Finite element method for simulating promotion of electrocatalytic oxygen evolution reaction by conical electrode under uniform magnetic field

Abstract

The invention relates to a finite element method for simulating an electro-catalysis oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field. The method comprises the following steps: based on a finite element model, establishing a conical electrode morphology, introducing physical and chemical characteristics of a material, setting an electromagnetic field, a fluid field and electrochemical reaction parameters, coupling the fluid field and the electrochemical field, setting reaction time and step length, and obtaining concentration field distribution, velocity field distribution and force field distribution obtained after simulation. Finite element simulation of the electrochemical process of the electrocatalytic oxygen evolution reaction is realized. Compared with the prior art, multi-physics field finite element simulation of coupling of four physics fields is achieved, and the response condition of the ferromagnetic conical structure to the magnetic field is reflected. In addition, by simulating the electro-catalysis process under the action of the magnetic field, the specific process of promoting electro-catalysis by the magnetic field can be known simply and clearly.

Description

Technical Field

[0001] The invention relates to the technical field of electrocatalytic simulation, and in particular to a finite element method for simulating a cone electrode promoting an electrocatalytic oxygen evolution reaction under a uniform magnetic field. Background Art

[0002] The electrocatalytic oxygen evolution reaction is a reaction that occurs on the anode side of the electrolyzer for hydrogen production, and it is an indispensable part of the development of hydrogen energy. During the electrochemical reaction of oxygen evolution, excessive current density will quickly consume the reactants near the electrode, and at the same time, the mass transfer capacity itself cannot replenish the reactants in time, thus forming a large concentration polarization, which greatly reduces the electrocatalytic efficiency. During the electrochemical process, the migration movement of charged ions can form an ion flow, so the magnetic field can be used in the electrochemical process to promote the movement of the fluid, thereby replenishing the reactants in time, reducing concentration polarization, and improving its reaction efficiency. The tip structure is a structure that is sensitive to the external field. It has a tip effect on the electric field, and there is a significant enhancement of the electric field at the tip, but its response to the magnetic field is still lacking research.

[0003] The finite element method is an effective multi-physics simulation method. At present, the finite element method has been well applied in the tip electric field enhancement and magnetic field-promoted electrochemical deposition process, but the research on the response of ferromagnetic tips to magnetic fields and the influence of tips on electrocatalysis under magnetic fields is still blank, and more specific theoretical simulations are needed. Summary of the invention

[0004] The purpose of the present invention is to provide a finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field in order to overcome the defects of the above-mentioned prior art. By solving the Maxwell equation, the Navier-Stokes equation, the Fick second law, and the Butler-Volmer equation simultaneously, a multi-physics field finite element simulation of four physical fields coupling is realized, and the response of the ferromagnetic conical structure to the magnetic field is reflected.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] The present invention provides a finite element method for simulating a conical electrode promoting an electrocatalytic oxygen evolution reaction under a uniform magnetic field, which is characterized by comprising: based on a finite element model, establishing the morphology of the conical electrode, introducing the physical and chemical properties of the material, setting the electromagnetic field, the fluid field and the electrochemical reaction parameters, coupling the fluid field with the electrochemical field, and setting the reaction time and the step length, obtaining the concentration field distribution, the velocity field distribution and the force field distribution obtained after the simulation, and realizing the finite element simulation of the electrochemical process of the electrocatalytic oxygen evolution reaction.

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

[0008] Furthermore, the radius of the cone bottom surface of the conical electrode morphology is adjusted by changing the size of the top angle and adjusting the ratio of the top arc radius D to the bottom radius d to adjust the curvature radius of the cone, thereby achieving regulation of the conical electrode morphology.

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

[0010] Furthermore, the electromagnetic field parameters include an external magnetic field H, a positive electrode potential V0, and a 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] Among them, J is the current density; E is the electric field; B is the magnetic induction intensity; V is the electric potential; and M is the magnetization intensity.

[0014] Furthermore, the fluid field parameters include initial velocity V0, Kelvin force Lorentz force F L The electrochemical reaction parameters include reaction temperature T, 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 and 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 the Butler-Volmer equation are solved on the basis of electromagnetic field coupling to obtain the physical and chemical data of each location in the fluid. The Navier-Stokes equation, Fick's second law, and the Butler-Volmer equation are:

[0016]

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

[0018] Furthermore, the calculation formula of the magnetic susceptibility of the electrolyte as a whole is:

[0019]

[0020] Among them, ci is the concentration of each component; is the molar magnetic susceptibility of each component; is the magnetic susceptibility of water;

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

[0022]

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

[0024] i0 is the exchange current density, and the calculation formula is:

[0025] i0=i 00 (c s / c0) γ

[0026] Among them, c s With c o are the electrode surface concentration and bulk concentration, respectively, i 00 is the initial exchange current density, and γ is 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] Among them, φ e is the electrode potential, φ is the solution potential, φ eq is the equilibrium electrode potential.

