Mass transfer to freely suspended particles at high P\'eclet number

TL;DR

This paper develops a theoretical framework for calculating mass transfer rates from particles in high Péclet number flows, validated by numerical simulations, revealing how particle shape and flow type influence surface flux.

Contribution

It generalizes asymptotic results for mass transfer to arbitrary particles in open flow paths at high Péclet numbers, including numerical validation and analysis of shape effects.

Findings

Surface flux depends on Péclet number, particle aspect ratio, and flow topology.

Slender prolate spheroids have higher flux than oblate spheroids with same surface area.

Flow type (irrotational or rotational) significantly influences transfer rates.

Abstract

In a theoretical analysis, we generalise well known asymptotic results to obtain expressions for the rate of transfer of material from the surface of an arbitrary, rigid particle suspended in an open pathline flow at large P\'eclet number, $\textrm{Pe}$. The flow may be steady or periodic in time. We apply this result to numerically evaluate expressions for the surface flux to a freely suspended, axisymmetric ellipsoid (spheroid) in Stokes flow driven by a steady linear shear. We complement these analytical predictions with numerical simulations conducted over a range of $\textrm{Pe} = 10^1 - 10^4$ and confirm good agreement at large P\'eclet number. Our results allow us to examine the influence of particle shape upon the surface flux for a broad class of flows. When the background flow is irrotational, the surface flux is steady and is prescribed by three parameters only: the P\'eclet number, the particle aspect ratio and the strain topology. We observe that slender prolate spheroids tend to experience a higher surface flux compared to oblate spheroids with equivalent surface area. For rotational flows, particles may begin to spin or tumble, which may suppress or augment the convective transfer due to a realignment of the particle with respect to the strain field.