Transport of helical gyrotactic swimmers in channels

Abstract

We develop a mechanistic model that describes the transport of gyrotactic cells with propulsive force and propulsive torque that are not parallel. In sufficiently weak shear this yields helical swimming trajectories, whereas in stronger shear cells can attain a stable equilibrium orientation. We obtain the stable equilibrium solution for cell orientation as a function of the shear strength and determine the feasibility region for equilibrium solutions. We compute numerically the trajectories of cells in two dimensional vertical channel flow where the shear is non-uniform. Depending on the parameter values, we show that helical swimmers may display classical gyrotactic focussing towards the centre of the channel or can display a new phenomenon of focussing away from the centre of the channel. This result can be explained by consideration of the equilibrium solution for cell orientation. In this study we consider only dilute suspensions where there is no feedback from cell swimming on the hydrodynamics, and both cell-wall and cell-cell interactions are neglected.