Simulation method for flow field distribution and deposition morphology in ultrafast laser-assisted electrochemical deposition

Abstract

The present invention relates to the technical field of electrodeposition, and relates to a simulation method for flow field distribution and deposition morphology in ultrafast laser-assisted electrochemical deposition. The steps of the method comprise: constructing, in multiphysics simulation software, a two-dimensional axisymmetric multiphysics coupled field model for heat transfer, solid and fluid heat transfer, tertiary current distribution, and laminar flow; constructing a geometric model of a deposition cell and a substrate, and setting laser properties, material physical parameters, and electrodeposition properties in the multiphysics simulation software; constructing an ultrafast laser heat transfer model on the basis of a two-temperature equation; setting initial and boundary conditions of the ultrafast laser heat transfer model, and constructing an electrodeposition field; coupling the ultrafast laser heat transfer model with the electrodeposition field to construct an ultrafast laser-assisted electrochemical deposition model; delineating a grid; and performing calculation and analysis. In the present invention, ultrafast laser is incorporated to perform multiphysics coupling of a thermal field, a flow field, an electric field, etc., and a two-temperature equation and tertiary current distribution are incorporated to the model, thereby achieving the accuracy and comprehensiveness of prediction models.

Description

Simulation Methods for Flow Field Distribution and Deposition Morphology in Ultrafast Laser-Assisted Electrochemical Deposition Technical Field

[0001] This invention belongs to the field of electrodeposition technology, specifically relating to a method for simulating the flow field distribution and deposition morphology of ultrafast laser-assisted electrochemical deposition. Background Technology

[0002] Electrodeposition technology plays an indispensable role in modern industry, especially in high-end and extreme manufacturing sectors, such as superhydrophobic surfaces, nanocrystalline coatings, 3D printing, and battery electrodes. However, due to the characteristics and inherent defects of electrodeposition technology, deposited layers often exhibit problems such as porous structure, pinholes, and high surface roughness. To address these challenges, various composite electrodeposition techniques have been proposed, such as ultrasonic-electrodeposition, magnetic field-electrodeposition, hard particle triboelectric electrodeposition, and laser-electrodeposition. These composite processing methods have proven effective in improving electrodeposition quality and the deposition effect of some composite materials. Among them, femtosecond lasers, with their small thermal range and high instantaneous power, utilize the photothermal and cavitation effects of pulsed lasers on the electrodeposition cathode surface to achieve multi-energy field composite processing with electrodeposition. However, since the invention and application of laser-electrochemical composite deposition technology, research on the mechanism of laser-electrochemical composite deposition has been limited. Therefore, finding a suitable method to predict the flow field distribution and deposition morphology during ultrafast laser-assisted electrodeposition is of great significance for clarifying the mechanism of ultrafast laser-assisted electrodeposition technology and for its advancement towards high-precision micro-nano additive manufacturing.

[0003] Existing technologies disclose experimental systems for pulsed laser-electrochemical composite deposition, revealing that lasers can generate a plasma-driven impact effect during electrochemical composite deposition. This pulsed laser impact effect creates a unique micro-area stirring effect, effectively improving the liquid-phase mass transfer environment, increasing the cathode overpotential, significantly refining grains, and reducing porosity within the deposit. However, experimental methods for studying the relationship between the flow field and deposition morphology during laser propagation in the deposition solution have the following limitations: firstly, the flow field changes are complex and difficult to observe experimentally; secondly, the experimental cost is high.

[0004] Existing technologies disclose finite element analysis models for nanosecond laser-electrochemical composite deposition of nickel. These models analyze the mechanisms of laser thermal, cavitation, and optical effects on mass transfer during electrodeposition, electrode reactions, and electrocrystallization, and find that nanosecond laser-electrochemical deposition significantly improves the mechanical properties of the deposited part. However, the lasers used in these models are all nanosecond lasers, and the analysis neglects the influence of the nanosecond laser's thermal effect on the deposition solution and the influence of the flow field on the deposition morphology, thus having certain limitations. Summary of the Invention

[0005] The technical problem to be solved:

[0006] To avoid the shortcomings of existing technologies, this invention provides a method for simulating the flow field distribution and deposition morphology of ultrafast laser-assisted electrochemical deposition. By adding an ultrafast laser to the substrate of the deposited body, multiple physical fields such as thermal field, flow field and electric field are coupled, and a two-temperature equation and a three-dimensional current distribution are introduced into the model to achieve the accuracy and comprehensiveness of the prediction model.

