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.