Electrophoretic motion of a colloidal cylinder near a plane wall

An analytical study is presented for the electrophoretic motion of a circular cylindrical particle in an electrolyte solution with a transversely imposed electric field near a large plane wall parallel to its axis in the quasisteady limit. The electric double layers at the solid surfaces are assumed to be thin relative to the particle radius and to the particle–wall gap width, but the polarization effect of the diffuse ions in the double layer surrounding the particle is incorporated. The presence of the confining wall causes two basic effects on the particle velocity: first, the local ionic electrochemical potential gradients on the particle surface are altered by the wall, thereby affecting the motion of the particle; secondly, the wall enhances the viscous retardation of the moving particle. Through the use of cylindrical bipolar coordinates, the transport equations governing this problem are solved and the wall effects on the electrophoresis of the cylinder are determined for various cases. The presence of the plane wall prescribed with the ionic electrochemical potentials consistent with the far-field distributions reduces the electrophoretic mobility of the particle, which depends upon the properties of the particle–solution system, the relative particle–wall separation distance, and the direction of the applied electric field relative to the plane wall. The direction of the electrophoretic migration of a cylindrical particle near a plane wall is different from that of the prescribed electric field, except when it is oriented parallel or perpendicular to the wall. The effects of the plane wall on the electrophoresis of a cylinder are found to be much more significant than those for a sphere at the same separation.