(151f) Instability of a Suspension of Swimming Bacteria

Many bacterial species including E. coli swim in a suspending fluid propelling themselves by rotating a bundle of flagella and occasionally tumbling to change their swimming direction. Experimental observations and numerical simulations indicate that spontaneous correlated motion of the cells and suspending fluid at sufficiently high bacteria concentrations, a phenomenon usually referred to as collective dynamics of bacteria. In this presentation, we will formulate averaged equations of motion for a bacterial suspension which includes an averaged stress induced by the cells' swimming. This stress depends on the cells' orientation distribution which can be altered by shearing motions in the fluid. A linear stability analysis indicates that a homogeneous, isotropic base state with no mean fluid velocity is unstable to shear waves at sufficiently high bacteria concentrations. The mechanism of the instability involves the coupling of the bacterial stress, the orientation distribution, and the fluid velocity disturbance. A shear flow increases the orientation distribution for bacteria swimming along the extensional axis of the flow. The cell body exerts a force in the direction of its motion while the tail exerts an equal and opposite force. This force dipole tends to reinforce the velocity disturbance when the cell is oriented along the extensional axis. We will also show that chemical attractants that induce a biased random walk of the cells in the base state tend to increase the growth rate of fluid disturbances. The destabilizing effect of attractants occurs due to their tendency to increase the mean tumbling time of the cells and due to the anisotropic orientation distribution they induce in the base state.