Nonlinear screening of spherical and cylindrical colloids: the case of 1:2 and 2:1 electrolytes.

From a multiple scale analysis, we find an analytic solution of spherical and cylindrical Poisson-Boltzmann theory for both a 1:2 (monovalent coions, divalent counterions) and a 2:1 (reversed situation) electrolyte. Our approach consists of an expansion in powers of rescaled curvature 1/ (kappaa), where a is the colloidal radius and 1/kappa the Debye length of the electrolytic solution. A systematic comparison with the full numerical solution of the problem shows that for cylinders and spheres, our results are accurate as soon as kappaa>1. We also report an unusual overshooting effect where the colloidal effective charge is larger than the bare one.