seen from the comparison of Examples 1-4 and Comparative Examples 1-4 above, the method of the present invention establishes a complete analytical chain of "parameter input - sound field distribution - ion concentration field - interface reaction - deposition thickness - experimental verification", which can explain why certain enhanced ultrasonic input conditions may not have better deposition effects, and can also explain why a moderate combination of ultrasonic power, a reasonable number of sound sources and an appropriate current density is more conducive to the formation of stable deposition behavior.

[0052] Figure 7 This is a comparison chart of the mechanism and experimental verification results of ultrasound-assisted zinc electrodeposition. Figure 7 To illustrate the correspondence between simulation results and experimental verification, the simulation section provides the acoustic and concentration field distributions within the electrolyte, while the experimental section provides the electrochemical response and final deposition results. These correspond to the process mechanism and result verification, respectively. Cyclic voltammetry, nucleation overpotential, Tafel curves, and cathodic polarization curves characterize reaction kinetics changes, while zinc layer thickness, deposition quality, and current efficiency characterize the deposition results. By cross-referencing the above experimental indicators with the simulation screening trends, the credibility of the parameter optimization method can be improved. Figure 7 As shown, the experimental results of cyclic voltammetry, nucleation overpotential, Tafel curves, cathodic polarization curves, zinc layer thickness, deposition quality, and current efficiency collectively demonstrate that, under the conditions described in the embodiments of this application, a moderate ultrasonic input is more conducive to the formation of stable interfacial mass transfer and deposition response than a higher power ultrasonic input.

[0053] In summary, the method of this invention couples the ultrasonic field, ion mass transfer, electrochemical reaction, and zinc deposition growth process through a three-dimensional transient finite element model, revealing the influence of ultrasonic frequency, ultrasonic input power, number of ultrasonic sources, and current density on zinc electrodeposition behavior. Simulation and experimental results together demonstrate that a reasonable combination of ultrasonic parameters and current density can effectively promote Zn deposition. 2+ Transport to the cathode interface limits local concentration disturbances caused by excessively strong acoustic fields and improves the stability of the zinc electrodeposition process.

[0054] The above are merely preferred embodiments of the present invention and do not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process, characterized in that, Includes the following steps: Step 1: Construct a three-dimensional transient finite element model of the ultrasonic-assisted zinc electrodeposition process. The three-dimensional transient finite element model includes an electrolyte region, a cathode, an anode, an inlet, an outlet, and at least one ultrasonic transducer located at the bottom of the reaction tank. Step 2: Define the sound pressure field and acoustic particle velocity field in the three-dimensional transient finite element model, and establish the relationship between the sound pressure field, acoustic particle velocity field, and Zn in the electrolyte. 2+ and H + The coupling relationship between the ion mass transfer field, the electrode interface reaction field, and the zinc deposition layer growth field; Step 3: Set the operating parameters for the ultrasonic-assisted zinc electrodeposition process. The operating parameters include at least the ultrasonic frequency, ultrasonic input power, number of ultrasonic sources, acid-zinc ratio, electrolyte flow rate, current density, and deposition time. Step 4: Mesh the three-dimensional transient finite element model, with local refinement at the electrode surface, near the ultrasonic transducer, and in the inlet and outlet regions. Then, use the transient finite element method to calculate the sound pressure distribution, acoustic particle velocity distribution, and Zn under different operating parameters. 2+ Concentration field, H + Concentration field and zinc deposition thickness; Step 5: Post-process the calculation results based on mean absolute sound pressure, relative standard deviation of the sound field, and Zn. 2+ Supply status, H + The effects of distribution state and deposition thickness variations on operating parameters on ultrasonic-assisted zinc electrodeposition behavior were evaluated, and optimal process parameters were screened. Step 6: The preferred process parameters are experimentally verified through electrochemical testing, deposition layer thickness testing, deposition quality determination, and current efficiency calculation.

2. The method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 1, characterized in that, The steps for constructing the three-dimensional transient finite element model in step 1 are as follows: Select the three-dimensional model and transient solution mode in the COMSOL Multiphysics simulation system; establish an electrolytic cell model with a reaction tank volume of 100 mL, the electrolytic cell model includes an aluminum cathode located in the middle, lead-silver alloy anodes symmetrically arranged on both sides of the cathode, an electrolyte region located between parallel electrodes, and an inlet and an outlet; set one or more ultrasonic transducers at the bottom of the reaction cell; use the electrolyte region, cathode, anode and ultrasonic transducers as a unified computational domain to calculate the coupling response between the acoustic field, ion mass transfer, electrochemical reaction and zinc deposition layer growth.

3. The method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 1, characterized in that, In step 2, when defining the physical field, a three-level current distribution model is used to describe ion transport and interfacial reactions in the electrolyte, and an acoustic frequency domain model is used to describe the propagation of ultrasound in the electrolyte. Specifically, this includes: Step 21: Define Zn 2+ and H + Transient mass transfer equations in electrolytes, which simultaneously consider diffusion, migration and convection; Step 22: Define the electrolyte phase current density and the solid phase current density, and establish the charge conservation relationship; Step 23: Define the zinc ion reduction deposition reaction and hydrogen evolution side reaction at the cathode interface, and calculate the local reaction current density using the Butler-Volmer equation; Step 24: Define the ultrasonic sound pressure field and the sound particle velocity field, and calculate the sound field distribution under different ultrasonic frequencies, ultrasonic input power and the number of ultrasonic sound sources; Step 25: Compare the sound field distribution with Zn 2+ and H + The concentration field, local reaction current density at the interface, and the evolution of zinc deposition thickness were coupled and then processed.

