Nernst-Planck equation: J = -D∇c - (zF/RT)Dc∇φ. Ion flux is driven by both concentration gradients (Fick's law) and electric field (electromigration). Watch Debye screening layers form at electrodes and steady-state profiles emerge.
Cations (+) accumulate near the negative electrode; anions (-) near the positive. The Debye length λ_D = √(εRT/F²Σcᵢzᵢ²) sets the screening scale.