Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

Abstract

A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for the particle velocity including two terms : the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere : (if the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit.