Fluid Mechanics Of Bacterial Suspensions: Tracer Transport And Concentration Instabilities Driven By Bacteria-Swimming-Induced Hydrodynamic Disturbances

Abstract

Swimming bacteria create hydrodynamic disturbances in the form of Stokesian force-dipoles and in this thesis we study the transport of passive tracer particles and instabilities that feature unstable bacteria concentration fluctuations in suspensions of swimming bacteria driven by those disturbances. We first calculate the effective diffusion coefficient of a passive, Brownian tracer particle in a uniform suspension of randomly swimming bacteria as a function of the bacterial concentration, geometry, motility, and the tracer Brownian diffusivity using theory and simulations based on binary interactions between bacteria and tracer particles and also experiments on bacterial suspensions seeded with colloidal tracers. Particular attention has been paid to understand the effect of the Brownian motion of the tracer and the tumbling of bacteria on the effective diffusivity of the tracer. Next, we analyze the stability of a bacterial suspension confined in a channel with an imposed cross-channel gradient of a chemical to which bacteria chemotactically respond. In the stationary base state without any fluid flow, the chemotaxis of bacteria leads to a net bacterial orientation along the chemical gradient direction and the chemotactic and diffusive fluxes of bacteria balance to yield an exponentially varying base-state bacterial concentration field across the channel. At the continuum level, the swimming induced forcedipoles of bacteria lead to an exponentially varying normal stress field across the channel and we show that such a base state is linearly unstable to fluctuations in the bacterial concentration if the mean bacteria concentration exceeds a critical value. This instability involves a coupling between the bacteria-stressdriven fluid flow and the bacterial concentration field and it leads to cellular convective patterns in the channel. Finally, we experimentally study the nearcontact-line dynamics of evaporating sessile drops of bacterial suspensions in which the evaporation-induced fluid flow results in accumulation of bacteria near the contact-line through the well-known "coffee ring" effect. Our experiments reveal a collective behavior of bacteria near the contact-line appearing in the form of periodic bacterial "jets" along the circumference of the drop. A qualitative reasoning of the problem suggests the possibility of a concentration instability driven by the active stress of swimming bacteria.