Low-Reynolds-number swimming in gels

Division of Engineering, Brown University - Providence, RI 02912, USA

^a hfu@unr.edu

Received: 6 April 2010
Accepted: 16 July 2010

Abstract

Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling-wave deformations in the “two-fluid” model of a gel, which treats the network and solvent as two coupled elastic and viscous continuum phases. We show that geometric nonlinearities must be incorporated to obtain physically meaningful results. We identify a transition between regimes where the network deforms to follow solvent flows and where the network is stationary. Swimming speeds can be enhanced relative to Newtonian fluids when the network is stationary. Compressibility effects can enhance swimming velocities. Finally, microscopic details of sheet-network interactions influence the boundary conditions between the sheet and network and the boundary conditions significantly impacts swimming speeds.