[0007] The technical solution of this invention is: a method for simulating the flow field distribution and deposition morphology of ultrafast laser-assisted electrochemical deposition, the specific steps of which are as follows:

[0008] In multiphysics simulation software, construct two-dimensional axisymmetric heat transfer, solid and fluid heat transfer, three-dimensional current distribution and laminar flow multiphysics coupled field models.

[0009] Construct geometric models of the deposition tank and substrate, and set laser properties, material physical parameters, and electrodeposition properties in multiphysics simulation software;

[0010] In multiphysics simulation software, an ultrafast laser heat transfer model is constructed based on the two-temperature equation;

[0011] Set the initial and boundary conditions for the ultrafast laser heat transfer model and construct the electrodeposition field;

[0012] By coupling the ultrafast laser heat transfer model with the electrodeposition field, an ultrafast laser-assisted electrochemical deposition model is constructed.

[0013] Mesh the ultrafast laser-assisted electrochemical deposition model;

[0014] A computational analysis was performed on the ultrafast laser-assisted electrochemical deposition model.

[0015] A further technical solution of the present invention is as follows: the multiphysics coupling field model assumes that ionization and plasma generation are not considered during ultrafast laser-assisted electrodeposition, the laser energy distribution is a standard Gaussian distribution, and the expression for the heat source term S(x,t) under Gaussian laser pulse irradiation is:

[0016] Where x is the distance from the laser-affected surface, t is the laser-affected time, α is the absorption depth, β = 4ln(2); R is the surface reflectivity to the laser; t p denoted as pulse width; J represents laser energy density.

[0017] A further technical solution of the present invention is: the method for establishing the multiphysics coupled field model is to use multiphysics simulation software to establish a two-dimensional axisymmetric solid heat transfer, solid and fluid heat transfer and three-dimensional current distribution model, select a laminar flow model, and select transient as the research mode.

[0018] A further technical solution of the present invention is: the physical fields used in the simulation calculation of the multiphysics coupled field model are the "solid heat transfer" and "solid and fluid heat transfer" physical fields, and the heat transfer equation in the solid is:

[0019] Where, ρ s C is the density of a solid. ps K represents the specific heat capacity of a solid. s Let be the thermal conductivity of the solid, T be the temperature, u be the velocity vector, q be the heat flux density, t be the time, and Q be the internal heat source.

[0020] The heat transfer equations used in liquids are the same as those used in solids;

[0021] The mass transfer governing equations in the physical field of "three-dimensional current distribution" are as follows:

[0022] Among them, R i J is the total electrolyte flux. i For electrolyte flux caused by diffusion and electromigration, z i U is the number of polar charges. m,j For ion mobility, c is the electrolyte potential. i Where i is the concentration of ions, D i Let be the diffusion coefficient of ion i, where the subscript i represents the ion type, m represents the mobility, l represents the electrolyte, and F represents the Faraday constant.

[0023] The governing equations for the cathode surface are as follows;

[0024] Where η is the overpotential. This is the external potential of the electrode. E is the electrolyte potential. eq For equilibrium potential, i loc,expr Where c is the local current density and c0 is the bulk oxide concentration. c represents the oxide concentration on the electrode surface. R The concentration of the bulk reducing agent. i represents the concentration of reducing agents on the electrode surface. loc i is the reaction current density lim Let F be the limiting diffusion current density, F be the Faraday constant, and i0 be the exchange current density.

[0025] The governing equations for single-phase fluid flow in laminar flow are based on the Navier-Stokes equations, as shown below:

[0026] The above formulas represent the conservation of mass, momentum, and energy, respectively; where f is the volume force, which is the liquid gravity in the simulation, I is the moment of inertia of the liquid, τ is the viscous stress tensor of the liquid, S is the strain rate tensor, ρ is the fluid density, p is the pressure, and C... p Let Q be the specific heat capacity and Q be the internal heat source.

[0027] A further technical solution of the present invention is as follows: the parameters that need to be set in the multiphysics simulation software are: pulse width, surface reflectivity to laser, laser power, beam radius, electronic lattice coupling coefficient, electronic heat capacity, electronic thermal conductivity, lattice heat capacity and lattice thermal conductivity in laser properties; solid density, solid specific heat capacity and solid thermal conductivity in solid properties; solution density, solution specific heat capacity and solution thermal conductivity in liquid properties; and anolyte potential, cathode potential, transfer coefficient, anion and cation charge number, anion and cation diffusion coefficient and initial electrolyte concentration in electrodeposition properties.

