title: Three-sphere swimmer in a nonlinear viscoelastic medium.
abstract: A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating out of phase to break reciprocal motion is analyzed. With a prescribed forcing of the rods acting on the three spheres, the swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynolds number, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlighting the effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that the three-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation of a polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in a Newtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutive relation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leading order, given a prescribed forcing between spheres.
authors.affiliation: Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom. curtis@maths.ox.ac.uk
authors.forename: Mark P
authors.initials: MP
authors.lastname: Curtis
authors.forename: Eamonn A
authors.initials: EA
authors.lastname: Gaffney
mesh_terms: D057446:Hydrodynamics; D009038:Motion; D017711:Nonlinear Dynamics; D012212:Rheology; D055682:Viscoelastic Substances
chemical_list: D055682:Viscoelastic Substances