From Single to Many: Swimming at Intermediate Reynolds Numbers

We propose a simple, self-propelled model swimmer which uses steady streaming flows for propulsion at intermediate Reynolds numbers (Re). Our model swimmer is composed of two unequal spheres that are tethered and oscillate in antiphase. For all Re>0, our reciprocal swimmer swims and interestingly, as Re increases, switches swimming direction from a small-sphere-leading to a large-sphere-leading regime. Varying a broad range of parameters (viscosity, amplitude, distance between the spheres, sphere radii and sphere-radii ratio), we identify a universal swimming transition at a critical Re. Flow fields are analyzed, and we determine that propulsion occurs as a result of the interfering steady streaming flows of the two spheres forced to oscillate close to one another. We also show that their bi-directional behavior is linked to their reversal in steady streaming flows. We continue by investigating interactions between multiple swimmers in both swimming regimes.