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

[0031] The present invention realizes multi-physics finite element simulation of four physical fields coupling by solving Maxwell equations, Navier-Stokes equations, Fick's second law, and Butler-Volmer equations, and reflects the response of ferromagnetic cone structure to magnetic field. In addition, by simulating the electrocatalytic process under the action of magnetic field, the specific process of magnetic field promoting electrocatalysis can be simply and clearly understood, thereby providing hydrogen energy industry workers with simple tools to guide the design of electrocatalytic material morphology. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a schematic diagram of the finite element modeling structure of the conical electrode in Example 1;

[0033] Figure 2 The figure is a flow chart 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 Description of the mark in:

[0035] 1- symmetry axis, 2- anode, 3- cathode. DETAILED DESCRIPTION

[0036] The specific implementation methods of the present invention are described in detail below through examples. These examples are implemented on the premise of the scheme described in the present invention, and provide detailed implementation methods and specific operating processes, but the protection scope of the present invention is not limited to the following examples.

[0037] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments. Any features such as structure / module name, control mode, algorithm, process or composition ratio not clearly described in this technical solution are regarded as 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. Figure 2 As shown, the following steps are included:

[0040] S1: Based on the finite element model, establish the conical electrode morphology. Figure 1 As shown, the conical electrode morphology is a two-dimensional symmetrical rotation model, including a symmetry axis 1, a conical anode 2 with a cone height of 1 μm obtained by rotating the symmetry axis, a cathode 3, and a cylindrical electrochemical cell with a height of 30 μm. Figure 1 The z, r, and θ in the figure represent the axial, radial, and circumferential directions of the model, respectively. The radius of the bottom surface of the cone of the conical electrode morphology is adjusted by changing the size of the vertex angle and adjusting the ratio of the top arc radius D to the bottom radius d to adjust the curvature radius of the cone, thereby achieving the regulation of the conical electrode morphology.

[0041] S2: Physical and chemical properties of the imported materials, including electrolyte conductivity σ l , electrode conductivity σs, magnetic permeability μ, relative dielectric constant ε, BH characteristics of electrocatalyst f(H), magnetic susceptibility of each component in the electrolyte χH2O, χK + , χOH - , initial concentration of each electrolyte component C OH -、C K+ , electrolyte viscosity μ and density ρ.

[0042] S3: Setting the electromagnetic field The electromagnetic field parameters include the external magnetic field H, the positive electrode potential V0, and the negative electrode potential V1, and solving the Maxwell equation to obtain the response of the ferromagnetic conical electrode to the electromagnetic field. The Maxwell equation is:

[0043]

[0044] Among them, J is the current density; E is the electric field; B is the magnetic induction intensity; V is the electric potential; and M is the magnetization intensity.

[0045] S4: Set the fluid field and electrochemical reaction parameters to couple the fluid field with the electrochemical field. The fluid field parameters include initial velocity V0, Kelvin force Lorentz force F L The electrochemical reaction parameters include reaction temperature T, 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 solved based on electromagnetic field coupling to obtain the physical and chemical data of fluid velocity u, overpotential μ, and concentration distribution c at various locations in the fluid;

[0046] The Navier–Stokes equation, Fick’s second law, and Butler–Volmer equation are:

[0047]

[0048] Among them, F L is the Lorentz force, F L =j×B, j is the current density formed by the ion flow, and B is the magnetic induction intensity; is the Kelvin force, χ sol is the magnetic susceptibility of the electrolyte as a whole, μ0 is the vacuum susceptibility; u m,i is the mobility of each component, which is positively correlated with the diffusion coefficient Di of each component; i0 is the exchange current density; α a , α c They are the anode charge transfer coefficient and the cathode charge transfer coefficient respectively; η is the overpotential, F is 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 is the electrode potential, φ is the solution potential, φ eq is the equilibrium electrode potential.

