Breakdown of a stationary solution to the Nernst–Planck–Poisson equations

Abstract
This report shows an oscillatory instability, at sufficiently high voltage, of a representative steády solution to equations describing the passage of current through an unstirred layer of electrolyte adjacent to an ideal cation exchange membrane. This instability may be the harbinger of further “turbulent-like” transitions that correspond to observed unsteadiness at high voltages.

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