A method for multi-physical field coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis

Abstract

The application discloses a kind of based on transient finite element analysis zinc electrodeposition process multi-physical field coupling simulation and process parameter optimization method, belong to electrodeposition process modeling analysis and parameter control technical field, specific steps include: in simulation platform, establish zinc electrodeposition three-dimensional transient model, coupling ion mass transfer and electrode interface reaction process;Set the structural parameters of electrodeposition system, process parameters and boundary conditions;The model is meshed and calculated using transient solution method, ion concentration field distribution and deposition thickness evolution results under different working conditions are obtained;According to the calculation results, the electrolyte flow rate, anode-cathode spacing, acid-zinc ratio and current density are optimized and controlled.The application can realize the coordinated control of main reaction and side reaction in zinc electrodeposition process, improve the interface mass transfer state, improve the compactness, uniformity and process stability of the deposition layer, and is used for zinc electrodeposition process optimization and related electrochemical deposition process design and control.

Description

Technical Field

[0001] This invention belongs to the field of electrodeposition process modeling analysis and parameter control technology, specifically involving a multi-physics field coupling simulation and process parameter optimization method for zinc electrodeposition process based on transient finite element analysis. Background Technology

[0002] Zinc electrodeposition is the process by which metallic zinc undergoes electrochemical reduction on the cathode surface to form a deposited layer. It is a crucial step in hydrometallurgical zinc refining and zinc plating. During zinc electrodeposition, the thickness, uniformity, and surface morphology of the deposited layer directly affect product quality and the stability of subsequent processes. This process is influenced by multiple factors, including ion mass transfer in the electrolyte, electrode interface reactions, and changes in operating parameters. When process conditions are not properly controlled, problems such as rough deposited layers, uneven thickness distribution, and enhanced hydrogen evolution side reactions can easily occur.

[0003] Currently, research on the zinc electrodeposition process mainly relies on experimental methods. While experimental studies can reflect the influence of different process conditions on the deposition results to some extent, the distribution of ion concentration within the electrolyte, mass transfer behavior near the interface, and the competitive relationship between main and side reactions are difficult to directly observe and accurately characterize experimentally. Therefore, relying solely on experimental methods requires numerous repeated experiments, which is not only time-consuming and costly, but also makes it difficult to systematically reveal the influence of different parameters on zinc electrodeposition behavior at the mechanistic level.

[0004] With the development of numerical simulation technology, computer simulation has become an important tool for analyzing zinc electrodeposition processes. COMSOL Multiphysics is a multiphysics simulation platform based on finite element analysis, which can be used to establish coupled models of electrochemical deposition processes and dynamically analyze ion concentration fields, interfacial reaction processes, and deposition behavior. However, existing research still lacks systematic analysis of the evolution of ion mass transfer and interfacial reactions under multi-parameter coupling, especially under different flow rates, anode-cathode spacing, acid-zinc ratios, and current densities. Further research is needed on how to accurately simulate and optimize process parameters using transient finite element methods. Summary of the Invention

[0005] Technical problem to be solved: In view of the shortcomings of the above-mentioned existing technologies, the present invention provides a multi-physics field coupled simulation and process parameter optimization method for zinc electrodeposition process based on transient finite element analysis. By constructing a three-dimensional transient model of zinc electrodeposition, the deposition behavior can be quantitatively described and the process parameters can be optimized and controlled. This can reduce the time and cost of a large number of repeated experiments and solve the problem that traditional experimental methods are difficult to directly characterize the internal ion distribution of electrolyte and the dynamic evolution of deposition process.

[0006] Technical solution: The present invention provides a multi-physics coupled simulation and process parameter optimization method for zinc electrodeposition process based on transient finite element analysis, comprising the following steps: Step 1: Construct a three-dimensional transient model of the zinc electrodeposition process in the COMSOL Multiphysics simulation platform. The three-dimensional transient model includes the cathode, anode and electrolyte regions, and sets the structural parameters and operating parameters of the zinc electrodeposition system according to the experimental setup and process conditions. Step 2: Globally define the physical field, boundary conditions, and material properties coupling ion mass transfer and electrode interface reaction during the zinc electrodeposition process, and set Zn 2+ H + and OH - Initial concentration, transport characteristics, and reaction parameters; Step 3: Based on the mass transfer characteristics and interfacial reaction features of the zinc electrodeposition process, the three-dimensional transient model is meshed; Step 4: Solve the three-dimensional transient model using the transient solution method. Set different electrolyte flow rate, anode-cathode distance, acid-zinc ratio and current density process parameters respectively, and calculate the ion concentration field distribution and deposition thickness evolution process in the zinc electrodeposition process under different working conditions. Step 5: Set the corresponding calculation time according to different working conditions. The first time scale is used for calculations based on the flow rate, anode-cathode spacing and current density conditions, and the second time scale is used for calculations based on the acid-zinc ratio condition. The second time scale is larger than the first time scale to characterize the influence of different parameters on the evolution process of the zinc electrodeposition system. Step 6: By post-processing and visualizing the calculation results, obtain the Zn values ​​under different working conditions. 2+ H + and OH - The concentration field distribution and deposition thickness variation patterns were investigated, and the influence of various process parameters on zinc electrodeposition behavior and side reactions was analyzed, thereby obtaining optimized zinc electrodeposition process parameters.

