On the peristaltic pumping

Abstract

Peristaltic pumping in a two-dimensional conduit using vibrations in the form of traveling waves has been investigated. Two qualitatively different responses producing vastly different flow rates have been identified, with a transition occurring at wavelengths of the order of the conduit opening. The flow rate is always proportional to the wave phase speed and the second power of the amplitude. Long waves produce sloshing which extends across the whole conduit producing a small, nearly wave-number-independent flow rate. The use of such in-phase waves on both walls nearly eliminates this flow while the use of out-of-phase waves maximizes it. Short waves affect the near-wall regions, which appear to the bulk of the fluid as moving walls. Such waves produce an order of magnitude larger flow rate, with its magnitude increasing proportionally to the second power of the wavenumber. Each vibrating wall produces its own wall boundary layer with an unmodulated core flow in the central zone of the conduit. The core flow looks like a Couette flow and reduces to a plug flow when both waves have identical amplitudes. The phase difference between such waves does not affect the flow rate. Wave tilting increases the flow rate similarly to the increase in distance between these waves. The use of waves characterized by a combination of wavenumbers increases the flow rate but only when the commensurability index is greater than one. The best performance is achieved by concentrating all wave energy in a single and largest achievable wavenumber.

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