A finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field.

Abstract

This invention relates to a finite element method for simulating the electrocatalytic oxygen evolution reaction (OER) promoted by a conical electrode under a uniform magnetic field. The method includes: establishing the morphology of the conical electrode based on a finite element model; incorporating the physicochemical properties of the material; setting electromagnetic, fluid, and electrochemical reaction parameters; coupling the fluid and electrochemical fields; setting the reaction time and step size; and obtaining the concentration, velocity, and force field distributions after simulation, thereby achieving a finite element simulation of the electrochemical process of the OER. Compared with existing technologies, this invention achieves multi-physics finite element simulation with four coupled physical fields and demonstrates the response of the ferromagnetic conical structure to the magnetic field. Furthermore, by simulating the electrocatalytic process under the action of a magnetic field, the specific process of magnetic field-promoted electrocatalysis can be understood simply and clearly.

Description

Technical Field

[0001] This invention relates to the field of electrocatalysis simulation technology, and in particular to a finite element method for simulating the promotion of the electrocatalytic oxygen evolution reaction by a conical electrode under a uniform magnetic field. Background Technology

[0002] The electrocatalytic oxygen evolution reaction (OER) is a reaction that occurs on the anode side of an electrolyzer for hydrogen production, and it is an indispensable part of the development of hydrogen energy. During the electrochemical reaction of OER, excessive current density rapidly consumes reactants near the electrode, while the mass transfer capacity itself cannot replenish the reactants in time, thus creating significant concentration polarization and greatly reducing electrocatalytic efficiency. In the electrochemical process, the migration of charged ions can form an ion flow; therefore, a magnetic field can be utilized to promote fluid movement, thereby replenishing reactants in a timely manner, reducing concentration polarization, and improving reaction efficiency. Tip structures are sensitive to external fields, exhibiting a tip effect in response to electric fields, with a significant enhancement of the electric field at the tip. However, their response to magnetic fields remains poorly studied.

[0003] The finite element method (FEM) is an effective multiphysics simulation method. Currently, the FEM has been well applied in tip electric field enhancement and magnetic field-assisted electrochemical deposition processes. However, research on the response of ferromagnetic tips to magnetic fields and the influence of magnetic fields on electrocatalysis remains largely unexplored, requiring more detailed theoretical simulations. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field. By simultaneously solving the Maxwell equation, the Navier-Stokes equation, Fick's second law, and the Butler-Volmer equation, a multi-physics finite element simulation of four coupled physical fields is achieved, demonstrating the response of the ferromagnetic conical structure to the magnetic field.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] This invention provides a finite element method for simulating the electrocatalytic oxygen evolution reaction (OER) promoted by a conical electrode under a uniform magnetic field. The method comprises: establishing the morphology of the conical electrode based on a finite element model; importing the physicochemical properties of the material; setting electromagnetic field, fluid field, and electrochemical reaction parameters; coupling the fluid field and the electrochemical field; setting the reaction time and step size; and obtaining the concentration field distribution, velocity field distribution, and force field distribution obtained after simulation, thereby realizing the finite element simulation of the electrochemical process of the OER.

[0007] Furthermore, the cone-shaped electrode morphology is a two-dimensional symmetric rotation model, including a symmetry axis, a cone-shaped anode and cathode with a cone height of 1 μm obtained by passing through the symmetry axis, and a cylindrical electrochemical cell with a height of 30 μm.

[0008] Furthermore, the radius of the cone base of the cone-shaped electrode can be adjusted by changing the size of the apex angle and adjusting the ratio of the top arc radius D to the bottom radius d, thereby achieving control over the cone electrode morphology.

[0009] Furthermore, the physicochemical properties of the material include the electrolyte conductivity σ. l Electrode conductivity σs, magnetic permeability μ, relative permittivity ε, BH characteristics of the electrocatalyst f(H), magnetic susceptibility of each component in the electrolyte χH2O, χK + χOH - Initial concentrations C of each electrolyte component OH -、C K+ Electrolyte viscosity μ and density ρ.