[0007] Preferably, the specific method for constructing the three-dimensional transient model in step 1 is as follows: Step 11: In the COMSOL Multiphysics simulation system, select the 3D modeling method, the electrochemical physics field module, and the transient analysis method; Step 12: Define the model parameters and model variables for the cathode, anode, and electrolyte regions in the zinc electrodeposition system, and set the operating parameters including electrolyte flow rate, anode-cathode distance, zinc acid ratio, and current density; Step 13: Construct a three-dimensional geometric model of the cathode, anode, and electrolyte regions in the zinc electrodeposition system.

[0008] Preferably, in step 2, when defining the physical field, the finite element analysis method is used to couple the ion mass transfer process in the electrolyte and the electrode interface reaction process, specifically including the following steps: Step 21: Define the governing equations for ion mass transfer in the zinc electrodeposition system. Based on the mass conservation equation and the diffusion-migration equation, establish the Zn... 2+ H + and OH - A transport model in the electrolyte was developed, and the corresponding initial concentration and boundary conditions were set. Step 22: Define the electrochemical reaction process at the electrode interface, which includes the reduction and deposition reaction of zinc ions and the hydrogen evolution side reaction of hydrogen ions, and establish the corresponding reaction kinetic model. Step 23: Couple the ion mass transfer process with the electrode interface reaction process to construct a multi-physics coupling model of the zinc electrodeposition process, which is used to describe the evolution of the ion concentration field over time and the variation law of deposition behavior.

[0009] Preferably, the model parameters defined in step 21 include: a reaction tank volume of 100 mL, an electrolyte system of zinc sulfate, an acid-zinc ratio of 3.0-3.6, a temperature of 38-46℃, and a flow rate of 100-300 mL·min. -1 The cathode is an aluminum plate located in the center, and the anode consists of two lead-silver alloy electrodes symmetrically distributed on both sides of the cathode. The distance between the anode and cathode is 15-30 mm, and the current density is 300-600 A·m. -2 .

[0010] Preferably, the standard for meshing the three-dimensional transient model in step 3 is as follows: In COMSOL Multiphysics simulation calculation, a regional meshing method is adopted, and different mesh sizes are set for different regions according to the structural characteristics and physical field changes of the cathode, anode, and electrolyte regions; in regions with intense ion mass transfer and interface reactions, the mesh is locally refined; in regions far from the electrode interface, a relatively coarse mesh is used; the mesh types include free triangular mesh, free quadrilateral mesh, and free tetrahedral mesh, and the electrode interface region is optimized in combination with the boundary layer mesh; and the optimal meshing scheme that meets the calculation accuracy requirements is determined through mesh independence verification.

[0011] Preferably, in step 4, the ion mass transfer and electrode interface reaction of the zinc electrodeposition process are numerically solved, and the governing equations are as follows: ; In the formula: The divergence of ion flux; Electrolyte flow rate; This represents the ion concentration gradient. For volumetric reaction source terms; ; In the formula: Where is the current density; F is the Faraday constant; The ionic charge number; and These are the reaction terms related to hydrogen ions and hydroxide ions, respectively. For charge source terms; ; In the formula: This refers to the ion concentration. is the ion product constant of water; ; In the formula: This refers to ion flux; The diffusion coefficient is denoted as . For mobility; This is the liquid phase potential; ; In the formula: This refers to the electrolyte current density. ; In the formula: Solid-state conductivity; This is the solid-state potential; ; ; In the formula: This represents the total current density. This is the local reaction current; It is the double-layer current; ; In the formula: The total reaction rate at the interface; The above governing equations were discretized using the finite element method, and the zinc electrodeposition process was numerically calculated using a transient solver to obtain the evolution of the ion concentration field and current distribution over time.

[0012] Preferably, in step 5, the calculation results of the zinc electrodeposition process are post-processed and analyzed, and the deposition behavior is characterized by the relationship between the evolution of the deposition layer morphology and the changes in materials. The expression is as follows: ; In the formula: Let be the concentration of species j in region d; Let be the rate of generation or consumption of species j in region d caused by the m-th reaction process; ; In the formula: Let be the initial concentration of species j; This represents the initial concentration of species j in region d; Let be the density of species j; Let be the molar mass of species j; This represents the change in the thickness of the deposited layer on the electrode surface. ; In the formula: The normal growth rate of the deposition interface; This represents the generation rate (positive) or consumption rate (negative) of species j in region d, which can be an electrolyte diffusion layer, an electrode surface, or the interior of a porous electrode, and is generated through the m-th reaction step. Indicates the molar mass of species j; This represents the density of species j.