[0028] A further technical solution of the present invention is: the method for constructing an ultrafast laser heat transfer model based on the dual-temperature equation is as follows:

[0029] In multiphysics simulation software, create a variable heat source term S(x,t);

[0030] In multiphysics simulation software, when adding a physics field, select "Solid Heat Transfer," rename it to "Electron Heat Transfer," and set the initial ambient temperature. Then, set the heat transfer mode to follow a two-temperature equation, resulting in a one-dimensional two-step heat conduction model with two temperatures.

[0031] Among them, C e For electron heat capacity; C l k is the lattice heat capacity. e T is the electronic thermal conductivity; e T represents the electron temperature. l Where is the lattice temperature; G is the electron-lattice coupling coefficient;

[0032] Then, the laser heat source term is selected as the variable heat source term S(x,t)-G(T). e -T l );

[0033] In the multiphysics simulation software, when adding a physics field, select "Solid Heat Transfer," rename it to "Lattice Heat Transfer," and set the initial ambient temperature. The heat transfer mode follows the two-temperature equation, and the laser heat source term is selected as G(T). e -T l This yields the ultrafast laser heat transfer model.

[0034] A further technical solution of the present invention is: the method for setting the initial and boundary conditions of the ultrafast laser heat transfer model and constructing the electrodeposition field is as follows:

[0035] In the multiphysics simulation software, select "Solid and Fluid Heat Transfer," set the solid as the substrate, and set the thermal conductivity, density, and isobaric heat capacity according to the substrate material. The liquid is the electrolyte, and its thermal conductivity and isobaric heat capacity environment are set according to the electrolyte properties. Set the initial temperature, where the heat source is from lattice heat transfer, i.e., the heat source term is G(T). e -T l );

[0036] In the multiphysics simulation software, select "Triple Current Distribution, Support Electrolyte", set the initial ambient temperature and initial electrolyte concentration; define the charge number of anions and cations in "Material Charge", and define the diffusion coefficient of anions and cations in "Electrolyte"; create the "Electrode Surface" module, rename it to Cathode Surface, and then set the "Electrode Reaction" to obtain the electrodeposition field;

[0037] The number of electrons participating in the cathode and the cathode transfer coefficient are set according to the properties of the simulated material.

[0038] The anode surface is set in the same way as above;

[0039] In the multiphysics simulation software, select "Laminar Flow" and set the boundary conditions in the flow field. The fluid in the flow field is subject to gravity. Select "Laminar Flow" and set the gravitational acceleration in the y-direction to -g_const in the "Gravity" option of "Laminar Flow". Also, select "Laminar Flow" for the fluid flow at the coupling interface of "Non-Isothermal Flow" in the multiphysics field, and select "Solid and Fluid Heat Transfer" for heat transfer.

[0040] A further technical solution of the present invention is as follows: the method for constructing the ultrafast laser-assisted electrochemical deposition model is to use the reference exchange current density and the reference equilibrium potential of the electrode reaction as functions of temperature. These two data are derived from the results of Tafel curve tests of materials at different temperatures in experiments. They are then taken into multiphysics simulation software as interpolation functions and applied to the reference exchange current density and the reference equilibrium potential of the electrode reaction module, thereby completing the coupling between the ultrafast laser heat transfer model and the electrodeposition field and constructing the ultrafast laser-assisted electrochemical deposition model.

[0041] A further technical solution of the present invention is: the geometric model of the deposition tank and the substrate is a two-dimensional axisymmetric model, and the interface between the substrate and the deposition liquid and the axis of symmetry are divided into a mesh refinement layer, and the remaining part is a mesh coarsening layer.

[0042] A further technical solution of the present invention is as follows: the calculation and analysis method is to select "transient" as the step type in the "study" module of the multiphysics simulation software, set the calculation step size to 0.1ps, and the calculation time to 40ps; select the physical field and variables to be studied for coupled solution, and analyze and process the temperature field, flow field and sediment morphology after the calculation is completed. Beneficial effects

[0043] The beneficial effects of this invention are as follows: Based on the dual-temperature equation and the Butler–Volmer equation, this invention derives and simulates the ultrafast laser heat transfer and electrodeposition processes, respectively. This allows for a more scientific and accurate simulation of the multi-physics coupling process of ultrafast laser-assisted electrodeposition, and it also solves the problem of neglecting the influence of laser thermal effects on deposition quality in existing studies. The ultrafast laser used in this invention is easier to fabricate in micro- and nano-scales than nanosecond lasers, and its short pulse duration does not cause thermal effects on surrounding materials.

