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Kinematics of a simple reciprocal model swimmer at intermediate Reynolds numbers

We computationally study the kinematics of a simple model reciprocal swimmer (asymmetric dumbbell) as a function of the Reynolds number (Re) and investigate how the onset and gradual increase of inertia impacts the swimming behavior: a reversal in the swim direction, flow directions, and the swim stroke. We divide the swim stroke into the expansion and compression of the two spheres and relate them to power and recovery strokes. We find that the switch in swim direction also corresponds to a switch in power and recovery strokes. We obtain expressions for the mean swimming velocity by collapsing the net displacement during expansion and compression under power law relationships with respect to Re, the swimmer's amplitude, and the distance between the two spheres. Analyzing the fluid flows, we see the averaged flow field during expansion always resembles a pusher and compression always a puller, but when averaged over the whole cycle, the flow that dominates is the one that occurs during the power stroke. We also relate the power and recovery strokes to the swimming efficiency during times of expansion and compression, and we find that the power stroke is, surprisingly, not always more efficient than the recovery stroke. Our results may have important implications for biology and ultimately the design of artificial swimmers.