Finite-length swimmer in a nonlinearly viscoelastic fluid

Many swimming microorganisms naturally encounter non-Newtonian, viscoelastic fluids, including mucus in airways, the stomach, and the reproductive tract. Most of the analytical work on swimming in such complex media has involved swimmers of infinite length, in both two-dimensional and three-dimensional geometries. I present an analytic calculation of a finite-length three-dimensional swimmer, the Golestanian 3-sphere swimmer, in the limit of small sphere radius relative to sphere separation and small displacement relative to sphere radius. I discuss the effect of nonlinear viscoelasticity on the swimming speeed and on the internal forces exerted by the spheres on one another. Finite-length corrections occur at second order in displacements, the same order as the Newtonian swimming speed and the viscoelastic corrections observed for infinite swimmers. For this finite-length swimmer, viscoelastic corrections to the swimming speed rely on spatial asymmetry in the swimming stroke amplitude.