Fine-tuning the dispersion of active suspensions with oscillatory flows

Abstract: The combined impact of axial stretching and cross-stream diffusion on the downstream transport of solute is termed Taylor dispersion. The dispersion of active suspensions is qualitatively distinct: viscous and external torques can establish non-uniform concentration fields with weighted access to shear, modifying mean drift and effective diffusivity. It would be advantageous to fine-tune the dispersion for systems such as bioreactors, where mixing or particle separation can improve efficacy. Here, we investigate the dispersion of active suspensions in a vertical channel driven by an oscillatory pressure gradient - Womersley flow - using gyrotactic swimmers (bottom-heavy cells subject to viscous torques). Preliminary experimental results reveal interesting dispersion phenomena, highly dependent on the oscillation parameters, motivating theoretical investigation. Employing Lagrangian simulations, we find that oscillatory flows can induce drift and increase lateral and downstream dispersion, with periodic mixing between left and right sides. Such flows can also be used to separate species with different motile behaviour. Eulerian numerical schemes typically require an approach to averaging in orientational space, such as generalised Taylor dispersion, with assumptions on translational and rotational time scales. For an oscillatory timescale commensurate with cell dynamics, we reveal the limitations of such approximations, beyond which the averaging techniques collapse.