[0013] Preferably, the post-processing and visualization analysis in step 6 specifically includes the following steps: Step 61: After the simulation calculation is completed, extract the data from the calculation results and output the ion concentration field distribution, deposition thickness and related calculation results as numerical data and image information; Step 62: Visualize the calculation results using the post-processing module. This can be done by adding a 3D plotting group or a 2D plotting group to visualize the Zn graph. 2+ H + and OH - The concentration field distribution and deposition thickness distribution are displayed and expressed. Step 63: Based on the calculation results, perform quantitative analysis on the ion concentration distribution and deposition thickness variation, and calculate the deposition uniformity, thickness variation trend and side reaction intensity under different working conditions; Step 64: By comparing and evaluating the visualization results and quantitative analysis results, analyze the influence of different process parameters on the zinc electrodeposition process, and optimize the electrolyte flow rate, anode-cathode distance, acid-zinc ratio and current density to obtain the optimal zinc electrodeposition process parameters.

[0014] Preferably, the electrolyte system is an acidic solution system containing zinc ions, and the solution includes Zn. 2+ H + and OH - Ionic components involved in mass transfer and reaction; the cathode is made of conductive metal material, and the anode is made of inert electrode or lead-based alloy material.

[0015] Preferably, in the three-dimensional transient model, the cathode and anode constitute an electrode system arranged opposite to each other, and the electrolyte region is located between the two electrodes; by adjusting the electrolyte flow rate and the distance between the anode and cathode, the ion transport path and concentration distribution in the electrolyte are controlled, thereby affecting the interface reaction process and deposition behavior.

[0016] Compared with the prior art, this invention application has the following significant advantages: 1. This invention utilizes a numerical simulation method based on COMSOL Multiphysics. By employing a three-level current distribution model to construct a coupled model of ion mass transfer and electrode interface reaction during the zinc electrodeposition process, it achieves the simulation of Zn... 2+ H + and OH - Visual analysis of concentration field and deposition behavior can effectively quantify the influence of different process parameters on zinc electrodeposition process, solving the problem that traditional experimental methods cannot directly characterize the internal ion distribution of electrolyte and the dynamic evolution of deposition process; 2. This invention establishes a three-dimensional transient model of the zinc electrodeposition process, coupling the ion mass transfer process, charge conservation relationship, and electrode interface reaction process for solution. This model can realistically reflect the changing behavior of zinc electrodeposition under different operating conditions and achieve dynamic prediction of the deposition layer growth process. Through simulation analysis, process conditions that are conducive to uniform growth of the deposition layer and suppression of side reactions can be obtained, thereby improving the compactness, uniformity, and process stability of the deposition layer. 3. The method of this invention can provide theoretical basis and technical support for zinc electrodeposition process design and parameter optimization, significantly reduce experimental trial and error costs and time, has good engineering application value, is conducive to the large-scale development of equipment, and is suitable for enterprise promotion and application. Attached Figure Description

[0017] Figure 1 This is a flowchart of the multiphysics coupling simulation and process parameter optimization method for zinc electrodeposition process based on transient finite element analysis according to the present invention.

[0018] Figure 2 This is a schematic diagram of the structure of the three-dimensional zinc electrodeposition model of the present invention; Figure 3 To obtain Zn under different flow rate conditions 2+ Ion concentration distribution diagrams ((a) Example 1; (b) Comparative Example 1); Figure 4 To obtain Zn under different anode-cathode spacing conditions 2+ Ion concentration distribution diagrams ((a) Example 2; (b) Comparative Example 2); Figure 5 To obtain OH under different acid-zinc ratio conditions -Ion concentration distribution diagrams ((a) Example 3; (b) Comparative Example 3); Figure 6 To obtain H under different current density conditions + Ion concentration distribution diagrams ((a) Example 4; (b) Comparative Example 4). Detailed Implementation

[0019] 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 1-6 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.

[0020] like Figure 1 As shown, the present invention provides a method for multi-physics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis, the method comprising the following specific steps.

