Steady state solution of the Poisson–Nernst–Planck equations

The exact steady state solution of the Poisson–Nernst–Planck equations (PNP) is given in terms of Jacobi elliptic functions. A more tractable approximate solution is derived which can be used to compare the results with experimental observations in binary electrolytes. The breakdown of the PNP for high concentration and high applied voltage is discussed.