Abstract

Bacteria survive and thrive in almost every environment on earth, including inside the human body. One factor that contributes to their success is the ability to swim relatively fast. We model a common form of motility in which long, passive flagellar filaments protruding from the cell body are turned by a rotary motor at the base of the filament; the turning filament propels the cell forward like a propellor. We model this mathematically by considering the cell and flagellum as bodies in a fluid governed by the equations of incompressible Stokes flow and use a combination of boundary element methods and the method of regularized stokeslets to numerically solve for the hydrodynamics. The cell body can typically be treated as a rigid object but the flagellum deforms in response to hydrodynamic stresses. We use a Kirchhoff rod model to describe the elastic dynamics of the flagellum and couple this with the hydrodynamic model. A remarkable diversity of bacterial morphologies exists in nature and we attempt to examine the consequences of various design parameters, such as the number and placement of flagella on the cell, the rigidity of the flagella, and the direction of thrust (pulling or pushing) from each flagellum. The motion of a bacterium near a solid surface is particularly sensitive to these factors. In addition to understanding the physics of bacterial motility, our results can be used to design bio-inspired microrobotic swimmers that perform as intended in the sometimes counterintuitive low-Reynolds-number world.

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