Equation of electrodiffusion

Definition

The equation of electrodiffusion[1] has the form

∇ Ji + ∂ni/∂t = 0
Ji = - Di(∇ ni + zie ni/(kBT) ∇φi)

where ni is a number of i – th ions, φ – electric potential, Di – the diffusion coefficient of i – th particles, kB – Boltzmann constant, T – temperature, zi – valence of the i – th kind of ions, e – electric charge. To find the electric potential φ the Poisson equation must be solved

∇T(ε0ε ∇ φ i) + ρ = 0
ρ = ∑i ρi

where ρi = zieni. Thus equations (1) and (2) both constitute the system of coupled equations.

References

  1. ^ M. Toda and R. Kubo, Statistical Physics II. Nonequilibrium Statistical Mechanics, Springer – Verlag 1985