Anomalous dispersion of microswimmer populations

Laxminarsimharao Vennamneni; Piyush Garg; Ganesh Subramanian

paper

Anomalous dispersion of microswimmer populations

arXiv:2212.01817

Abstract

We examine the longitudinal dispersion of spheroidal microswimmers in pressure-driven channel flow. When time scales corresponding to swimmer orientation relaxation, and diffusion in the gradient and flow directions, are well separated, a multiple scales analysis leads to the shear-enhanced diffusivity governing the long-time spread of the swimmer population along the flow\,(longitudinal) direction. For large $P e_{r}$ , $P e_{r}$ being the rotary Peclet number, this diffusivity scales as $O (P e_{r}^{4} D_{t})$ for $1 \leq κ ≲ 2$ , and as $O (P e_{r}^{\frac{10}{3}} D_{t})$ for $κ = \infty$ , $D_{t}$ being the (bare)\,swimmer translational diffusivity and $κ$ the swimmer aspect ratio. For $2 ≲ κ < \infty$ , swimmers collapse onto the centerline with increasing $P e_{r}$ , leading to an anomalously reduced diffusivity of $O (P e_{r}^{5 + C (κ)} D_{t})$ . Here, $C (κ) < - 1$ characterizes the algebraic decay of swimmer concentration outside an $O (P e_{r}^{- 1})$ central core, with the anomalous exponent governed by large velocity variations sampled by the few swimmers outside this core. $C (κ)$ dips below $- 5$ for $κ ≳ 10$ , leading to a flow-independent bound of $O (κ^{10} D_{t})$ for the dispersion of sufficiently slender swimmers.

6 pages of the main text and 6 pages of supplementary information