(585c) The Long-Time Self-Diffusivity of Catalytic Colloidal Particles

We study the long-time self-diffusivity of a catalytic probe particle in a dilute suspension of reactant bath particles. The first order chemical reaction of the bath particles takes place at the surface of the catalytic particle; both types of particles are assumed solid spheres of the radii large in comparison with the solvent molecules. We neglect the hydrodynamic interactions between the particles and calculate the first correction?proportional to the volume fraction of the bath particles?to the long-time self-diffusivity. In motionless disperse medium, this very correction is negative and depends on the Damköhler number, which is a measure of relative impacts of the diffusion and chemical reaction. With increase in the Damköhler number, the absolute value of the correction initially grows and then decay inversely proportional to the Damköhler number. In case of advection of the catalytic particle through the reactant ones, the effect of chemical reaction is more complicated. The intensity of advection is characterized by the Péclet number. The longitudinal and transversal components of the self-diffusivity differ, since there is a preferential direction due to the advection. However, the qualitative behavior of these two components with variation of the problem parameters is similar, only the quantitative distinction is found. In the absence of chemical reaction, the corrections to the self-diffusivity change their signs with increase in the Péclet number and become positive. The chemical reaction, in turn, rather weakens this effect; again with growth of the Damköhler number, the correction to the self-diffusivity vanishes. The interested reader is referred to Zia & Brady (2010) for the case of inert probe particles, which serves as basis of this work.