Electrostatic interaction of a spherical particle in the vicinity of a circular orifice

Electrostatic interaction of a charged spherical particle in the vicinity of an orifice plane has been investigated in this paper. The particle can creep along the axis of the orifice and is immersed in a bulk electrolyte. By solving the Poisson--Boltzmann problem, we have obtained the effective electrostatic interaction for several values of reduced orifice radius \tildeh, including the cases of \tildeh>1, \tildeh=1 and \tildeh<1. Two kinds of boundary conditions of the orifice plane are considered. One is constant potential model corresponding to a conducting plane, the other is constant charge model. In the constant potential model, there is an electrostatic attraction between the particle and the orifice plane when they get close to each other, while there is a pure electrostatic repulsion in the constant charge model. The interactions in both boundary models are sensitive to the parameters of the reduced orifice radius, the reduced particle--orifice distance, surface charge densities of the particle and orifice plane, and the reduced Debye screen constant corresponding to the salt-ion concentration and ion valence.