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 |
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| Seminar: | Seminar on Probability and its Application |
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| Speaker: | Brian Haines, PSU |
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| Abstract: |
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| 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 |
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| Date: | 09 / 25 / 2009 |
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| Time: | 02:30pm - 03:25pm |
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