[0044] This invention utilizes the COMSOL finite element multiphysics simulation software to establish a physical model for ultrafast laser-assisted electrodeposition, thereby realizing the simulation and prediction of the flow field distribution and deposition morphology in the electrolyte. This solves the problem of difficulty in observing the physical process of ultrafast laser-assisted electrodeposition during the experiment, and avoids factors that affect the deposition quality during the experiment by simulating and predicting the experiment, thus saving experimental costs. Attached Figure Description

[0045] Figure 1 is a flowchart of the flow field distribution and deposition morphology prediction method based on COMSOL for ultrafast laser-assisted electrodeposition according to an embodiment of the present invention;

[0046] Figure 2 is a schematic diagram of the geometrical physical model and mesh generation of the flow field distribution and deposition morphology prediction method based on COMSOL for ultrafast laser-assisted electrodeposition according to an embodiment of the present invention.

[0047] Figure 3 is a schematic diagram of the flow field distribution example of ultrafast laser-assisted electrodeposition based on COMSOL in an embodiment of the present invention;

[0048] Figure 4 is an exemplary schematic diagram of the deposition morphology of ultrafast laser-assisted electrodeposition based on COMSOL according to an embodiment of the present invention. Detailed Implementation

[0049] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0050] To address the problems existing in current technologies, this invention provides a method for predicting the flow field distribution and deposition morphology of ultrafast laser-assisted electrodeposition (ELED) based on COMSOL. A physical model of ELED is established using COMSOL finite element simulation software, and multi-physics coupling simulation is performed to model the flow field distribution and deposition morphology distribution in the electrolyte. This solves the problem that the flow field distribution and deposition morphology of the electrolyte during ELED are difficult to observe experimentally. Based on COMSOL software, this invention incorporates an ultrafast laser at the substrate of the deposited material, coupling multiple physical fields such as thermal, flow, and electric fields. The two-temperature equation and the Butler–Volmer equation are introduced into the model to achieve accuracy and comprehensiveness in the prediction model. This solves the problem that existing studies have not considered the influence of the laser's thermal effect on the deposition solution, and consequently, its impact on the deposition morphology.

[0051] The above technical solution will be further explained below with reference to the accompanying drawings:

[0052] Referring to Figure 1, an exemplary flowchart of a method for calculating the flow field distribution and deposition morphology of ultrafast laser-assisted electrodeposition based on COMSOL is provided. This embodiment includes the following steps for calculating the flow field distribution and deposition morphology of ultrafast laser-assisted electrodeposition:

[0053] S1: Construct a two-dimensional axisymmetric heat transfer, solid and fluid heat transfer, three-dimensional current distribution, and laminar flow multiphysics coupled field model in the multiphysics simulation software COMSOL.

[0054] S2: Construct geometric models of the deposition tank and substrate, and set laser properties, material physical parameters, and electrodeposition properties in multiphysics simulation software;

[0055] S3: In multiphysics simulation software, an ultrafast laser heat transfer model is constructed based on the dual-temperature equation;

[0056] S4: Set the initial and boundary conditions for the ultrafast laser heat transfer model and construct the electrodeposition field;

[0057] S5: Couple the ultrafast laser heat transfer model with the electrodeposition field to construct an ultrafast laser-assisted electrochemical deposition model;

[0058] S6: Mesh the ultrafast laser-assisted electrochemical deposition model;

[0059] S7: Calculation and analysis of the ultrafast laser-assisted electrochemical deposition model.

[0060] In this embodiment, S1 includes: model assumptions and model building;

[0061] The model assumes that ionization and plasma generation are not considered during ultrafast laser-assisted electrodeposition, the laser energy distribution follows a standard Gaussian distribution, and the heat source term S(x,t) under Gaussian laser pulse irradiation is expressed as follows:

[0062] Where: x is the distance from the laser-acting surface, t is the laser-acting time, α is the absorption depth, β=4ln(2); R is the surface reflectivity to the laser; t p denoted as pulse width; J represents laser energy density.

[0063] It should be noted that, in order to improve computational efficiency, the model was simplified before it was built, and a two-dimensional axisymmetric multiphysics model was established.

[0064] The model was established using COMSOL software to create a two-dimensional axisymmetric solid heat transfer, solid-fluid heat transfer, and tertiary current distribution model. A laminar flow model was selected, and the study mode was chosen as transient. The equations involved in the model are shown below:

[0065] The simulation calculations use the "solid heat transfer" and "solid and fluid heat transfer" physics fields. The heat transfer equation in the solid is:

[0066] Where, ρ s C is the density of a solid. ps K represents the specific heat capacity of a solid. s Let be the thermal conductivity of the solid, T be the temperature, u be the velocity vector, q be the heat flux density, t be the time, and Q be the internal heat source.

