Collective Hydrodynamics of Swimming Bacteria: A Living Fluid

Cornell University, Ithaca NY

Investigators

Abstract

National Science Foundation - Division of Chemical &Transport Systems ? Particulate & Multiphase Processes Program (1415) Proposal Number: 0730579 Principal Investigators: Koch, Donald Affiliation: Cornell University Proposal Title: Collective Hydrodynamics of Swimming Bacteria: A Living Fluid Suspensions of swimming micro-organisms such as the bacterium E. coli constitute a unique type of non-Newtonian fluid that can exhibit a negative-viscosity instability, enhanced mixing by secondary flows resulting from a negative first normal stress difference, break up due to concentration-gradient-induced stresses, and migration phenomena that facilitate novel separation methods. While the physical mechanism by which a single bacterium swims, pushing itself through the fluid with a flagella bundle that turns like a screw, is well understood, the equations of motion governing a suspension of bacteria have not been derived previously. In the proposed study, we will derive these equations starting from a fundamental description of bacteria-fluid interactions, solve the equations for several representative flows, and observe these flows experimentally. Intellectual Merit: A bacteria cell exerts a drag force on the fluid while its flagella exert an equal and opposite force, leading to a force dipole which on average creates a pressure in the direction of mean cell orientation. This situation may be contrasted with a stretched polymer which exerts a tension in the direction of its orientation. In a weak shear flow, a bacterium orients with the extensional axis of the flow and reinforces the extensional motion. Thus, above a critical cell concentration, the suspension has a negative viscosity and a quiescent suspension will be unstable to the formation of spontaneous fluid motion. We believe that this instability explains previous experimental observations of vortical motions in systems of swimming bacteria. We plan to use particle tracking of both bacteria and passive colloidal particles to probe this instability. The alignment of bacteria along streamlines in a strong shear flow will create a negative first normal stress difference (or streamline pressure) in contrast to the positive first normal stress difference (or streamline tension) for polymer solutions. Both non-Newtonian fluids can enhance mixing due to secondary flows caused by streamline curvature in a curved microfluidic channel, but, as we shall confirm, the vortices will be centered on the inside of a channel bend for bacteria and on the outside for a polymer solution. Broader Impacts: The applications of our studies include a novel method to separate bacteria based on their chemotactic behavior, a new ?active? fluid for micro-fluidic mixing whose activity can be modulated by biochemical inputs, and insights into the manner in which cells disperse or collect themselves into clusters as they respond to biochemical cues. People have a natural curiosity about the collective behavior of living things. Our studies which link such collective behaviors to the principles of momentum and mass transport and kinetic theory descriptions of suspensions will provide a means to engage and inspire students to think about connections between biology and engineering. We will exploit these opportunities in our undergraduate and graduate curricula and in the Nanobiotechnology Center's outreach program for high school teachers.