[0021] (I) A three-dimensional transient model of the zinc electrodeposition process was constructed in the COMSOL Multiphysics simulation platform. The three-dimensional transient model includes the cathode, anode, and electrolyte regions. The structural and operational parameters of the zinc electrodeposition system were set according to the experimental setup and process conditions. For example... Figure 2 As shown in the three-dimensional transient model, the cathode and anode constitute an electrode system arranged opposite to each other, with the electrolyte region located between the two electrodes. By adjusting the electrolyte flow rate and the distance between the anode and cathode, the ion transport path and concentration distribution in the electrolyte are controlled, thereby affecting the interfacial reaction process and deposition behavior. The electrolyte system is an acidic solution system containing zinc ions, including Zn. 2+ H + and OH - The ionic components involved in mass transfer and reaction; the cathode uses a conductive metal material, and the anode uses an inert electrode or a lead-based alloy material. The specific construction method of the three-dimensional transient model is as follows: (1) Select the three-dimensional modeling method, electrochemical physical field module and transient analysis method in the COMSOL Multiphysics simulation system; (2) Define the model parameters and model variables of the cathode, anode and electrolyte regions in the zinc electrodeposition system, and set the operating parameters including electrolyte flow rate, anode-cathode distance, zinc acid ratio and current density; (3) Construct a three-dimensional geometric model of the cathode, anode and electrolyte regions in the zinc electrodeposition system.

[0022] (II) Globally define the physical field, boundary conditions, and material properties of the coupling between ion mass transfer and electrode interface reaction during the zinc electrodeposition process, and set Zn 2+ H + and OH - The initial concentration, transport characteristics, and reaction parameters were determined. When defining the physical field, the finite element method was used to couple the ion mass transfer process in the electrolyte and the electrode interface reaction process, specifically including the following steps: (1) Define the governing equation for ion mass transfer in the zinc electrodeposition system, and establish the Zn equation based on the mass conservation equation and the diffusion-migration equation. 2+ H + and OH - A transport model in the electrolyte was established, and corresponding initial concentrations and boundary conditions were set. The model parameters were defined as follows: reaction tank volume 100 mL, electrolyte is zinc sulfate system, acid-zinc ratio 3.0-3.6, temperature 38-46℃, and flow rate 100-300 mL / min. -1 The cathode is an aluminum plate located in the center, and the anode consists of two lead-silver alloy electrodes symmetrically distributed on both sides of the cathode. The distance between the anode and cathode is 15-30 mm, and the current density is 300-600 A·m. -2 .

[0023] (2) Define the electrochemical reaction process at the electrode interface, including the reduction and deposition reaction of zinc ions and the hydrogen evolution side reaction of hydrogen ions, and establish the corresponding reaction kinetic model. (3) The ion mass transfer process is coupled with the electrode interface reaction process to construct a multi-physics field coupling model of zinc electrodeposition process, which is used to describe the evolution of ion concentration field over time and the change law of deposition behavior.

[0024] (III) Based on the mass transfer characteristics and interfacial reaction features of the zinc electrodeposition process, the three-dimensional transient model was meshed. The meshing criteria were as follows: In the COMSOL Multiphysics simulation calculation, a regional meshing method was adopted, and different mesh sizes were set for different regions according to the structural characteristics and physical field changes of the cathode, anode, and electrolyte regions. In regions with intense ion mass transfer and interfacial reactions, the mesh was locally refined. In regions far from the electrode interface, a relatively coarse mesh was used. The mesh types included free triangular meshes, free quadrilateral meshes, and free tetrahedral meshes, and the electrode interface region was optimized in combination with the boundary layer mesh. The optimal meshing scheme that met the calculation accuracy requirements was determined through mesh independence verification.

[0025] (iv) The three-dimensional transient model was solved using a transient solution method. Different process parameters, including electrolyte flow rate, anode-cathode spacing, zinc acid-to-acid ratio, and current density, were set to calculate the ion concentration field distribution and deposition thickness evolution during zinc electrodeposition under different operating conditions. The ion mass transfer and electrode interface reactions during zinc electrodeposition were numerically solved, and the governing equations are as follows: ; In the formula: The divergence of ion flux; Electrolyte flow rate; This represents the ion concentration gradient. For volumetric reaction source terms; ; In the formula: Where is the current density; F is the Faraday constant; The ionic charge number; and These are the reaction terms related to hydrogen ions and hydroxide ions, respectively. For charge source terms; ; In the formula: This refers to the ion concentration. is the ion product constant of water; ; In the formula: This refers to ion flux; The diffusion coefficient is denoted as . For mobility; This is the liquid phase potential; ; In the formula: This refers to the electrolyte current density. ; In the formula: Solid-state conductivity; This is the solid-state potential; ; ; In the formula: This represents the total current density. This is the local reaction current; It is the double-layer current; ; In the formula: The total reaction rate at the interface; The above governing equations were discretized using the finite element method, and the zinc electrodeposition process was numerically calculated using a transient solver to obtain the evolution of the ion concentration field and current distribution over time.