[0067] It should be noted that the velocity vector u in the heat transfer equation of a solid is zero.

[0068] The heat transfer equation in liquids is consistent with that in solids.

[0069] The mass transfer governing equations in the physical field of the "tertiary current distribution" are as follows:

[0070] Among them, R i J is the total electrolyte flux. i For electrolyte flux caused by diffusion and electromigration, z i U is the number of polar charges. m,j For ion mobility, c is the electrolyte potential. i Where i is the concentration of ions, D i Let be the diffusion coefficient of ion i, where the subscript i represents the ion type, m represents the mobility, l represents the electrolyte, and F represents the Faraday constant.

[0071] The governing equations for the cathode surface are as follows;

[0072] Where η is the overpotential. This is the external potential of the electrode. E is the electrolyte potential. eq For equilibrium potential, i loc,expr Where c is the local current density and c0 is the bulk oxide concentration. c represents the oxide concentration on the electrode surface. R The concentration of the bulk reducing agent. i represents the concentration of reducing agents on the electrode surface. loc i is the reaction current density lim Let F be the limiting diffusion current density, F be the Faraday constant, and i0 be the exchange current density.

[0073] The governing equations for single-phase fluid flow in laminar flow are based on the Navier-Stokes equations, as shown below:

[0074] The above formulas represent the conservation of mass, momentum, and energy, respectively; where f is the volume force, which is the liquid gravity in the simulation, I is the moment of inertia of the liquid, τ is the viscous stress tensor of the liquid, S is the strain rate tensor, ρ is the fluid density, p is the pressure, and C... p Let Q be the specific heat capacity and Q be the internal heat source.

[0075] It should be noted that after laser heating, the temperature in the laser-irradiated area rises rapidly, causing a decrease in the density and viscosity of the solution, thus initiating thermal convection. Heat transfer gradually raises the surrounding temperature, expanding the range of thermal convection and thus stirring the electrolyte, affecting the electrodeposition effect. Because laser-assisted electrodeposition involves non-equilibrium physical processes that influence heat transfer and fluid flow, it is necessary to solve the governing equations for energy conservation, momentum conservation, and mass conservation to predict the temperature field distribution, fluid flow, and deposition morphology during laser-assisted electrodeposition.

[0076] In this embodiment, S2 includes: establishing a two-dimensional axisymmetric model with a deposition tank size of 5µm × 5µm and a substrate size of 1µm × 5µm; dividing the area between the substrate and the deposition liquid and the axis of symmetry as a mesh refinement layer, and the remaining area as a mesh coarsening layer. In the global definition of the COMSOL simulation software, the following properties are set: pulse width, surface reflectivity to the laser, laser power, beam radius, electronic lattice coupling coefficient, electronic heat capacity, electronic thermal conductivity, lattice heat capacity, and lattice thermal conductivity; solid properties are set: solid density, solid specific heat capacity, and solid thermal conductivity; liquid properties are set: solution density, solution specific heat capacity, and solution thermal conductivity; and electrodeposition properties are set: anode potential, cathode potential, transfer coefficient, cation and anion charge number, cation and anion diffusion coefficient, and initial electrolyte concentration.

[0077] It should be noted that due to the multi-physics coupling and deposition morphology involved at the interface between the substrate and the deposition liquid, mesh refinement is necessary to improve simulation accuracy and computational efficiency. Ultrafast laser heat transfer follows a two-temperature equation, therefore, parameters such as electronic lattice coupling coefficient, electronic heat capacity, electronic thermal conductivity, lattice heat capacity, and lattice thermal conductivity need to be considered. The formula for calculating electronic thermal conductivity is shown below;

[0078] in, And η is a material-related constant, T F Fermi temperature, T, representing the material e For electron temperature, T l For lattice temperature, μ e =T e / T F ,μ l =T l / T F .

[0079] In this embodiment, step S3 includes the following steps:

[0080] S3.1: In the COMSOL simulation software, select "Define" to create the variable heat source term S(x,t). The expression for S(x,t) under Gaussian laser pulse irradiation is:

[0081] Where x is the distance from the laser-affected surface, t is the laser-affected time, α is the absorption depth, β = 4ln(2); R is the surface reflectivity to the laser; t p denoted as pulse width; J represents laser energy density.

