It has long been known that some microswimmers seem to swim counter-intuitively faster when the viscosity of the surrounding fluid is increased, whereas others slow down. This conflicting dependence of the swimming velocity on the viscosity is poorly understood theoretically. Here we explain that any mechanical microswimmer with an elastic degree of freedom in a simple Newtonian fluid can exhibit both kinds of response to an increase in the fluid viscosity for different viscosity ranges, if the driving is weak. The velocity response is controlled by a single parameter Γ, the ratio of the relaxation time of the elastic component of the swimmer in the viscous fluid and the swimming stroke period. This defines two velocity-viscosity regimes, which we characterize using the bead-spring microswimmer model and analyzing the different forces acting on the parts of this swimmer. The analytical calculations are supported by lattice-Boltzmann simulations, which accurately reproduce the two velocity regimes for the predicted values of Γ.
In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we study a microswimmer model composed of deformable beads connected with springs. We determine the velocity of the swimmer analytically, starting from the forces driving the motion and assuming that the oscillations in the effective radii of the beads are known and are much smaller than the radii themselves. We find that to the lowest order, only the driving frequency mode of the surface oscillations contributes to the swimming velocity, and that this velocity may both rise and fall with the deformability of the beads depending on the spring constant. To test these results, we run immersed boundary lattice Boltzmann simulations of the swimmer, and show that they reproduce both the velocity-promoting and velocity-hindering effects of bead deformability correctly in the predicted parameter ranges. Our results mean that for a general swimmer, its elasticity determines whether passive deformations of the swimmer body, induced by the fluid flow, aid or oppose the motion.
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