Boundary effects on the electrophoretic motion of cylindrical particles: Concentrically and eccentrically-positioned particles in a capillary

The bounded electrophoretic motion of a cylindrical particle in a circular cylindrical microchannel is explored for two cases: (1) the particle is located on the centerline of a channel (concentrically), with a symmetric wall boundary condition since gap width is constant throughout; and (2) the particle is at an eccentric location in the channel, with an asymmetric boundary condition set by the walls. The objective is to determine the effect of different boundary conditions, geometries, and physical properties on the velocity and orientation of the cylinder with respect to the boundary. A theoretical model for the motion of the cylinder is presented and the problem is solved numerically. The steady-state simulations show that the velocity of the cylinder is reduced at small gap widths for the concentric case, but the velocity is increased at small gap widths for the eccentric case. When the cylinder is angled with respect to the horizontal in the symmetric case or is near the boundary in the asymmetric case, vertical and rotational components of velocity are predicted. In such cases, transient simulations are appropriate for most accurately representing particle motion. Two such simulations are included herein and show both horizontal and vertical translation plus rotation of the particle as a function of time. Asymmetric electric field contours and fluid velocity streamlines around a cylindrical particle in a cylindrical channel, resulting in electrophoretic translation and rotation of the particle.