方程名称

表达式

固相锂离子浓度分布

$\frac{\partial c_s\left(x,t,r\right)}{\partial t}-\frac{D_s}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial c_s\left(x,t,r\right)}{\partial r}\right)=0$

液相锂离子浓度分布

$\frac{\partial }{\partial t}{\epsilon }_e{c}_e\left(x,t\right)=\frac{\partial }{\partial x}\left(D_e^{eff}\frac{\partial }{\partial x}{c}_e\left(x,t\right)\right)+\left(1-t_{+}\right)\frac{j_f\left(x,t\right)}{F}$

固相电势分布

$\frac{\partial }{\partial x}\left({\sigma }^{eff}\frac{\partial }{\partial x}{\varphi }_s\left(x,t\right)\right)-j_f\left(x,t\right)=0$

液相电势分布

$\frac{\partial }{\partial x}\left({\kappa }^{eff}\frac{\partial }{\partial x}{\varphi }_e\left(x,t\right)\right)+\frac{\partial }{\partial x}\left({\kappa }_D^{eff}\frac{\partial }{\partial x}\ln c_e\left(x,t\right)\right)+j_f\left(x,t\right)=0$

Butler-Volmer方程

$j_f\left(x,t\right)=a{i}_0\left[\exp \left(\frac{{\alpha }_{a}F}{RT}\eta \right)-\exp \left(\frac{-{\alpha }_{c}F}{RT}\eta \right)\right]$

输出端电压

$V\left(t\right)={\varphi }_s\left(L,t\right)-{\varphi }_s\left(0,t\right)-R_c\cdot I_{app}\left(t\right)$