[0026] (V) Calculation times were set according to different operating conditions. A first time scale was used for calculations based on flow velocity, anode-cathode spacing, and current density conditions, while a second time scale was used for calculations based on the acid-zinc ratio condition. The second time scale was longer than the first time scale to characterize the influence of different parameters on the evolution of the zinc electrodeposition system. The calculation results of the zinc electrodeposition process were post-processed and analyzed. The deposition behavior was characterized by the relationship between sedimentary layer morphology evolution and material changes, as expressed below: ; In the formula: Let be the concentration of species j in region d; Let be the rate of generation or consumption of species j in region d caused by the m-th reaction process; ; In the formula: Let be the initial concentration of species j; This represents the initial concentration of species j in region d; Let be the density of species j; Let be the molar mass of species j; This represents the change in the thickness of the deposited layer on the electrode surface. ; In the formula: The normal growth rate of the deposition interface; This represents the generation rate (positive) or consumption rate (negative) of species j in region d, which can be an electrolyte diffusion layer, an electrode surface, or the interior of a porous electrode, and is generated through the m-th reaction step. Indicates the molar mass of species j; This represents the density of species j.

[0027] (vi) By post-processing and visualizing the calculation results, Zn under different working conditions is obtained. 2+ H + and OH - The concentration field distribution and deposition thickness variation patterns were analyzed, and the influence of various process parameters on zinc electrodeposition behavior and side reactions was investigated to obtain optimized zinc electrodeposition process parameters. Post-processing and visualization analysis specifically include the following steps: (1) After the simulation calculation is completed, the calculation results are extracted and the ion concentration field distribution, deposition thickness and related calculation results are output as numerical data and image information. (2) The calculation results are visualized through the post-processing module. By adding 3D or 2D plotting groups, the Zn... 2+ H + and OH - The concentration field distribution and deposition thickness distribution are displayed and expressed. (3) Based on the calculation results, quantitative analysis was performed on the ion concentration distribution and deposition thickness variation, and deposition uniformity, thickness variation trend and side reaction intensity under different working conditions were calculated. (4) By comparing and evaluating the visualization results and quantitative analysis results, the influence of different process parameters on the zinc electrodeposition process is analyzed, and the electrolyte flow rate, anode-cathode distance, acid-zinc ratio and current density are optimized to obtain the optimal zinc electrodeposition process parameters.

[0028] Specifically, Examples 1-4 and Comparative Examples 1-4 are used to compare and illustrate the multiphysics coupling simulation and process parameter optimization method for zinc electrodeposition process based on transient finite element analysis provided by the present invention.

[0029] Example 1: In the COMSOL Multiphysics simulation system, a 3D model of zinc electrodeposition with a reaction tank volume of 100 mL was established using the "3D model" mode. The cathode was an aluminum plate located in the center, and the anode was a lead-silver alloy electrode symmetrically distributed on both sides of the cathode, with a cathode-cathode distance of 30 mm. Electrolyte materials were selected, an electrolyte system with an acid-zinc ratio of 3.0 was constructed, and ion mass transfer and related physical parameters were defined. The process parameters for zinc electrodeposition were set, with the current density set to 300 A·m. -2 The flow rate is 250 mL / min. -1 Boundary conditions were set to define the electrochemical reaction region on the electrode surface, and corresponding current density boundary conditions were set. The three-dimensional model of the cathode, anode, and electrolyte regions was meshed using free tetrahedral meshes. A transient solution method was used to perform numerical calculations on the model, with the calculation time (first time scale) set to 3600 s. The calculation results were then post-processed and analyzed.

[0030] Example 2: In the COMSOL Multiphysics simulation system, a 3D model of zinc electrodeposition with a reaction tank volume of 100 mL was established using the "3D model" mode. The cathode was an aluminum plate located in the center, and the anode was a lead-silver alloy electrode symmetrically distributed on both sides of the cathode, with a cathode-cathode distance of 20 mm. Electrolyte materials were selected, and an electrolyte system with an acid-zinc ratio of 3.0 was constructed. Ion mass transfer and related physical parameters were defined. The process parameters for zinc electrodeposition were set, with the current density set to 300 A·m. -2 The flow rate is 250 mL·min -1Boundary conditions were set to define the electrochemical reaction region on the electrode surface, and corresponding current density boundary conditions were set. The three-dimensional model of the cathode, anode, and electrolyte regions was meshed using free tetrahedral meshes. A transient solution method was used to perform numerical calculations on the model, with the calculation time (first time scale) set to 3600 s. The calculation results were then post-processed and analyzed.

