Electrophoresis of a colloidal sphere with double-layer polarization in a microtube

A theoretical study is presented for the electrophoretic motion of a spherical particle in an electrolyte solution along the axis of a circular microtube, whose wall may be either insulating or prescribed with the linear far-field electric potential distribution. The electric double layers adjoining the charged particle surface and tube wall are finitely thin, and the polarization of the diffuse layer at the particle surface is allowed. The general solutions to the electrostatic and hydrodynamic governing equations are constructed in combined cylindrical and spherical coordinates, and the boundary conditions are enforced on the tube wall by the Fourier transform and along the particle surface by a collocation method. The collocation results for the electrophoretic mobility of the confined particle, which agree well with the asymptotic formulas obtained by using a method of reflections, are obtained for various values of the particle, wall, and solution characteristics. An insulating tube wall and a tube wall with the far-field potential distribution affect the electrophoresis of the particle quite differently. Although the particle mobility in a tube with uncharged wall in general decreases with an increase in the particle-to-tube radius ratio a/b, it can increase with an increase in a/b as this ratio is close to unity for some cases because of the competition between the wall effects of hydrodynamic retardation and possible electrochemical enhancement on the particle migration. When the zeta potential of the tube wall is comparable to that of the particle, the electroosmotic flow of the bulk fluid induced by the tube wall dominates the electrokinetic migration of the particle.