[0049] The calculation formula of the magnetic susceptibility of the electrolyte as a whole is:

[0050]

[0051] Among them, ci is the concentration of each component; is the molar magnetic susceptibility of each component; is the magnetic susceptibility of water;

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

[0053]

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

[0055] i0 is the exchange current density, and the calculation formula is:

[0056] i0=i 00 (c s / c0) γ

[0057] Among them, c s With c o are the electrode surface concentration and bulk concentration, respectively, i 00 is the initial exchange current density, and γ is the exchange current density coefficient.

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

[0059] The above description of the embodiments is to facilitate the understanding and use of the invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to these embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and 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 present invention should be within the scope of protection 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 conical electrode morphology is established, the physical and chemical properties of the material are imported, the electromagnetic field, fluid field and electrochemical reaction parameters are set, the fluid field and the electrochemical field are coupled, and the reaction time and step size are set. The concentration field distribution, velocity field distribution and force field distribution obtained after simulation are obtained, thereby realizing the finite element simulation of the electrochemical process of the electrocatalytic oxygen evolution reaction.

2. According to claim 1, a finite element method for simulating the promotion of electrocatalytic oxygen evolution reaction by a conical electrode under a uniform magnetic field, characterized in that: The conical electrode morphology is a two-dimensional symmetrical rotation model, including a symmetry axis, a conical anode and cathode with a cone height of 1 μm obtained by rotating around the symmetry axis, and a cylindrical electrochemical cell with a height of 30 μm.

3. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 1, characterized in that: The radius of the cone bottom surface of the conical electrode morphology is adjusted by changing the size of the top angle and adjusting the ratio of the top arc radius D to the bottom radius d to adjust the curvature radius of the cone, thereby achieving regulation of the conical electrode morphology.

4. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 1, characterized in that: The physicochemical properties of the material include electrolyte conductivity σ l , electrode conductivity σs, magnetic permeability μ, relative dielectric constant ε, BH characteristics of electrocatalyst f(H), magnetic susceptibility of each component in the electrolyte χH2O, χK + , χOH - , initial concentration of each electrolyte component C OH- , C K+ , electrolyte viscosity μ and density ρ.

5. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 1, characterized in that: The electromagnetic field parameters include an external magnetic field H, a positive electrode potential V0, and a negative electrode potential V1, and the Maxwell equation is solved to obtain the response of the ferromagnetic conical electrode to the electromagnetic field.

6. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 5, characterized in that: The Maxwell equation is: Among them, J is the current density; E is the electric field; B is the magnetic induction intensity; V is the electric potential; and M is the magnetization intensity.

7. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 1, characterized in that: The fluid field parameters include initial velocity V0, Kelvin force Lorentz force F L The electrochemical reaction parameters include reaction temperature T, 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 and the exchange current density coefficient γ.

8. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 1, characterized in that: The fluid field is coupled with the electrochemical field, and the Navier-Stokes equation, Fick's second law, and the Butler-Volmer equation are solved on the basis of electromagnetic field coupling to obtain the physical and chemical data of each location in the fluid. The Navier-Stokes equation, Fick's second law, and the Butler-Volmer equation are: Among them, F L is the Lorentz force, F L =j×B, j is the current density formed by the ion flow, and B is the magnetic induction intensity; is the Kelvin force, χ sol is the magnetic susceptibility of the electrolyte as a whole, μ0 is the vacuum susceptibility; u m,i is the mobility of each component, which is positively correlated with the diffusion coefficient Di of each component; i0 is the exchange current density; α a , α c are the anode charge transfer coefficient and the cathode charge transfer coefficient respectively; η is the overpotential, and F is the Faraday constant.

9. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 8, characterized in that: The calculation formula of the magnetic susceptibility of the electrolyte as a whole is: Among them, ci is the concentration of each component; is the molar magnetic susceptibility of each component; H2o is the magnetic susceptibility of water; The mobility of each component u m,i The calculation formula is: Among them, D i is the diffusion coefficient of each component; R is the ideal gas constant; T is the reaction temperature; i0 is the exchange current density, and the calculation formula is: i0=i 00 (c s / c0) γ Among them, c s With c o are the electrode surface concentration and bulk concentration, respectively, i 00 is the initial exchange current density, and γ is the exchange current density coefficient.

10. The finite element method for simulating the electrocatalytic oxygen evolution reaction promoted by a conical electrode under a uniform magnetic field according to claim 8, characterized in that: The anode charge transfer coefficient and cathode charge transfer coefficient satisfy α a +α c =4; Overpotential satisfies η=φ e -φ-φ eq , Among them, φ e is the electrode potential, φ is the solution potential, φ eq is the equilibrium electrode potential.

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