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Chapman-Jouret Effect

The movement of ions across a membrane due to a potential difference, contributing to battery self-discharge and impacting electrolyte behavior.
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The statement of the theorem

Let J\mathbf{J} be the ionic flux vector across a semi-permeable membrane separating two electrolyte solutions with potentials ϕ1\phi_1 and ϕ2\phi_2. The potential-driven flux J\mathbf{J} is generally modeled by the Nernst-Planck equation, which accounts for concentration gradients and potential gradients:\nJi=−Di(∇Ci+ziFRTCi∇ϕF)where Di is the diffusion coefficient, Ci is the concentration, zi is the valence, and F is the Faraday constant. \mathbf{J}_i = -D_i \left( \nabla C_i + \frac{z_i F}{RT} C_i \nabla \frac{\phi}{F} \right) \quad \text{where } D_i \text{ is the diffusion coefficient, } C_i \text{ is the concentration, } z_i \text{ is the valence, and } F \text{ is the Faraday constant.}
Source: Wikipedia