[0010] Furthermore, the electromagnetic field parameters include the applied magnetic field H, the positive electrode potential V0, and the negative electrode potential V1, and the Maxwell equation is solved to obtain the response of the ferromagnetic conical electrode to the electromagnetic field.

[0011] Furthermore, the Maxwell equation is:

[0012]

[0013] Where J is the current density; E is the electric field; B is the magnetic flux density; V is the electric potential; and M is the magnetization.

[0014] Furthermore, the fluid field parameters include the initial velocity V0 and the Kelvin force. Lorentz force F L The electrochemical reaction parameters include reaction temperature T and ion diffusion coefficient D. OH - D K + Charge Z OH - Z K + Anode charge transfer coefficient α a Cathode charge transfer coefficient α C Equilibrium potential E eq Initial exchange current density i 00 With the exchange current density coefficient γ.

[0015] Furthermore, the fluid field is coupled with the electrochemical field, and the Navier–Stokes equation, Fick's second law, and Butler-Volmer equation are solved based on the electromagnetic field coupling to obtain physicochemical data at various points in the fluid. The Navier–Stokes equation, Fick's second law, and Butler-Volmer equation are as follows:

[0016]

[0017] Among them, F L For Lorentz force, F L = j × B, where j is the current density generated by the ion flow and B is the magnetic induction intensity; For Kelvin, χ sol μ0 is the overall magnetic susceptibility of the electrolyte, and μ0 is the magnetic susceptibility of vacuum; u m,i The mobility of each component is positively correlated with the diffusion coefficient Di of each component; i0 is the exchange current density; α a α c η is the anode charge transfer coefficient, F is the cathode charge transfer coefficient, and η is the overpotential. F is the Faraday constant.

[0018] Furthermore, the formula for calculating the overall magnetic susceptibility of the electrolyte is as follows:

[0019]

[0020] Where ci represents the concentration of each component; denoted as the molar magnetic susceptibility of each component; The magnetic susceptibility of water;

[0021] The mobility u of each component m,i The calculation formula is:

[0022]

[0023] Among them, D i R is the diffusion coefficient of each component; T is the ideal gas constant; and T is the reaction temperature.

[0024] i0 is the exchange current density, calculated using the following formula:

[0025] i0 = i 00 (c s / c0) γ

[0026] Among them, c s With c o These represent the electrode surface concentration and the bulk concentration, respectively. 00 Let γ be the initial exchange current density, and γ be the exchange current density coefficient.

[0027] Furthermore, the anode charge transfer coefficient and the cathode charge transfer coefficient satisfy α a +α c =4;

[0028] Overpotential satisfies η = φ e -φ-φ eq ,

[0029] Where, φ e φ is the electrode potential, and φ is the solution potential. eq To balance the electrode potential.

[0030] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0031] This invention achieves multi-physics finite element simulation of four coupled physical fields by simultaneously solving the Maxwell equation, Navier-Stokes equation, Fick's second law, and Butler-Volmer equation, demonstrating the response of the ferromagnetic cone structure to a magnetic field. Furthermore, by simulating the electrocatalytic process under the influence of a magnetic field, the specific process of magnetic field-driven electrocatalysis can be clearly understood, thus providing hydrogen energy industry professionals with a simple tool to guide the morphology design of electrocatalytic materials. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the finite element modeling structure of the cone-shaped electrode in Example 1;

[0033] Figure 2 This is a schematic diagram of a finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field.

[0034] Figure 1 Explanation of the markings in the text:

[0035] 1-Axis of symmetry, 2-Anode, 3-Cathode. Detailed Implementation

[0036] The following examples illustrate specific implementations of the present invention. These examples are carried out based on the solution described in the present invention, and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following examples.

[0037] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Any structural / module names, control modes, algorithms, processes, or composition ratios not explicitly stated in this technical solution are considered common technical features disclosed in the prior art.

