Kinematics of a simple reciprocal model swimmer at intermediate Reynolds numbers

Scallop Theorem and Swimming at the Mesoscale

“…2(d)]. Notably, our swimmer dynamics is comparable to that of a neutrally buoyant deforming dumbbell at low Re f [20,21], where, indeed, self-propulsion in the direction of the small bead was also found.…”

“…1(b)], and the swimmer can be described as a puller in the investigated range of parameters. Notably, similar flow fields are also generated in neutrally buoyant deforming dumbbells [20,21], showing that the small inertia of the fluid does not qualitatively change the swimmer's behavior.…”

“…This is commonly achieved by the inertial dynamics of the fluid [17,18], here characterized by the Reynolds number Re f ¼ ρ f LŪ=η (ρ f and η being the fluid density and viscosity, L the swimmer body length, and U the average swimming speed). For example, the inclusion of inertia in the dynamics can be achieved by using steady streaming [19][20][21], vortex generation [22], or turbulent flows [23]. The possibilities for the exploitation of the swimmer's own inertia were first suggested a decade ago by Gonzalez-Rodriguez and Lauga [24], opening the debate on and additional investigations of swimming in this regime [20,21,25].…”

“…For example, the inclusion of inertia in the dynamics can be achieved by using steady streaming [19][20][21], vortex generation [22], or turbulent flows [23]. The possibilities for the exploitation of the swimmer's own inertia were first suggested a decade ago by Gonzalez-Rodriguez and Lauga [24], opening the debate on and additional investigations of swimming in this regime [20,21,25]. Interestingly, recent experiments and simulations have shown that mesoscopic structures, i.e., 100 μm to 1 cm in scale, display coasting effects [26][27][28] while generating fluid flows with a time-reversible behavior [29,30].…”

“…With no fitting parameters, the agreement is excellent, with the error not exceeding 10%. The strongest deviations are found around the peak velocity, where the nonzero fluid inertia may play a small role [18,20,21]. Furthermore, from reading out the stroke amplitude obtained in experiments, the measured velocities can be compared to the model using Eq.…”