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

Electrostatic interaction of a charged spherical particlein the vicinity of an orifice plane has been investigated in thispaper. The particle can creep along the axis of the orifice and isimmersed in a bulk electrolyte. By solving the Poisson--Boltzmannproblem, we have obtained the effective electrostatic interactionfor several values of reduced orifice radius $tilde{h}$, includingthe cases of $tilde{h}>1$, $tilde{h}=1$ and $tilde{h}<1$. Twokinds 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 theorifice plane when they get close to each other, while there is apure electrostatic repulsion in the constant charge model. Theinteractions in both boundary models are sensitive to the parametersof the reduced orifice radius, the reduced particle--orificedistance, surface charge densities of the particle and orificeplane, and the reduced Debye screen constant corresponding to thesalt-ion concentration and ion valence.