Numerical Analysis of Small Deformation of Flexible Helical Flagellum of Swimming Bacteria

Abstract

Formulations are conducted to numerically analyze the effect of flexible flagellum of swimming bacteria. In the present model, a single-flagellate bacterium is assumed to consist of a rigid cell body of the prolate spheroidal shape and a flexible flagellum of the helical form. The resistive force theory is applied to estimate the force exerted on the flagellum. The torsional as well as the bending moments determine the curvature and the torsion of the deformed flagellum according to the Kirchhoff model for an elastic rod. The unit tangential vector along the deformed flagellum is calculated by applying evolution equations for space curves, and also a deformed shape of the flagellum is obtained.