Analysis of Small Deformation of Flexible Helical Flagellum of Swimming Bacteria

Abstract

Formulations are conducted to analyse the effect of flexible flagellum of swimming bacteria. In the present model, the single-flagellated bacterium is assumed to consist of a rigid cell body of the prolate spheroidal shape and a flexible helical flagellum. The resistive force theory is applied to estimate the forces exerted on the flagellum. The torsional as well as the bending moments determine the curvature and the torsion of the deformed rod according to the Kirchhoff model for elastic rod. The unit tangential vector along the deformed flagellum is calculated applying a generalized type of the Frenet-Serret equation, and also the deformed shape of the flagellum is obtained. © 2003, The Japan Society of Mechanical Engineers. All rights reserved.