Nernst–Planck equation

The time dependent form of the Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces: It is named after Walther Nernst and Max Planck. The time dependent form of the Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces: It is named after Walther Nernst and Max Planck. It describes the flux of ions under the influence of both an ionic concentration gradient ∇c and an electric field E = −∇φ −∂A/∂t. Where J is the diffusion flux density, t is time, D is the diffusivity of the chemical species, c is the concentration of the species, z is the valence of ionic species, e is the elementary charge, kB is the Boltzmann constant, T is the temperature, u {displaystyle u} is velocity of fluid, ϕ {displaystyle phi } is the electric potential, A {displaystyle mathbf {A} } is the magnetic vector potential. If the diffusing particles are themselves charged they are influenced by the electric field. Hence the Nernst–Planck equation is applied in describing the ion-exchange kinetics in soils.