Sookkyung Lim (University of Cincinnati)-Hydrodynamics of bundling/unbundling helical flagella driven by rotary motors
Mathematics - Colloquium
Friday, October 5, 2012
11:00 AM-12:00 PM
ABSTRACT: The immersed boundary (IB) method was originally developed to study the fluid dynamics of heart valves, which are elastic membranes immersed in viscous fluid. The IB method has been generalized in many ways and applied to many biological problems. In this talk, we present a general version of the immersed boundary method combined with the unconstrained Kirchhoff rod theory, which is applied to study the fluid dynamics of bacterial flagella in bundle formation.
A thin elastic flagellar filament (rod) in the Kirchhoff model that resists bending and twisting can be modeled as a ``three-dimensional space curve'' together with an orthonormal triad (material frame) at each point of the rod. The space curve represents the centerline of the rod and the triad indicates the amount of bend and twist. This is a well-established theory in the statics and dynamics of thin elastic filaments without fluid. Combining Kirchhoff rod theory with the standard models of viscous incompressible fluids will allow us to study the complicated hydrodynamics of bacterial swimming. In the original IB method, the immersed boundary interacts with the fluid by moving at the local fluid velocity and applying force locally to the fluid. In the generalized method, the interaction of the immersed boundary with the fluid now involves not only translation of the immersed boundary points at the local fluid velocity, but also rotation of the associated triads at the local fluid angular velocity.
This new version is very useful to study biological fluid mechanics of filamentous structures such as bacterial flagella, DNA strand, and sea cable.
Suggested Audiences: Adult, College
Last Modified: September 18, 2012 at 10:48 AM