Generalised Taylor dispersion of chiral microswimmers

Transport phenomena of microswimmers in fluid flows play a crucial role in various biological processes, including bioconvection and cell sorting. In this paper, we investigate the dispersion behavior of chiral microswimmers in a simple shear flow utilizing the generalized Taylor dispersion (GTD) theory, motivated by biased locomotion of bacterial swimmers known as bacterial rheotaxis. We thus focus on the influence of shear-induced torque effects due to particle chirality, employing an extended Jeffery equation for individual deterministic dynamics. We then numerically calculate macroscopic parameters including averaged swimming velocity and effective diffusion tensor using spherical harmonic expansion, and argue the obtained results based on the fixed points and their stability of the orientational dynamical systems. Our results reveal that chiral effects induce biased locomotion and we observe qualitative transitions in the orientational distribution with increasing Pecl\'et number, aligning with previous experimental findings. The diffusion tensor analysis highlights significant reduction in the diffusion coefficient perpendicular to the flow plane due to chirality. This suggests potential applications in flow-mediated cell separation and we numerically demonstrate such chirality-induced fluid transportation. The presented methods will be useful in predicting and controlling dispersion behaviors of such chiral microswimmers.