The equation of electrodiffusion^{[1]} has the form
∇ J_{i} + ∂n_{i}/∂t = 0 |
J_{i} = - D_{i}(∇ n_{i} + z_{i}e n_{i}/(k_{B}T) ∇φ_{i}) |
where n_{i} is a number of i – th ions, φ – electric potential, D_{i} – the diffusion coefficient of i – th particles, k_{B} – Boltzmann constant, T – temperature, z_{i} – valence of the i – th kind of ions, e – electric charge. To find the electric potential φ the Poisson equation must be solved
∇^{T}(ε_{0}ε ∇ φ _{i}) + ρ = 0 |
ρ = | ∑_{i} | ρ_{i} |
where ρ_{i} = z_{i}en_{i}. Thus equations (1) and (2) both constitute the system of coupled equations.