Novel characteristics of valveless pumping

This study investigates the occurrence of valveless pumping in a fluid-filled system consisting of two open tanks connected by an elastic tube. We show that directional flow can be achieved by introducing a periodic pinching applied at an asymmetrical location along the tube, and that the flow direction depends on the pumping frequency. We propose a relation between wave propagation velocity, tube length, and resonance frequencies associated with shifts in the pumping direction using numerical simulations. The eigenfrequencies of the system are estimated from the linearized system, and we show that these eigenfrequencies constitute the resonance frequencies and the horizontal slope frequencies of the system; "horizontal slope frequency" being a new concept. A simple model is suggested, explaining the effect of the gravity driven part of the oscillation observed in response to the tank and tube diameter changes. Results are partly compared with experimental findings.