(224a) Hydrodynamic Instabilities of Chemotactic Bacteria

Over the past decade, experimental studies of swimming micro-organisms and numerical simulations of hydrodynamically interacting self-propelled particles have shown that such living fluids exhibit collective dynamical motions on length scales large compared with the size of an individual swimmer even in the absence of any hydrodynamic or chemical gradients.  A continuum theory showed that living fluids consisting of pushers such as bacteria are subject to a hydrodynamic instability that involves the coupling of the shear motion caused by the active stress produced by the swimmers and their orientation distribution.  Recent experiments, however, suggest that even more vigorous convective motions may arise in bacterial suspensions subject to chemical gradients.  In this talk we discuss a new mechanism of instability that arises from the coupling of the bacteria concentration and the competition between chemotactic driven and the convective motions produced by an active stress.  The stability of a suspension of chemotactic bacteria confined in an infinitely long channel and subjected to a stationary, linear chemo-attractant gradient is investigated. While swimming, individual bacteria exert a force dipole on the fluid which at the continuum level leads to a stress depending upon the bacterial orientation and number density fields. The presence of the attractant gradient causes bacteria to tumble less frequently when swimming along the gradient leading to a mean orientation and a non-zero chemotactic drift velocity.   A balance of the fluxes due to chemotaxis and the random run-tumble motion of bacteria yields an exponentially varying number density profile across the channel in the base state. The associated bacterial stress field is also exponentially varying and is normal. This spatially non-uniform base state is unstable to fluctuations in the bacterial concentration exceeds a critical value determined by a Peclet number defined as Pe = U₀ H/D where U₀ is the chemotactic velocity, D the run-and-tumble diffusivity and H the channel thickness.  The instability resulting from the coupling between the active stress driven fluid flow and the bacterial concentration manifests as rectangular convection patterns driven by spanwise bacterial clusters.