# 如何选择正确的电流分布接口？

2014年 2月 10日

### 回顾基本方程

Nernst-Planck 方程：

(1)

\textbf{N}_i = -D_i\nabla c_i-z_i u_{m,i} F c_i\nabla \phi_l+c_i\textbf{u}

(2)

\textbf{i}_l = -F \left(\nabla \sum_i z_iD_i c_i\right)-F^2\nabla \phi_l \sum_i z^2_i u_{m,i} c_i+\textbf{u}F\sum_i z_ic_i

\nabla\cdot\mathbf{i}_l=Q_l

### 一次电流分布

COMSOL Multiphysics 的一次电流分布 接口定义了两个相关变量：一个是电解质电势（\phi_l\），另一个是电极电势（\phi_s\）。基于上述的一次电流分布假设，可得以下方程:

### 二次电流分布

(3)

i_{loc,m} = i_{0,m}\left(e^\frac{\alpha_{a,m} F \eta_m}{RT}-e^\frac{-\alpha_{c,m} F \eta_m }{RT}\right)

-\textbf{i}_s \cdot \textbf{n} = \textbf{i}_l \cdot \textbf{n} = i_\mathrm{DL} + \sum_m{i_{loc,m}}

### 三次电流分布

COMSOL 软件中的三次电流分布 接口求解了电解质电位（\phi_l\）、电极电位（\phi_s\）和一组物质浓度 c_i。根据上述假设，可得到以下方程：

### 总结思考

#### 评论 (4)

##### WYZFJ
2024-05-19

I have a mystery I haven’t figured out. In general, the definition of electrode potential in textbooks or literature is more complex, but it is emphasized that the electrode potential is not equal to the potential difference between the electrode and the solution. However, I found that COMSOL’s definition of electrode potential is this. Does this definition cause the simulation results to be inconsistent with the objective physical facts? Thank you!

##### chong shi
2024-05-24 COMSOL 员工

The electrode potential is the difference in potential between the solid-liquid interface, and it is not directly defined in COMSOL. Generally, only the solid-phase potential is defined, while the liquid-phase potential and lectrode potential are calculated based on interface dynamics and solution properties.

2024-06-24

##### chong shi
2024-06-25 COMSOL 员工