On an Asymptotic Solution of the Poisson—Boltzmann Equation—The Moderately Charged Cylinder

Abstract

The Poisson—Boltzmann equation is considered in the case of a uniformly charged circular cylinder in an environment containing added electrolyte. The problem is recognized to be a ``singular perturbation'' problem and a uniformly valid asymptotic approximation is found in the case of a ``moderately charged'' cylinder, with the surprising result that the solution to the Debye—Hückel equation is an appropriate approximate solution. Results of numerical integration of the Poisson—Boltzmann equation are included to verify the validity of the analytic results.