Nernst–Planck equation

The Nernst–Planck equation describes ionic flux as the combined effects of concentration gradients, electric fields, and fluid motion.

Fick's laws of diffusion: Relations describing diffusive flux in response to concentration gradients. The diffusion term in the Nernst–Planck equation extends Fickian transport to charged species.
Ionic strength: A measure of electrolyte concentration weighted by the square of each ion's charge. It helps characterize how surrounding ions affect transport and electrostatic interactions.
Poisson–Nernst–Planck equations: A coupled model combining ionic flux equations with electrostatic potential determined by charge density. This common extension solves for concentrations and electric potential together.
Maxwell–Stefan diffusion: A multicomponent diffusion framework based on friction between species rather than independent Fickian fluxes. It handles coupled species interactions more explicitly than the usual Nernst–Planck form.
Walther Nernst: A German physical chemist whose work established foundational relations in electrochemistry and thermodynamics. His electrochemical work contributed the framework for describing ion motion in potential fields.
Electrochemical potential: A thermodynamic potential combining chemical and electrical contributions for a charged species. Its gradient provides a unified driving force for ionic transport.
Diffusion coefficient: A parameter measuring how rapidly particles spread by diffusion in a medium. It sets the strength of concentration-driven flux.
Donnan equilibrium: An unequal distribution of diffusible ions across a membrane caused by impermeant charged species. Nernst–Planck transport can model how membrane ion distributions approach this equilibrium.
Dissipationless transport: Transport in which carriers move over distances without significant scattering. Nernst–Planck assumes continuum diffusive behavior, unlike ballistic motion.
Max Planck: A German theoretical physicist who founded quantum theory and contributed broadly to theoretical physics. The equation bears his name alongside Nernst's, though it is not a quantum-transport law.

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Diffusion equationRelated: Its diffusion term extends the basic equation to ionic transport under electric forces.