The Nernst–Planck equation is a conservation of mass equation used to describe the motion of chemical species in a fluid medium. It describes the flux of ions under the influence of both an ionic concentration gradient and an electric field . 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:
- t is time,
- D is the diffusivity of the chemical species,
- c is the concentration of the species, and u is the velocity of the fluid,
- z is the valence of ionic species,
- e is the elementary charge,
- is the Boltzmann constant
- T is the temperature.
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