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.

Capture rate consequences of multispherule aggregate formation in gases—combined roles of direct interception and interspherule momentum “shielding”

“…A3: The N >> 1 cluster aggregates and, for comparison, their isolated spherules (N D 1), experience the same internal flow field in a matte of prescribed solid "targets" (here micron-sized cylindrical fibers) under the same gas flow conditions (area-averaged gas velocity, density, and viscosity). A4: While Stk N is sub-critical for "pure inertial impaction" 1 we will also assume here that Stk N is small enough to neglect what we have called significant "inertial enrichment" (of the local particle concentration in the vicinity of the target forward stagnation region [Fernandez de la Mora and Rosner 1981Rosner , 1982). This effect is a consequence of the fact that the suspended particle "phase" (viewed as an interpenetrating "fluid") is "compressible" even though the carrier gas velocity is sufficiently subsonic to be considered an "incompressible" fluid.…”

“…This effect is a consequence of the fact that the suspended particle "phase" (viewed as an interpenetrating "fluid") is "compressible" even though the carrier gas velocity is sufficiently subsonic to be considered an "incompressible" fluid. Based on the low-Re/high Pe calculations included in Fernandez de la Mora and Rosner (1982) for both isolated spheres and cylinders, the ability to neglect "inertial enrichment" of the local particle concentration will probably require that Stk N be less than ca. 0.2.…”

Density-ratio effects on the capture of suspended particles in aquatic systems

“…While the critical Stokes number is believed to indicate when inertia starts to affect the capture of small particles (Phillips & Kaye 1999), inertial effects on particle trajectories have been observed even when St is well below the critical value, owing to the compressibility of the particle phase (Robinson 1956;Michael 1968; Fernandez de la Mora & Rosner 1982;Fernandez de la Mora 1986). Strictly speaking, the critical Stokes number defines the minimum necessary St for ideal 'point' particles (initially with the same velocity as the fluid) to reach the collector when moving along the 198 A. Espinosa-Gayosso, M. Ghisalberti, G. N. Ivey and N. L. Jones stagnation streamline.…”

“…Davies & Peetz 1956;Fuchs 1964; Fernandez de la Mora & Rosner 1982;Fernandez de la Mora 1986;Flagan & Seinfeld 1988;Wessel & Righi 1988;Friedlander 2000;Haugen & Kragset 2010). However, such studies are not applicable to aquatic systems, as they are characterised by one or more of the following conditions: (i) very high particle density ratios (ρ + 1), (ii) a focus on a narrow range of flow conditions (usually inviscid or creeping flow fields, which can be described analytically), (iii) neglect of the finite particle size (r p 1), and/or (iv) a focus on a range of St where inertial impaction is entirely dominant.…”