Three-sphere swimmer in a nonlinear viscoelastic medium

摘要

A simple model for a swimmer consisting of three colinearly linked spheres attached by rods and oscillating outnof phase to break reciprocal motion is analyzed.With a prescribed forcing of the rods acting on the three spheres,nthe swimming dynamics are determined analytically in both a Newtonian Stokes fluid and a zero Reynoldsnnumber, nonlinear, Oldroyd-B viscoelastic fluid with Deborah numbers of order one (or less), highlightingnthe effects of viscoelasticity on the net displacement of swimmer. For instance, the model predicts that thenthree-sphere swimmer with a sinusoidal, but nonreciprocal, forcing cycle within an Oldroyd-B representation ofna polymeric Boger fluid moves a greater distance with enhanced efficiency in comparison with its motility in anNewtonian fluid of the same viscosity. Furthermore, the nonlinear contributions to the viscoelastic constitutivenrelation, while dynamically nontrivial, are predicted a posteriori to have no effect on swimmer motility at leadingnorder, given a prescribed forcing between spheres.