[0082] S3.2: In the COMSOL simulation software, add a physics field, select "Solid Heat Transfer," and rename it to "Electron Heat Transfer." Set the initial ambient temperature to 298.15K; and set the heat transfer method to follow a two-temperature equation. The following is a one-dimensional two-step heat conduction model with two temperatures:

[0083] Among them, C e For electron heat capacity; C l k is the lattice heat capacity. e T is the electronic thermal conductivity; e T represents the electron temperature. l is the lattice temperature; G is the electron-lattice coupling coefficient.

[0084] Then, the laser heat source term is selected as the variable heat source term S(x,t)-G(T). e -T l );

[0085] S3.3: In the COMSOL simulation software, add a physics field and select "Solid Heat Transfer," rename it to "Lattice Heat Transfer," and set the initial ambient temperature to 298.15K; the heat transfer mode follows a two-temperature equation, and the laser heat source term is selected as G(T). e -T l This yields the ultrafast laser heat transfer model.

[0086] In this embodiment, step S4 includes the following steps:

[0087] This implementation involves multi-physics coupling of thermal, electric, and flow fields, requiring the setting of corresponding parameters and initial conditions.

[0088] S4.1: In the COMSOL simulation software, select "Solid and Fluid Heat Transfer". Set the solid as the substrate and configure the thermal conductivity, density, and isobaric heat capacity according to the substrate material. Set the liquid as the electrolyte and configure the thermal conductivity and isobaric heat capacity environment according to the electrolyte properties. The initial temperature is 298.15K, and the heat source is lattice heat transfer; therefore, set the heat source term to G(T). e -T l This yields the ultrafast laser heat transfer model.

[0089] S4.2: In the COMSOL simulation software, select "Triple Current Distribution, Support Electrolyte", set the initial ambient temperature to 298.15K and the initial electrolyte concentration; then define the charge number of anions and cations in "Material Charge" and the diffusion coefficient of anions and cations in "Electrolyte". Create an "Electrode Surface" module, rename it to "Cathode Surface", and then set the "Electrode Reaction" to obtain the electrodeposition field; the governing equation for the cathode surface is as follows;

[0090] in, This is the external potential of the electrode. Here, c is the electrolyte potential, and c0 is the bulk oxide concentration. c represents the oxide concentration on the electrode surface. R The concentration of the bulk reducing agent. i represents the concentration of reducing agents on the electrode surface. loc i is the reaction current density lim This represents the limiting diffusion current density.

[0091] Furthermore, the temperature in the governing equation for the cathode surface is the heat transfer result from the "solid and fluid heat transfer" module.

[0092] Then, the number of electrons participating in the cathode and the cathode transfer coefficient are set according to the properties of the simulated material.

[0093] The anode surface is set in the same way as above.

[0094] S4.3: In the COMSOL simulation software, select "Laminar Flow" and set the boundary conditions in the flow field. The fluid in the flow field is subject to gravity. In the "Gravity" option of "Laminar Flow", set the gravitational acceleration in the y-direction to -g_const. Also, for the fluid flow at the coupling interface of "non-isothermal flow" in the multiphysics field, select "Laminar Flow" and for heat transfer, select "Solid and Fluid Heat Transfer".

[0095] In this embodiment, S5 is: the reference exchange current density and the reference equilibrium potential of the electrode reaction are both functions of temperature. These two data are derived from the results of Tafel curve tests of materials at different temperatures in the experiment. They are taken into COMSOL and used as interpolation functions to apply to the reference exchange current density and reference equilibrium potential of the electrode reaction module.

[0096] In this embodiment, S6 is: selecting a free triangular mesh, as shown in Figure 2.

[0097] Because the interface between the substrate and the deposition fluid involves multi-physics coupling and deposition morphology, mesh refinement is necessary to improve simulation accuracy and computational efficiency. Furthermore, since the model used is a two-dimensional axisymmetric model, mesh refinement was also applied to the axis of symmetry region.

[0098] To improve computational efficiency, the mesh cell size is selected to be finer near the laser heat source area, as shown in the upper region of Figure 2; the mesh size is selected to be coarser away from the laser heat source area, as shown in the lower region of Figure 2.

[0099] It should be noted that if a fine mesh is used for all areas, the computation time will be very long; however, fine meshing is only performed in areas where the physical field is complex (the finer the mesh in these areas, the higher the simulation accuracy), thereby improving the simulation accuracy and computational efficiency.

