Electrophoretic velocity of ion-releasing colloidal particles

By means of a matched asymptotic expansions approach the electrophoretic velocity and zeta potential of a catalytic particle that uniformly releases ions have been investigated. Attention is focused on large, compared to diffuse layer, particles characterized, beside the surface potential $\Phi_s$, by the Damk\"{o}hler number Da that represents the ratio of the surface reaction rate to the diffusive transfer one. For vanishing Da, we recover the classical Smoluchowski formula for the electrophoretic velocity which states that the zeta potential of the particle is equal to $\Phi_s$ and that the migration direction is determined by its sign. For small values of Da we show that the migration velocity is controlled mostly by $\Phi_s$ and affected by an ion release only slightly. However, even small Da can induce the electrophoresis of electro-neutral particles that would be immobile if inert. For larger Da the direction of migration and the sign of zeta potential become independent on $\Phi_s$ and are solely determined by the difference in diffusivity of released cations and anions. Still, the surface potential affects the magnitude of the particle velocity.