ASYMPTOTIC SOLUTION OF POISSON-BOLTZMANN EQUATION FOR A CHARGED SPHERE AND IMPLICATIONS

The Poisson-Boltzmann equation is solved for the exterior of a sphere carrying a fixed surface charge, in the limit as the ionic strength tends to zero, by a perturbation method. The result (known already from the work of Gronwall, La Mer & Sandved, 1928) is that the Poisson-Boltzmann solution is uniformly approximated by the Debye-Hückel solution. The sphere problem is used to illustrate a proposed sufficient condition which can be applied to more general problems. For such problems, satisfaction of the condition implies that the Debye-Hiickel solution uniformly approximates the Poisson-Boltzmann solution. Some problems satisfying the criterion are briefly discussed. © 1969.