Modeling a two-link rigid swimmer scalloping in linear viscoelastic fluid

Abstract

In his renowned lecture on Life at low Reynolds number, E.M. Purcell established that a rigid swimmer comprised of two links cannot swim in a viscous Newtonian fluid due to the reciprocal nature of its movements. Viscoelastic fluid, on the other hand, has a characteristic time scale associated with stress relaxation and can impart asymmetrical stresses on the body of a swimmer to propel it forward. This work focuses on developing a theoretical model for the fluid-structure interactions that influence the swimming of a two-link specimen in viscoelastic fluid. Because the oscillation of the slender rods that comprise the links of the swimmer elicit a response from the surrounding fluid at various frequencies, the modeling consisted of a complex Fourier analysis. This paper discusses in detail the physics of the specimen's swimming and the equations that govern its movement in the fluid. The work done has been purely theoretical; however, a numerical simulation to validate the theory will be conducted as future work.