Boundary Effects on the Electrophoretic Motion of a Charged Particle in a Spherical Cavity

Although boundary interactions can be important in many electrophoretic systems, existing theoretical analyses of these phenomena have been limited to systems with very small double-layer thicknesses. We have developed an exact analytical solution for the boundary effects on the electrophoretic velocity of a charged particle in a spherical cavity using the linearized Poisson-Boltzmann equation, with the resulting expression being valid for all double-layer thicknesses and all particle/pore sizes. The boundary effect for very thin double layers is fairly weak (with a first-order correction of order λ³, where λ is the ratio of the particle to cavity radii) since the velocity disturbance under these conditions varies as r^-3 . The boundary effect for large double-layer thicknesses is much more significant, with the first-order correction being of order λ¹ due to the r^-1 dependence of the velocity disturbance when the double layer spans the entire cavity. The charge on the boundary alters the electrophoretic particle motion through the development of an induced charge on the particle and through the generation of an electroosmotic recirculation flow in the spherical cavity. The different dependence of these phenomena on the particle size can actually cause the electrophoretic velocity of small and large particles to be in opposite directions. These results provide important physical insights into the role of boundary effects on the electrophoretic motion of a charged spherical particle.