Oscillatory Flow Networks with Valves

Zero Reynolds number Newtonian fluids exhibit perfect time-reversal symmetry even when flowing through highly asymmetric static geometries. However, flexible structures coupled to fluid forces can act as valves and promote preferential flow in one direction. Inspired by the lymphatic system, we study the flow response of a system driven by peristalsis through channels containing valves. Taken together, peristalsis with valves can act like a pump to drive fluid against adverse pressure gradients. When the valve asymmetry is small, the flow response can be decoupled into a purely peristalsis term and a term describing the rectification of oscillations by valves. When the valve asymmetry is large, flow is prevented in the reverse direction, so even at large amplitudes, retrograde peristalsis cannot drive flow against the valve direction. In this regime, the flow is independent of the direction of peristaltic waves and grows proportional to the amplitude of peristalsis. This observation has been confirmed experimentally and quantified using a non-reciprocity metric analogous to that in mechanical meta-materials. This effect becomes even more apparent in networks with branches and loops where it is argued that valves should be placed in such a way as to prevent percolating clusters containing no valves.