Entropy (statistical thermodynamics)

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 $\nabla c$ and an electric field $E=-\nabla \phi -{\frac {\partial \mathbf {A} }{\partial t}}$. 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:

${\frac {\partial c}{\partial t}}=\nabla \cdot \left[D\nabla c-uc+{\frac {Dze}{k_{B}T}}c(\nabla \phi +{\frac {\partial \mathbf {A} }{\partial t}})\right]$

Where

• 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,
• $k_{B}$ is the Boltzmann constant
• T is the temperature.

If the diffusing particles are themselves charged they influence the electric field on moving. Hence the Nernst–Planck equation is applied in describing the ion-exchange kinetics in soils.

See also

• Goldman-Hodgkin-Katz equation
• Bioelectrochemistry

Notes

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