Effect of tapering on elastic filament microswimming under planar body actuation

Abstract

This paper is concerned with microswimming of elastic filaments at low Reynolds number. The microswimmer is composed of a rigid spherical head attached to an elastic filament tail of varying cross section (taper). The swimming is actuated by periodic planar oscillation of slope at the head–tail junction. The actuation mechanism is considered to be embedded in the head body sending flexural waves traveling down the filament length. This causes elastohydrodynamic interactions between the filament and the fluid producing a net propulsive thrust on the head. The swimming speed is calculated by balancing this thrust against the viscous drag on the swimmer head. The paper analyzes effects of filament tapering on the propulsive thrust, swimming speed and energy efficiency. Three types of taper functions (linear, quadratic and exponential) are analyzed within the small amplitude approximation of the governing equations assuming filament inextensibility. The simulation results are generated with respect to the variations of filament length, taper ratio and actuation frequency. The analysis concludes that the nonlinear taper (quadratic and exponential) enhances the performance of microswimmer by 1 to 2 orders of magnitude in comparison to the linearly tapered and the uniform cross section (non-tapered) filaments.