4. The method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 3, characterized in that, The governing equations for ion mass transfer, charge conservation, interfacial reaction, and zinc deposition thickness evolution in steps 21 to 23 are as follows: ； ； Furthermore, when there is no homogeneous charge generation or consumption within the electrolytic liquid phase, ; ； ； ； ； ； ； ； ； In the formula: C i N represents the concentration of component i; i R is the molar flux of component i; i For volumetric reaction source terms; i l Z is the electrolyte phase current density; F is the Faraday constant; z i D is the ionic charge number. i u is the diffusion coefficient; i For mobility; The liquid phase potential is u; the electrolyte velocity is i. s σ is the solid-state current density; s Solid-state conductivity; n is the solid-state potential; b i is the unit normal vector of the electrode-electrolyte interface; app i represents the applied current density; locm ν represents the local reaction current density at the m-th interface; i n is the stoichiometric coefficient; m Let δ be the number of electrons transferred in the m-th interfacial reaction; Zn M represents the zinc deposition thickness. Zn For the molar mass of zinc; i Zn n represents the local current density during zinc deposition. Zn ρ represents the number of electrons transferred in the zinc electrodeposition reaction. Zn The density of metallic zinc; i loc i is the local reaction current density at the electrode interface; i0 is the exchange current density; α a and α c These are the charge transfer coefficients of the anode and cathode, respectively; η is the overpotential; R is the number of moles; T is the temperature; E eq ε is the equilibrium potential; exp(•) is an exponential function with the natural constant e as the base.

5. The method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 3, characterized in that, The governing equations for the sound pressure field and the sound particle velocity field in step 24 are: ； ； ； ； ； ； In the formula: ρ is the fluid density; v is the fluid velocity; c is the speed of sound; p is the sound pressure; k ep t is the bulk modulus of the fluid medium; t is time; P t For frequency domain sound pressure; q d It is a dipole source; ω is the angular frequency; Q m ε is a single-pole source; W is the average acoustic energy density; S is the acoustic power; and S is the cross-sectional area of ​​the ultrasonic probe.

6. The method for multi-physics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 1, characterized in that, The electrolyte flow rate, inlet velocity, and dimensionless mass transfer parameters described in step 3 satisfy the following relationship: ； ； ； ； ； ； In the formula: Q is the volumetric flow rate; U in A represents the average inlet velocity. in d is the inlet cross-sectional area; in D is the inlet pipe diameter. h Re is the hydraulic diameter; Re is the Reynolds number; S c S is the Schmitt number; h L is the Sherwood number; c D is the mass transfer characteristic length; i ρ is the diffusion coefficient of component i in the electrolyte; μ is the dynamic viscosity; and ρ is the electrolyte density.

7. The method for multi-physics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 1, characterized in that, In step 5, the average absolute sound pressure level is used to evaluate the overall intensity of the sound field, and the relative standard deviation of the sound field is used to evaluate the spatial uniformity of the sound field. The relative standard deviation of the sound field is: ； In the formula: s is the relative standard deviation of the sound field; P i is the sound pressure amplitude at the i-th node; is the average sound pressure amplitude; P is the average absolute sound pressure; i is the node number; n is the total number of nodes.

8. The method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 1, characterized in that, The operating parameters in step 3 include: ultrasonic frequency of 25-40kHz, ultrasonic input power of 5-30W, number of ultrasonic sound sources of 1-5, and current density of 300-600A•m. -2 The acid-zinc ratio was 3.0, and the simulated deposition time was 6 hours.

9. The method for multiphysics coupling simulation and process parameter optimization of ultrasonic-assisted zinc electrodeposition process according to claim 1, characterized in that, Step 6 involves electrochemical testing, including cyclic voltammetry, nucleation overpotential testing, Tafel curve testing, and cathodic polarization curve testing. The experimental verification utilizes a system constructed with a constant-temperature water bath, constant-current power supply, peristaltic pump, acrylic electrolytic cell, two lead-silver alloy anodes, and an aluminum cathode, employing ultrasonic input powers of 10W, 20W, and 30W, and a current of 300 A•m. -2 and 600A•m -2 The current density was compared, and the deposition time for each group was 1.5 hours.

10. A multiphysics coupling simulation and process parameter optimization system for ultrasonic-assisted zinc electrodeposition using the method described in any one of claims 1-9, characterized in that, include: The model building module is used to build a three-dimensional transient finite element model of the ultrasonic-assisted zinc electrodeposition process. The three-dimensional transient finite element model includes an electrolyte region, a cathode, an anode, an inlet, an outlet, and at least one ultrasonic transducer disposed at the bottom of the reaction tank. The physics field definition module is used to define the sound pressure field and acoustic particle velocity field in the three-dimensional transient finite element model, and to establish the relationship between the sound pressure field, acoustic particle velocity field and Zn in the electrolyte. 2+ and H + The coupling relationship between the ion mass transfer field, the electrode interface reaction field, and the zinc deposition layer growth field; A parameter setting module is used to set operating parameters; the operating parameters include at least ultrasonic frequency, ultrasonic input power, and the number of ultrasonic sound sources. The mesh generation and solution module is used to generate a mesh for the three-dimensional transient finite element model. Local mesh refinement is applied to the electrode surface, near the ultrasonic transducer, and inlet and outlet regions, while a relatively coarse mesh is used in the electrolyte bulk region. The transient finite element solution method is then used to calculate the sound pressure distribution, acoustic particle velocity distribution, and Zn content under different operating parameters. 2+ Concentration field, H + Concentration field and zinc deposition thickness; The post-processing evaluation module is used to evaluate the sound field based on mean absolute sound pressure level, relative standard deviation of sound field, and Zn. 2 + Supply status, H + The effects of distribution patterns and deposition thickness variations on operating parameters on ultrasonic-assisted zinc electrodeposition behavior were evaluated, and optimal process parameters were screened.

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