(282g) Reaction-Enhanced Diffusivity

Investigation of a random (Brownian) motion of a chemically active particle is of a crucial importance for many applications, such as a mixing intensification in chemical engineering, dynamics of self-motile objects in biology and medicine, and many others.

We consider a long-time self-diffusivity of a catalytic particle embedded in a dilute suspension of both reactant and product particles. The hard-sphere interactions between the catalytic particle and both species are taken into account, with an effective radius of the interaction greater than the solid core of the catalytic particle. Hydrodynamic interactions are taken into account for a large (in comparison with both reactant and product particles) catalytic particle. The relative role of hydrodynamic interactions is governed by the ratio of the excluded volume model and the real radius of the particle.

We obtain that the long-time self-diffusivity comprises three terms: that one of the pure liquid and the corrections due to both reactant and product particles. The latter corrections are proportional to the concentration of the corresponding species.

The reactant contribution to the self-diffusivity leads to additional hindrance to the Brownian motion for slow chemical reaction; this hindrance is even larger than that for a suspension of nonreacting particles. In the opposite case of a fast chemical reaction, the reactant contribution tends to zero, because the concentration of reactant particles vanishes at the surface of the catalytic one.

The product contribution is not of fixed sign; depending on the ratio of diffusivities (inverse radii) of reactant and product species, it can either help to the diffusion (for larger product particles) or hinder it (for small product particles). In the limiting case of a fixed flux of the products, when reactant particles diffuse much faster than product ones, the long-time self-diffusivity becomes maximal. This result is in a qualitative agreement with experiments, numerical and analytical results by other authors.

Hydrodynamic interactions lead to decrease in the absolute value of the corrections for both contributions.