[0031] Example 3: In the COMSOL Multiphysics simulation system, a 3D model of zinc electrodeposition with a reaction tank volume of 100 mL was established using the "3D model" mode. The cathode was an aluminum plate located in the center, and the anode was a lead-silver alloy electrode symmetrically distributed on both sides of the cathode, with a cathode-cathode distance of 20 mm. Electrolyte materials were selected, and an electrolyte system with an acid-zinc ratio of 3.4 was constructed. Ion mass transfer and related physical parameters were defined. The process parameters for zinc electrodeposition were set, with the current density set to 300 A·m. -2 The flow rate is 250 mL / min. -1 Boundary conditions were set to define the electrochemical reaction region on the electrode surface, and corresponding current density boundary conditions were set. The three-dimensional model of the cathode, anode, and electrolyte regions was meshed using free tetrahedral meshes. A transient solution method was used to perform numerical calculations on the model, with the calculation time (second time scale) set to 10800 s. The calculation results were then post-processed and analyzed.

[0032] Example 4: In the COMSOL Multiphysics simulation system, a 3D model of zinc electrodeposition with a reaction tank volume of 100 mL was established using the "3D model" mode. The cathode was an aluminum plate located in the center, and the anode was a lead-silver alloy electrode symmetrically distributed on both sides of the cathode, with a cathode-cathode distance of 20 mm. Electrolyte materials were selected, and an electrolyte system with an acid-zinc ratio of 3.4 was constructed. Ion mass transfer and related physical parameters were defined. The process parameters for zinc electrodeposition were set, with the current density set to 600 A·m. -2 The flow rate is 250 mL / min. -1 Boundary conditions were set to define the electrochemical reaction region on the electrode surface, and corresponding current density boundary conditions were set. The three-dimensional model of the cathode, anode, and electrolyte regions was meshed using free tetrahedral meshes. A transient solution method was used to perform numerical calculations on the model, with the calculation time (first time scale) set to 3600 s. The calculation results were then post-processed and analyzed.

[0033] Comparative Example 1: The difference from Example 1 is that, while keeping other conditions unchanged, the electrolyte flow rate was changed from 250 mL / min. -1 Adjust to 100 mL·min -1Other conditions remain the same as in Example 1.

[0034] Comparative Example 2: The difference from Example 2 is that, while keeping other conditions unchanged, the distance between the anode and cathode was adjusted from 20 mm to 30 mm, and the other conditions remained the same as in Example 2.

[0035] Comparative Example 3: The difference from Example 3 is that, while keeping other conditions unchanged, the zinc acid ratio was adjusted from 3.4 to 3.0, and the other conditions remained the same as in Example 3.

[0036] Comparative Example 4: The difference from Example 4 is that, while keeping other conditions unchanged, the current density was increased from 600 A·m -2 Adjusted to 300 A·m -2 The remaining conditions are the same as in Example 4.

[0037] The specific process parameters of Embodiments 1-4 and Comparative Examples 1-4 of the present invention are shown in Table 1.

[0038] Table 1. Specific process parameters for Examples 1-4 and Comparative Examples 1-4: .

[0039] As shown in Table 1, all embodiments and comparative examples were constructed based on the same three-dimensional zinc electrodeposition model. The main differences lie in the variations of process parameters such as flow rate, anode-cathode spacing, acid-zinc ratio, and current density. The flow rate range was 100-300 mL / min. -1 The anode-cathode spacing is 15-30 mm, the acid-zinc ratio is 3.0-3.6, and the current density is 300-600 A•m. -2 Ion concentration distribution and deposition behavior under different parameter conditions, such as Figures 3-6 As shown.

[0040] Combination Figures 3-6 The results of the embodiments and comparative examples are analyzed as follows: (1) The effect of flow velocity: comparison Figure 3 As can be seen from Example 1 and Comparative Example 1, under the condition of keeping the anode-cathode spacing, acid-zinc ratio and current density constant, as the flow rate increases from 100 mL / min... -1 Increase to 250 mL·min -1 Zn in electrolyte 2+ The mass transfer capacity was significantly enhanced, and the concentration boundary layer became thinner, indicating that appropriately increasing the flow rate helps improve ion transport conditions, thereby reducing the competitive effect of the hydrogen evolution side reaction on the main reaction. When the flow rate is low, the ion supply is insufficient and the local concentration polarization phenomenon is aggravated, which is not conducive to the stable progress of the deposition process.

[0041] (2) The influence of the distance between the anode and cathode: comparison Figure 4 As shown in Example 2 and Comparative Example 2, when other conditions remain unchanged, reducing the anode-cathode distance from 30 mm to 20 mm shortens the migration path of ions in the electrolyte, makes the concentration gradient distribution more uniform, and reduces the ion transport resistance in the system, which is beneficial to improving the uniformity of the deposition process. When the anode-cathode distance is large, the transport distance of ions in the electrolyte increases, leading to uneven concentration distribution in local areas, which adversely affects the deposition process.

[0042] (3) Effect of acid-zinc ratio: Comparison Figure 5 As can be seen from Example 3 and Comparative Example 3, when the acid-zinc ratio increases from 3.0 to 3.4, the acid-base environment of the system changes, affecting the OH- - The distribution of these factors regulates the competition between the main and side reactions, significantly impacting the morphology and compactness of the sedimentary layer. Furthermore, this process requires a relatively long timescale (10800 s) to fully realize its influence.