[0038] Example 1

[0039] This embodiment provides a finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field, such as... Figure 2 As shown, it includes the following steps:

[0040] S1: Based on the finite element model, establish the morphology of the cone-shaped electrode. For example... Figure 1 As shown, the cone-shaped electrode morphology is a two-dimensional symmetric rotational model, including a symmetry axis 1, a cone-shaped anode 2 with a cone height of 1 μm obtained by passing through the symmetry axis, a cathode 3, and a cylindrical electrochemical cell with a height of 30 μm. Figure 1 In the model, z, r, and θ represent the axial, radial, and circumferential directions, respectively. The radius of the cone base of the conical electrode morphology is adjusted by changing the size of the apex angle and adjusting the ratio of the top arc radius D to the bottom radius d, thereby controlling the cone electrode morphology.

[0041] S2: Physicochemical properties of the imported material, including electrolyte conductivity σ l Electrode conductivity σs, magnetic permeability μ, relative permittivity ε, BH characteristics of the electrocatalyst f(H), magnetic susceptibility of each component in the electrolyte χH2O, χK + χOH - Initial concentrations C of each electrolyte component OH -、C K+ Electrolyte viscosity μ and density ρ.

[0042] S3: Set the electromagnetic field parameters, including the applied magnetic field H, the positive electrode potential V0, and the negative electrode potential V1, and solve Maxwell's equations to obtain the response of the ferromagnetic conical electrode to the electromagnetic field. The Maxwell's equations are:

[0043]

[0044] Where J is the current density; E is the electric field; B is the magnetic flux density; V is the electric potential; and M is the magnetization.

[0045] S4: Set the fluid field and electrochemical reaction parameters to couple the fluid field with the electrochemical field. The fluid field parameters include the initial velocity V0 and Kelvin force. Lorentz force F L The electrochemical reaction parameters include reaction temperature T and ion diffusion coefficient D. OH - D K + Charge Z OH - Z K + Anode charge transfer coefficient α a Cathode charge transfer coefficient αC Equilibrium potential E eq Initial exchange current density i 00 The exchange current density coefficient γ is used. Based on electromagnetic field coupling, the Navier–Stokes equation, Fick's second law, and Butler-Volmer equation are solved to obtain physicochemical data on fluid velocity u, overpotential μ, and concentration distribution c at various points in the fluid.

[0046] The Navier–Stokes equations, Fick's second law, and Butler-Volmer equations are as follows:

[0047]

[0048] Among them, F L For Lorentz force, F L = j × B, where j is the current density generated by the ion flow and B is the magnetic induction intensity; For Kelvin, χ sol μ0 is the overall magnetic susceptibility of the electrolyte, and μ0 is the magnetic susceptibility of vacuum; u m,i The mobility of each component is positively correlated with the diffusion coefficient Di of each component; i0 is the exchange current density; α a α c Let be the anode charge transfer coefficient and the cathode charge transfer coefficient, respectively; η be the overpotential; and F be the Faraday constant. The anode charge transfer coefficient and the cathode charge transfer coefficient satisfy α. a +α c =4; η is the overpotential, and the overpotential satisfies η = φ e -φ-φ eq , φ e φ is the electrode potential, and φ is the solution potential. eq To balance the electrode potential.

[0049] The formula for calculating the overall magnetic susceptibility of the electrolyte is:

[0050]

[0051] Where ci represents the concentration of each component; denoted as the molar magnetic susceptibility of each component; The magnetic susceptibility of water;

[0052] The mobility u of each component m,i The calculation formula is:

[0053]

[0054] Among them, D i R is the diffusion coefficient of each component; T is the ideal gas constant; and T is the reaction temperature.

[0055] i0 is the exchange current density, calculated using the following formula:

[0056] i0 = i 00 (c s / c0) γ

[0057] Among them, c s With c o These represent the electrode surface concentration and the bulk concentration, respectively. 00 Let γ be the initial exchange current density, and γ be the exchange current density coefficient.

[0058] S5: Set the reaction time and step size to obtain the concentration field distribution, velocity field distribution and force field distribution after simulation, and realize the finite element simulation of the electrochemical process of the electrocatalytic oxygen evolution reaction.

[0059] The above description of the embodiments is provided to enable those skilled in the art to understand and use the invention. It will be apparent to those skilled in the art that various modifications can be made to these embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made by those skilled in the art based on the disclosure of the present invention without departing from the scope of the invention should be within the protection scope of the present invention.

