Effects of salt addition on the ion distribution enclosed in a cylinder and a sphere

The electric potential and ion distributions within a cylinder and a sphere at various salt concentration have been obtained analytically by solving t he Poisson-Boltzmann equation in terms of series solutions. At a fixed rati o of co-ion to counterion concentrations at the center of the aqueous core (alpha < 1) or a given amount of added salt, the existence of the upper lim it of the counterion concentration at the center has been observed regardle ss of the surface charge density. It is a consequence of counterion condens ation on the charged surface. The upper limit depends on the value of a and increases rapidly when alpha --> 1. At high surface charge density, the co unterions are strongly attracted to the surrounding of the surface. A bound ary layer with the thickness inversely proportional to the surface charge d ensity is formed. Both the effects of curvature and salt addition hence bec ome unimportant, and the surface potential is primarily determined by the s urface charge density.