PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Manfred Denker.

Title:Effective Viscosity and Dynamics of Dilute Bacterial Suspensions: A Three-Dimensional Model with Stochastic Tumbling
Seminar:Seminar on Probability and its Application
Speaker:Brian Haines, PSU
We present a Stochastic PDE model for dilute suspensions of bacteria in a three-dimensional Stokesian fluid. This model is used to calculate the statistically-stationary bulk deviatoric stress and effective viscosity of the suspension from the microscopic details of the interaction of an elongated body with the background flow. A bacterium is modeled as a prolate spheroid with self-propulsion provided by a point force, which shows up in the model as an inhomogeneous delta function in the PDE. The bacterium is also subject to a stochastic torque in order to model tumbling (random reorientation). Due to a bacterium's asymmetric shape, interactions with a prescribed generic background flow, such as pure shear or planar shear, cause the bacterium to preferentially align in certain directions. Due to the stochastic torque, the steady-state distribution of orientations is unique for a given background flow. Under this distribution of orientations, self-propulsion produces a reduction in the effective viscosity. For sufficiently weak background flows, the effect of self-propulsion on the effective viscosity dominates all other contributions, leading to an effective viscosity of the suspension that is lower than the viscosity of the ambient fluid. This is in agreement with recent experiments on suspensions of Bacillus subtilis.

Room Reservation Information

Room Number:MB106
Date:09 / 25 / 2009
Time:02:30pm - 03:25pm