[0100] In this embodiment, S7 is: in the COMSOL simulation software, select "transient" as the step type in the "study" module, set the calculation step size to 0.1ps, and the calculation time to 40ps; select the physical field and variables to be studied for coupled solution, and analyze and process the temperature field, flow field, and sediment morphology after the calculation is completed.

[0101] The calculation results are shown in Figures 3 and 4, which realize the prediction of the flow field distribution and deposition morphology in ultrafast laser-assisted electrodeposition.

[0102] In summary, this example utilizes COMSOL finite element simulation software to establish a physical model of ultrafast laser-assisted electrodeposition, and performs multi-physics coupling simulation of the flow field distribution and deposition morphology distribution in the electrolyte. This solves the problem that the flow field distribution and deposition morphology of the electrolyte are difficult to observe experimentally during ultrafast laser-assisted electrodeposition, and also addresses the issue that existing studies have not considered the influence of the thermal effect of the laser on the deposition liquid, and consequently, on the deposition morphology.

[0103] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for simulation of flow field distribution and deposition morphology in ultrafast laser-assisted electrochemical deposition, characterized in that The specific steps are as follows: A two-dimensional axisymmetric heat transfer, solid and fluid heat transfer, third-order current distribution and laminar flow multi-physics coupling field model is constructed in a multi-physics simulation software; A geometric model of the deposition tank and the substrate is constructed, and laser properties, physical parameters of the material and electro-deposition properties are set in the multi-physics simulation software; An ultrafast laser heat transfer model is constructed based on a two-temperature equation in the multi-physics simulation software; Initial and boundary conditions of the ultrafast laser heat transfer model are set, and an electro-deposition field is constructed; The ultrafast laser heat transfer model is coupled with the electro-deposition field to construct an ultrafast laser-assisted electrochemical deposition model; The ultrafast laser-assisted electrochemical deposition model is meshed; The ultrafast laser-assisted electrochemical deposition model is calculated and analyzed.

2. The method of claim 1, wherein the method is characterized by: The model assumption of the multi-physical field coupling field model is that ionization and plasma generation are not considered in the process of ultrafast laser-assisted electrodeposition, the laser energy distribution is a standard Gaussian distribution, and the expression of the heat source term S(x, t) under Gaussian laser pulse irradiation is: where x is the distance from the laser-affected surface, t is the laser-affected time, a is the absorption depth, and β = 4ln(2); R is the reflectivity of the surface to the laser; t p is the pulse width; and J is the laser fluence.

3. The method of claim 2, wherein the method is characterized by: The method for establishing the multi-physics coupling field model is that a two-dimensional axisymmetric solid heat transfer, solid and fluid heat transfer and third-order current distribution model is established by using a multi-physics simulation software, a laminar flow model is selected, and a transient state is selected as the research mode.

4. The method of claim 3, wherein the method is characterized by: The physical field used in the simulation calculation of the multi-physical field coupling field model is "solid heat transfer" and "solid and fluid heat transfer" physical field, and the heat transfer equation in the solid is: where p s is the solid density, C ps is the specific heat capacity of the solid, K s is the thermal conductivity of the solid, T is the temperature, u is the velocity vector, q is the heat flux density, t is the time, and Q represents internal heat sources; The heat transfer equation used in the liquid is consistent with that in the solid; The mass transfer control equations in the "three times current distribution" physical field are as follows: where R i is the total flux of electrolyte, J i is the flux of electrolyte due to diffusion and electromigration, z i is the number of charges with polarity, u m,j is the ionic mobility, E is the electrolyte potential, c i D is the ion concentration, i i D is the diffusion coefficient of ion i, subscript i is the ion species, m is the mobility, l is the electrolyte, and F is the Faraday constant; where the governing equations for the cathode surface are given by wherein η is the overpotential, for the electrode external potential, E is the electrolyte potential eq E is the equilibrium potential loc,expr i is the local current density, c0is the bulk oxide concentration, for the electrode surface oxide concentration, c R for the bulk reduced oxide concentration, c for the electrode surface reduction product concentration, i loc for the reaction current density, i lim for the limiting diffusion current density, F is the Faraday constant, and i0is the exchange current density. The governing equations for single-phase fluid flow in laminar flow are based on the Navier-Stokes equations, which are given as follows: The above formulas are mass conservation, momentum conservation, and energy conservation, respectively; where f is the body force, which in the simulation is the liquid gravity, I is the moment of inertia of the liquid, τ is the viscous stress tensor of the liquid, S is the strain rate tensor, p is the fluid density, p is the pressure, C p is the specific heat capacity, and Q is the internal heat source.

