Resistive Force Theory-Based Analysis of Magnetically Driven Slender Flexible Micro-Swimmers

Abstract

Resistive force theory is concise and reliable approach to resolve flow-induced viscous forces on submerged bodies at low Reynolds number flows. In this paper, the theory is adapted for very thin shell-type structures, and a solution procedure within a nonlinear finite element framework is presented. Flow velocity proportional drag forces are treated as configuration-dependent external forces and embedded in a commercial finite element solver (ABAQUS) through user element subroutine. Furthermore, incorporation of magnetic forces induced by external fields on magnetic subdomains of such thin-walled structures is addressed using a similar perspective without resolving the magnetic field explicitly. The treatment of viscous drag forces and the magnetic body couples is done within the same user element formalism. The formulation and the implementation are verified and demonstrated by representative examples including the bidirectional swimming of thin strips with magnetic ends.