Electrophoretic motion of an arbitrary prolate body of revolution toward an infinite conducting wall

Abstract

The electrophoretic motion of an arbitrary prolate body of revolution perpendicular to an infinite conducting planar wall is investigated by a combined analytical–numerical method. The electric field is exerted normal to the conducting planar wall and parallel to the axis of revolution of the particle. The governing equations and boundary conditions are obtained under the assumption of electric double layer thin compared to the local particle curvature radius and the spacing between the particle and the boundary. The axisymmetrical electrostatic and hydrodynamic equations are solved by the method of distribution of singularities along a certain line segment on the axis of revolution inside the particle. The analytical expressions for fundamental singularities both of electrostatic and hydrodynamic equations in the presence of the infinite planar wall are derived. Employing a piecewise parabolic approximation for the density function and applying the boundary collocation method to satisfy the boundary conditions on the surface of the particle, a system of linear algebraic equations is obtained which can be solved by matrix reduction technique.Solutions for the electrophoretic velocity of the colloidal prolate spheroid are presented for various values ofa/banda/d, whereaandbare the major and minor axes of the particle respectively anddis the distance between the centre and the wall. Numerical tests show that convergence to at least four digits can be achieved. For the limiting cases ofa=bord→ ∞, our results agree quite well with the exact solutions of electrophoresis of a sphere moving perpendicularly to an infinite planar wall or of a prolate spheroid in an unbounded fluid. As expected, owing to the effect of the wall, the electrophoretic mobility of the particle decreases monotonically for a given spheroid as it gets closer to the wall. Another important feature is that the wall effect on electrophoresis will reduce with the increase of slenderness ratio of the prolate spheroid at the same value ofa/d. The boundary effect on the particle mobility and flow pattern in electrophoresis differ significantly from those of the corresponding sedimentation problem and the wall effect on the electrophoresis is much weaker than that on the sedimentation. In order to demonstrate the generality of the proposed method, the convergent results for prolate Cassini ovals are also given in the present paper.