Valveless pumping at low Reynolds numbers

Pumping at low Reynolds number is a ubiquitously encountered feature, both in biological organisms and engineered devices. Generating net flow requires the presence of an asymmetry in the system, which traditionally comes from geometric flow rectifiers. Here, we study a valveless system of $N$ oscillating pumps in series, where the asymmetry comes not from the geometry but from time, that is the phase shifts between the pumps. Experimental and theoretical results are in very good agreement. We provide the optimal phase shifts leading to the maximal net flow in the continuous $N\rightarrow \infty$ limit, larger by 25\% than that of a traditional peristaltic sinusoidal wave. Our results pave the way for the design of more efficient microfluidic pumps.