Claims

1. A finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field, characterized in that, include: Based on the finite element model, the morphology of the conical electrode was established, the physicochemical properties of the material were introduced, and electromagnetic field parameters, fluid field parameters, and electrochemical reaction parameters were set. The fluid field and electrochemical field were coupled, and the reaction time and step size were set to obtain the concentration field distribution, velocity field distribution, and force field distribution after simulation, thus realizing the finite element simulation of the electrochemical process of the electrocatalytic oxygen evolution reaction. The cone-shaped electrode morphology is a two-dimensional symmetric rotation model, including a symmetry axis, a cone-shaped anode and cathode with a cone height of 1 μm obtained by passing through the symmetry axis, and a cylindrical electrochemical cell with a height of 30 μm. The radius of the cone base of the cone-shaped electrode is adjusted by changing the size of the apex angle and adjusting the ratio of the top arc radius D to the bottom radius d, thereby controlling the cone electrode morphology. The physicochemical properties of the material include electrolyte conductivity σ. l Electrode conductivity σs, magnetic permeability μ, relative permittivity ε, BH characteristics of the electrocatalyst f(H), magnetic susceptibility of each component in the electrolyte χH2O, χK + χOH - Initial concentrations C of each electrolyte component OH- C K+ Electrolyte viscosity μ and density ρ; By coupling the fluid field with the electrochemical field and solving the Navier-Stokes equation, Fick's second law, and Butler-Volmer equation based on electromagnetic field coupling, physicochemical data at various points in the fluid are obtained. The Navier-Stokes equation, Fick's second law, and Butler-Volmer equation are as follows: in, For Lorentz force, , j is the current density generated by the ion flow, and B is the magnetic induction intensity; For Kelvin, , The overall magnetic susceptibility of the electrolyte. The magnetic susceptibility of vacuum; The migration rate of each component is given by the diffusion coefficient D of each component. k Positive correlation; For exchange current density; , These are the anode charge transfer coefficient and the cathode charge transfer coefficient, respectively. This represents the overpotential, and F is the Faraday constant.

2. The finite element method for promoting the electrocatalytic oxygen evolution reaction using a conical electrode under a uniform magnetic field, as described in claim 1, is characterized in that... The electromagnetic field parameters include the applied magnetic field H, the positive electrode potential V0, and the negative electrode potential V1. Maxwell's equations are solved to obtain the response of the ferromagnetic conical electrode to the electromagnetic field.

3. The finite element method for promoting the electrocatalytic oxygen evolution reaction using a conical electrode under a uniform magnetic field, as described in claim 2, is characterized in that... The Maxwell equations are as follows: Where J is the current density; E is the electric field; B is the magnetic flux density; V is the electric potential; and M is the magnetization.

4. The finite element method for promoting the electrocatalytic oxygen evolution reaction using a conical electrode under a uniform magnetic field, as described in claim 1, is characterized in that... The fluid field parameters include the initial velocity V0 and the Kelvin force F. ∇B Lorentz force F L The electrochemical reaction parameters include reaction temperature T and ion diffusion coefficient D. OH - D K + Charge Z OH - Z K + Anode charge transfer coefficient α a Cathode charge transfer coefficient α C Equilibrium potential E eq Initial exchange current density i 00 With the exchange current density coefficient γ.

5. The finite element method for promoting the electrocatalytic oxygen evolution reaction using a conical electrode under a uniform magnetic field, as described in claim 1, is characterized in that... The formula for calculating the overall magnetic susceptibility of the electrolyte is: Among them, c k The concentration of each component; denoted as the molar magnetic susceptibility of each component; The magnetic susceptibility of water; Mobility of each component The calculation formula is: in, The diffusion coefficients of each component are denoted as . is the ideal gas constant; T is the reaction temperature; The formula for calculating the exchange current density is: Among them, c s With c o These represent the electrode surface concentration and the bulk concentration, respectively. The initial exchange current density, This is the exchange current density coefficient.

6. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field, as described in claim 1, is characterized in that... The anode charge transfer coefficient and the cathode charge transfer coefficient satisfy the following conditions: ; Overpotential satisfies , in, The electrode potential is... The solution potential, To balance the electrode potential.

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