DEEP ELECTROPHORETIC PENETRATION AND DEPOSITION OF CERAMIC PARTICLES INSIDE POROUS SUBSTRATES .1. ANALYTICAL MODEL

The electrophoretic penetration of colloidal silica particles into a carbon-carbon porous substrate is investigated. The carbon substrate is immersed in a solution containing the particles and positioned between two electrodes. An electric potential gradient between the electrodes is used to drive the solute (silica particles) into the pores. Three driving mechanisms are identified: the hydrodynamic drag force exerted on the particles due to the electroosmotic flow of the solvent inside the pores, the electrophoretic force exerted on the particles, and the stochastic Brownian force due to thermal fluctuations of the solvent molecules. While subjected to these forces, the particles may reach the walls of the pore and the short range van der Waals forces may cause their capturing and deposition onto the walls. The objectives of this paper are to predict the penetration depth of a single ceramic particle moving inside a porous substrate under the effect of an electric potential gradient, to derive the nondimensional parameters characterizing the motion of the ceramic particles, and to gain a physical insight on the various mechanisms governing penetration. Qualitatively, the results are that penetration depths are governed by a favorable (if large) Peclet number and unfavorable (if large) Damkohler number. Quantitative results are also provided.