[0043] (4) Effect of current density: Comparison Figure 6 As can be seen from Example 4 and Comparative Example 4, when the current density increases from 300 A·m -2 Increased to 600 A·m -2 At higher current densities, the thickness of the zinc electrodeposited layer increases significantly, indicating that increasing the current density enhances the driving force of the deposition reaction. However, excessively high current densities may also exacerbate concentration polarization and hydrogen evolution side reactions. On the other hand, when the current density is too low, the deposition rate is slow, making it difficult to form a relatively dense deposition layer structure. Therefore, increasing the current density within a certain range is beneficial to improving deposition efficiency.

[0044] In summary, the multiphysics coupling simulation and process parameter optimization method for zinc electrodeposition based on transient finite element analysis proposed in this invention can effectively reveal the interaction between ion mass transfer and interfacial reactions by systematically analyzing key process parameters such as flow rate, anode-cathode spacing, acid-zinc ratio, and current density. By rationally controlling the combination of various parameters, the efficiency of Zn electrodeposition can be improved. 2+ Achieving a better balance between supply and side reaction suppression enables stable control and process optimization of the deposition process. This invention utilizes the COMSOL Multiphysics simulation system to numerically simulate the actual process, which not only intuitively reflects the ion distribution and deposition behavior characteristics inside the electrolyte, but also provides a reliable basis for experimental parameter design, reducing experimental trial and error costs. It has significant theoretical and practical value for the optimization of zinc electrodeposition processes and their engineering applications.

[0045] 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 zinc electrodeposition process based on transient finite element analysis, characterized in that, Includes the following steps: Step 1: Construct a three-dimensional transient model of the zinc electrodeposition process in the COMSOL Multiphysics simulation platform. The three-dimensional transient model includes the cathode, anode and electrolyte regions, and sets the structural parameters and operating parameters of the zinc electrodeposition system according to the experimental setup and process conditions. Step 2: Globally define the physical field, boundary conditions, and material properties coupling ion mass transfer and electrode interface reaction during the zinc electrodeposition process, and set Zn 2+ H + and OH - Initial concentration, transport characteristics, and reaction parameters; Step 3: Based on the mass transfer characteristics and interfacial reaction features of the zinc electrodeposition process, the three-dimensional transient model is meshed; Step 4: Solve the three-dimensional transient model using the transient solution method. Set different electrolyte flow rate, anode-cathode distance, acid-zinc ratio and current density process parameters respectively, and calculate the ion concentration field distribution and deposition thickness evolution process in the zinc electrodeposition process under different working conditions. Step 5: Set the corresponding calculation time according to different working conditions. The first time scale is used for calculations based on the flow rate, anode-cathode spacing and current density conditions, and the second time scale is used for calculations based on the acid-zinc ratio condition. The second time scale is larger than the first time scale to characterize the influence of different parameters on the evolution process of the zinc electrodeposition system. Step 6: By post-processing and visualizing the calculation results, obtain the Zn values ​​under different working conditions. 2+ H + and OH - The concentration field distribution and deposition thickness variation patterns were investigated, and the influence of various process parameters on zinc electrodeposition behavior and side reactions was analyzed, thereby obtaining optimized zinc electrodeposition process parameters.

2. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, The specific method for constructing the three-dimensional transient model in step 1 is as follows: Step 11: In the COMSOL Multiphysics simulation system, select the 3D modeling method, the electrochemical physics field module, and the transient analysis method; Step 12: Define the model parameters and model variables for the cathode, anode, and electrolyte regions in the zinc electrodeposition system, and set the operating parameters including electrolyte flow rate, anode-cathode distance, zinc acid ratio, and current density; Step 13: Construct a three-dimensional geometric model of the cathode, anode, and electrolyte regions in the zinc electrodeposition system.

3. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, In step 2, when defining the physical field, the finite element analysis method is used to couple the ion mass transfer process in the electrolyte and the electrode interface reaction process, specifically including the following steps: Step 21: Define the governing equations for ion mass transfer in the zinc electrodeposition system. Based on the mass conservation equation and the diffusion-migration equation, establish the Zn... 2+ H + and OH - A transport model in the electrolyte was developed, and the corresponding initial concentration and boundary conditions were set. Step 22: Define the electrochemical reaction process at the electrode interface, which includes the reduction and deposition reaction of zinc ions and the hydrogen evolution side reaction of hydrogen ions, and establish the corresponding reaction kinetic model. Step 23: Couple the ion mass transfer process with the electrode interface reaction process to construct a multi-physics coupling model of the zinc electrodeposition process, which is used to describe the evolution of the ion concentration field over time and the variation law of deposition behavior.

4. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 3, characterized in that, The model parameters defined in step 21 include: a reaction tank volume of 100 mL, an electrolyte system of zinc sulfate, an acid-zinc ratio of 3.0-3.6, a temperature of 38-46℃, and a flow rate of 100-300 mL / min. -1 The cathode is an aluminum plate located in the center, and the anode consists of two lead-silver alloy electrodes symmetrically distributed on both sides of the cathode. The distance between the anode and cathode is 15-30 mm, and the current density is 300-600 A·m. -2 .

5. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, The criteria for meshing the three-dimensional transient model in step 3 are as follows: In COMSOL Multiphysics simulation calculations, a regional meshing method is adopted. Based on the structural characteristics and physical field changes of the cathode, anode, and electrolyte regions, different mesh sizes are set for different regions. In regions with intense ion mass transfer and interfacial reactions, the mesh is locally refined. In regions far from the electrode interface, a relatively coarse mesh is used. The mesh types include free triangular meshes, free quadrilateral meshes, and free tetrahedral meshes. The electrode interface region is optimized by combining boundary layer meshes. The optimal meshing scheme that meets the calculation accuracy requirements is determined through mesh independence verification.

6. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, In step 4, the ion mass transfer and electrode interface reaction in the zinc electrodeposition process are numerically solved, and the governing equations are as follows: ； In the formula: The divergence of ion flux; Electrolyte flow rate; This represents the ion concentration gradient. For volumetric reaction source terms; ； In the formula: Where is the current density; F is the Faraday constant; The ionic charge number; and These are the reaction terms related to hydrogen ions and hydroxide ions, respectively. For charge source terms; ； In the formula: This refers to the ion concentration. is the ion product constant of water; ； In the formula: This refers to ion flux; The diffusion coefficient is denoted as . For mobility; This is the liquid phase potential; ； In the formula: This refers to the electrolyte current density. ； In the formula: Solid-state conductivity; This is the solid-state potential; ； ； In the formula: This represents the total current density. This is the local reaction current; It is the double-layer current; ； In the formula: The total reaction rate at the interface; The above governing equations were discretized using the finite element method, and the zinc electrodeposition process was numerically calculated using a transient solver to obtain the evolution of the ion concentration field and current distribution over time.

7. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, In step 5, the calculation results of the zinc electrodeposition process are post-processed and analyzed. The deposition behavior is characterized by the evolution of sedimentary layer morphology and the relationship between material changes. The expression is as follows: ； In the formula: Let be the concentration of species j in region d; Let be the rate of generation or consumption of species j in region d caused by the m-th reaction process; ； In the formula: Let be the initial concentration of species j; This represents the initial concentration of species j in region d; Let be the density of species j; Let be the molar mass of species j; This represents the change in the thickness of the deposited layer on the electrode surface. ； In the formula: The normal growth rate of the deposition interface; This represents the generation rate (positive) or consumption rate (negative) of species j in region d, which can be an electrolyte diffusion layer, an electrode surface, or the interior of a porous electrode, and is generated through the m-th reaction step. Indicates the molar mass of species j; This represents the density of species j.

8. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, Step 6, post-processing and visualization analysis, specifically includes the following steps: Step 61: After the simulation calculation is completed, extract the data from the calculation results and output the ion concentration field distribution, deposition thickness and related calculation results as numerical data and image information; Step 62: Visualize the calculation results using the post-processing module. This can be done by adding a 3D plotting group or a 2D plotting group to visualize the Zn graph. 2+ H + and OH - The concentration field distribution and deposition thickness distribution are displayed and expressed. Step 63: Based on the calculation results, perform quantitative analysis on the ion concentration distribution and deposition thickness variation, and calculate the deposition uniformity, thickness variation trend and side reaction intensity under different working conditions; Step 64: By comparing and evaluating the visualization results and quantitative analysis results, analyze the influence of different process parameters on the zinc electrodeposition process, and optimize the electrolyte flow rate, anode-cathode distance, acid-zinc ratio and current density to obtain the optimal zinc electrodeposition process parameters.

9. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, The electrolyte system is an acidic solution system containing zinc ions, and the solution includes Zn. 2+ H + and OH - Ionic components involved in mass transfer and reaction; the cathode is made of conductive metal material, and the anode is made of inert electrode or lead-based alloy material.

10. The method for multiphysics coupling simulation and process parameter optimization of zinc electrodeposition process based on transient finite element analysis according to claim 1, characterized in that, In the three-dimensional transient model, the cathode and anode constitute an electrode system arranged opposite to each other, and the electrolyte region is located between the two electrodes. By adjusting the electrolyte flow rate and the distance between the anode and cathode, the ion transport path and concentration distribution in the electrolyte are controlled, thereby affecting the interfacial reaction process and deposition behavior.

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