Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number recent works have investigated dimer models that swim at intermediate Reynolds numbers ${\textit Re} \approx 1$ –1000. These show interesting results (e.g. switches direction as a function inertia) but vary seem to be case specific. Here, we introduce general model investigate behaviour an asymmetric spherical oscillating length for small-amplitude motion {Re}}$ . our analysis make important distinction between particle fluid both which need considered separately. We asymptotically expand Navier–Stokes equations in limit obtain system linear partial differential equations. Using combination numerical (finite element) analytical (reciprocal theorem, method reflections) methods solve dimer's speed there are two mechanisms give rise motion: boundary conditions (an effective slip velocity) stresses. Each mechanism driven by classes sphere–sphere interactions, one sphere's (1) background flow induced other's motion, (2) geometric asymmetry presence. thus unify explain behaviours observed other works. Our how sensitive, counterintuitive rich motility parameter space finite inertia particles fluid.