  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.
