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.