PARTICLE INTERACTIONS IN ELECTROPHORESIS .3. AXISYMMETRICAL MOTION OF MULTIPLE SPHERES

A semianalytic study is presented for the axisymmetric electrophoretic motion of a finite chain of rigid spheres along their line of centers. The spheres may differ in radius and in zeta potential and they are allowed to be unequally spaced. The thin-double-layer assumption is employed. Using a collocation technique, the electrostatic and hydrodynamic governing equations are solved in the quasisteady situation and the particle interaction effects are calculated for various cases. The numerical solutions on convergence can be obtained to any desired degree of accuracy by the increase of the collocation points on each sphere surface. For the electrophoretic motion of two-sphere systems, our results for the particle interaction coefficients agree very well with the exact calculations using spherical bipolar coordinates. For the cases of two or three spheres touching one another, the numerical calculations for the particle interaction effects, which compare quite favorably with the formulae analytically derived, illustrate that the large spheres dominate the migration of the linear cluster of spheres. All of our data also demonstrate the fact that the electrophoretic velocity of each particle is unaffected by the presence of the others if all of the particles have the same zeta potential. © 1990.