Fluid Inertia and the Scallop Theorem

Our paper on Fluid inertia and the scallop theorem has been submitted and is on the arXiv. This was a collaboration with Chris Rycroft and Nick Derr.

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim.

Recent work has investigated a simple model swimmer, an asymmetric spherical dimer of oscillating length, in a variety of contexts. Analytical, numerical, and experimental studies have shown a dense (i.e. inertial) dimer swims in Stokes flow. Similarly, numerical study shows a dimer in fluid of intermediate Reynolds number (Re = 1-1000) swims in a direction that varies depending on the degree of fluid inertia. Here, we introduce a general model for the inertial flow produced by an oscillating dimer at small amplitudes. We find the model's predictions match those of the dense Stokes swimmers in the appropriate limit, and that the behavior in inertial fluid is consistent with previous numerical analysis.

March 10, 2022