|Title:||Asymptotic and numerical analysis of PDE models for suspensions of micro-swimmers: interaction and effective viscosity.|
|Seminar:||CCMA Luncheon Seminar|
|Speaker:||Vitaliy Gyrya, Penn State University, Mathematics Department|
|      Recently, there have been a number of experimental studies convincingly demonstrating that a suspension of self-propelled bacteria (microswimmers in general) may have an effective viscosity significantly smaller than the viscosity of the fluid without inclusions.
This is in sharp contrast with suspensions of rigid passive inclusions, whose presence always increases the effective viscosity.|
We introduce two PDE models for a suspension of microswimmers in a Newtonian fluid and study their well-posedness. The first model was used for an asymptotic study of swimmer-swimmer interactions at large distances (with L. Berlyand, I. Aronson, and D. Karpeev).
The second model (with K. Lipnikov, I. Aronson, and L. Berlyand) was used to analyze the effective viscosity of suspensions of microswimmers in two regimes:
- small concentration (dilute, no swimmer-swimmer interactions)
- moderate concentration (all swimmer-swimmer and swimmer-fluid interactions resolved).
The dilute regime was studied analytically using symmetries of the model, the background flow, and the swimmers. The moderate concentration regime is not tractable for analytical analysis and therefore was studied numerically, using the novel Mimetic Finite Difference discretization for Stokes equation (developed jointly with L. Beirao da Veiga, K. Lipnikov and G. Manzini). Our theoretical results agree with experiments performed at Argonne. Based on our analysis, we were able to identify and explain the nature of the mechanisms responsible for the decrease of the effective viscosity in physical experiments.
Room Reservation Information
|Date:||10 / 16 / 2009|
|Time:||12:00pm - 01:30pm|