Cross-channel distribution and streamwise dispersion of micro-swimmers in a vertical channel flow: A study on the effects of shear, particle shape, and convective inertial torque

Abstract

In quiescent water, gyrotactic micro-swimmers swim upward on average. This anti-gravity swimming behavior is usually thought to be caused by micro-swimmers' bottom-heaviness. However, recent research has shown the importance of convective inertial torque in the orientational dynamics of settling elongated particles, and the torque can cooperate with self-propulsion to result in an effective gyrotactic mechanism. In this paper, we compare the cross-channel distribution and streamwise dispersion of micro-swimmers with and without convective inertial torque in a two-dimensional vertical channel flow, using a recently proposed generalized Taylor dispersion method. Meanwhile, we incorporate other effects such as shear-shape interaction and wall accumulation. Reflective boundary condition and Robin boundary condition are imposed to represent periodic boundaries and mimic motility-induced wall accumulation effect, respectively. For non-gyrotactic inertialess elongated micro-swimmers, a transition from high-shear trapping regime to low-shear trapping regime appears, consistent with results in previous studies. For micro-swimmers with an effective gyrotaxis intensity resulting from the convective inertial torque, their macroscopic transport properties are essentially the same as those of inertialess micro-swimmers with the same aspect ratio and an equal physical gyrotaxis intensity. The non-monotonic variations of effective drift velocity and dispersivity as functions of the flow rate are also characterized. Additionally, upstream swimming behavior, which is reflected by negative drift velocity, is found in weak flows for both gyrotactic micro-swimmers and non-gyrotactic micro-swimmers with motility-induced wall accumulation.

Gyrotactic trapping of micro-swimmers in simple shear flows: a study directly from the fundamental Smoluchowski equation

“…α 0 = 0 in (2.5). We also discuss cases with non-settling rod-like (α 0 = 1) micro-swimmers in Appendix D. However, cases with settling elongated micro-swimmers is not discussed in this paper, because the settling speed will become orientation-dependent (Ardekani et al 2017;Clifton, Bearon & Bees 2018), and the possible inertial torque can be a non-negligible effect Gustavsson et al 2019;Qiu et al 2021;Wang, Jiang & Chen 2022).…”

Migration of confined micro-swimmers subject to anisotropic diffusion

“…2021; Debnath et al. 2022; Wang, Jiang & Chen 2022 a , 2023). To reflect the transient evolution of and , we denote the transient drift velocity and dispersivity as and , respectively.…”

“…For further research interest, the transient evolution of these transport coefficients can feature the temporal process in the anisotropic diffusion of active ellipsoids long before the Taylor dispersion regime (Guan et al 2021;Debnath et al 2022;Wang, Jiang & Chen 2022a, 2023. To reflect the transient evolution of Ū and D, we denote the transient drift velocity and dispersivity as U x (t) and D T (t), respectively.…”

Accumulation and alignment of elongated gyrotactic swimmers in turbulence

“…In laminar flows, spherical cells accumulate in the center of downwelling vertical pipe flows 4,10 , become trapped in a thin layer of high shear in horizontal shear flows 11,12 . Gyrotactic swimmers are found to accumulate due to gravitactic focusing and wall accumulation in channel Poiseuille flows 13,14 . In turbulent flows, gyrotactic motility can generate small-scale clusters that are dynamically evolving, both when the effect of the fluid acceleration is included or not [15][16][17] .…”