TRAJECTORIES OF CHARGED TRACER PARTICLES AROUND A CHARGED SPHERE IN ASIMPLE SHEAR-FLOW

The trajectories of electrically charged tracer particles travelling a round a charged sphere subjected to a simple shear flow have been calc ulated. This is a limiting case of the relative trajectories of two un equal-sized spheres when the radius ratio a1/a2 approaches zero. Until now these trajectories have been calculated by assuming the additivit y of hydrodynamic and electrostatic forces, while neglecting the elect roviscous coupling forces. These electroviscous forces are long range and can significantly alter the relative trajectories of spheres. When a1/a2 --> 0, it is found that these trajectories depend on two parame ters, alpha and beta, which depend on the surface charge density of th e tracer particle and the sphere. The relative trajectories of charged particles are qualitatively different from those of neutral particles . There exist six intervals of alpha-values for which the trajectories of the tracer particle show different features. Several new types of trajectory appear, besides the open and closed trajectories for neutra l particles, which we refer to as uni- and bidirectional infinite leng th trajectories, uni- and bidirectional finite length trajectories, op en returning trajectories, and prolate, oblate and circular closed tra jectories. This richness of possible trajectories is the result of thr ee electrokinetic phenomena, affecting particle motion: electro-osmoti c slip, electrophoretic and diffusiophoretic motion.