Rate invariance and scallop theorem in viscosity gradients

Self-propulsion at low-Reynolds numbers requires a swimmer to deform its body in a non-reciprocal manner in order to achieve locomotion (i.e. the sequence of shapes taken by the body must be different from the same sequence played in reverse). This is known as Purcell's scallop theorem, and it is fundamental for the study of both biological and artificial microorganisms. This theorem is only valid for an inertialess, force- and torque-free swimmer moving in an unbounded and otherwise quiescent Newtonian fluid. Mechanisms have been proposed to allow locomotion of reciprocal swimmers, including finite inertia, elasticity in the fluid, and hydrodynamic interactions. Recent studies have focused their attention on the dynamics of low-Reynolds number swimmers moving in fluids of variable viscosity. Since a non-homogeneous viscosity breaks the translational symmetry of the swimmer's environment, in this talk we ask the question: Are viscosity gradients sufficient to escape the constraints of the scallop theorem?