5. The method of claim 4, wherein the method further comprises: The parameters that need to be set in the multi-physics simulation software include pulse width in laser properties, surface reflectivity to laser, laser power, beam radius, electron lattice coupling coefficient, electron heat capacity, electron thermal conductivity, lattice heat capacity and lattice thermal conductivity; solid density, solid specific heat capacity and solid thermal conductivity in solid properties; solution density, solution specific heat capacity and solution thermal conductivity in liquid properties; anode potential, cathode potential, transfer coefficient, cation and anion charge number, cation and anion diffusion coefficient and initial concentration of electrolyte in electro-deposition properties.

6. The method of claim 5, wherein the method further comprises: The method for constructing the ultrafast laser heat transfer model based on the two-temperature equation is that: A variable heat source term S(x, t) is created in the multi-physics simulation software; In the multi-physics simulation software, when adding a physical field, "solid heat transfer" is selected to create an electron heat transfer, and the environment initial temperature is set; And set the heat transfer mode in accordance with the double temperature equation, get one-dimensional two-step heat conduction model of double temperature: where C e is the electronic heat capacity; C l is the lattice heat capacity; k e is the electronic thermal conductivity; T e is the electronic temperature; T l is the lattice temperature; G is the electron-lattice coupling coefficient; Then the laser heat source term selects the variable heat source term S(x, t) - G(T e -T l ); In the multi-physical field simulation software, when adding the physical field, select to create "solid heat transfer", rename it as lattice heat transfer, and set the initial temperature of the environment; The heat transfer form is subject to the two-temperature equation, and the laser heat source term selects G(T e -T l ), that is, the ultrafast laser heat transfer model is obtained.

7. The method of claim 6, wherein the method further comprises: The method for setting the initial and boundary conditions of the ultrafast laser heat transfer model and constructing the electro-deposition field is that: In the multi-physics simulation software, "solid and fluid heat transfer" is selected, the solid is set as the substrate, the thermal conductivity, density and isobaric heat capacity of the substrate are set according to the material of the substrate, the liquid is set as the electrolyte, and the thermal conductivity and constant-pressure heat capacity environment are set according to the properties of the electrolyte; Set the initial temperature, where the heat source comes from the lattice heat transfer, i.e. the heat source term is G(T e -T l ); In the multi-physics simulation software, "third-order current distribution, supporting electrolyte" is selected, the environment initial temperature and the initial concentration of the electrolyte are set; the cation and anion charge number is defined at "material charge", and the cation and anion diffusion coefficient is defined at "electrolyte"; an "electrode surface" module is created, which is renamed as cathode surface, and then "electrode reaction" is set, that is, the electro-deposition field is obtained; The cathode electron number and cathode transfer coefficient are set according to the properties of the simulated material; The anode surface is set in the same way; In the multi-physics simulation software, "laminar flow" is selected, the boundary conditions in the flow field are set, and the fluid in the flow field is subjected to the action of gravity; in the "laminar flow" of the "laminar flow", the y-direction gravity acceleration is set as -g_const; and in the multi-physics, the coupling interface of "non-isothermal flow" is selected as "laminar flow", and the heat transfer is selected as "solid and fluid heat transfer".

8. The method of claim 7, wherein the method further comprises: The method for constructing the ultrafast laser-assisted electrochemical deposition model is that the reference exchange current density and the reference equilibrium potential of the electrode reaction are both taken as functions of temperature, the two data are derived from the results of the Tafel curve test of the material at different temperatures in the experiment, are taken to the multi-physical field simulation software as an interpolation function, and are applied to the reference exchange current density and the reference equilibrium potential of the electrode reaction module, that is, the coupling of the ultrafast laser heat transfer model and the electrodeposition field is completed, and the ultrafast laser-assisted electrochemical deposition model is constructed.

9. The method of claim 8, wherein the method further comprises: The geometric model of the deposition tank and the substrate is a two-dimensional axisymmetric model, the interface between the substrate and the deposition liquid and the symmetric axis are divided into a grid refinement layer, and the remaining part is a grid coarsening layer.

10. The method of claim 9, wherein the method is characterized by: The method for calculation and analysis is that in the multi-physical field simulation software, the step type of the "study" module is selected as "transient", the calculation step is set as 0.1 ps, the calculation time is set as 40 ps, the physical field and the variable that need to be studied are selected for coupled solution, and after the calculation is completed, the temperature field, the flow field and the deposition morphology are analyzed and processed.

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