Low Reynolds Number Swimming with Slip Boundary Conditions

Abstract

We investigate the classical Taylor's swimming sheet problem in a viscoelastic fluid, as well as in a mixture of a viscous fluid and a viscoelastic fluid. Extensions of the standard Immersed Boundary (IB) Method are proposed so that the fluid media may satisfy partial slip or free-slip conditions on the moving boundary. Our numerical results indicate that slip may lead to substantial speed enhancement for swimmers in a viscoelastic fluid and in a viscoelastic two-fluid mixture. Under the slip conditions, the speed of locomotion is dependent in a nontrivial way on both the viscosity and elasticity of the fluid media. In a two-fluid mixture with free-slip network, the swimming speed is also significantly affected by the drag coefficient and the network volume fraction.