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We use numerical simulations to address locomotion at zero Reynolds number inviscoelastic (Giesekus) fluids. The swimmers are assumed to be spherical, toself-propel using tangential surface deformation, and the computations areimplemented using a finite element method. The emphasis of the study is on thechange of the swimming kinematics, energetics, and flow disturbance fromNewtonian to viscoelastic, and on the distinction between pusher and pullerswimmers. In all cases, the viscoelastic swimming speed is below the Newtonianone, with a minimum obtained for intermediate values of the Weissenberg number,$We$. An analysis of the flow field places the origin of this swimmingdegradation in non-Newtonian elongational stresses. The power required forswimming is also systematically below the Newtonian power, and always adecreasing function of $We$. A detail energetic balance of the swimming problempoints at the polymeric part of the stress as the primary $We$-decreasingenergetic contribution, while the contributions of the work done by the swimmerfrom the solvent remain essentially $We$-independent. In addition, we observenegative values of the polymeric power density in some flow regions, indicatingpositive elastic work by the polymers on the fluid. The hydrodynamicefficiency, defined as the ratio of the useful to total rate of work, is alwaysabove the Newtonian case, with a maximum relative value obtained atintermediate Weissenberg numbers. Finally, the presence of polymeric stressesleads to an increase of the rate of decay of the flow velocity in the fluid,and a decrease of the magnitude of the stresslet governing the magnitude of theeffective bulk stress in the fluid.

Self-propulsion in viscoelastic fluids: pushers vs. pullers