Pumping flow model in a microchannel with propagative rhythmic membrane contraction

Abstract

A pumping flow model in a microchannel with a single attached membrane subjected to propagative contraction is presented in this article. The lubrication theory is used to approximate the induced flow field at a low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. Unlike our previously derived pumping model "nonpropagative" where at least two membranes that operate with time-lag are required to produce unidirectional flow, the present results demonstrate that an inelastic channel with a single membrane contraction that operates in a "propagative" mode can produce unidirectional flow and work as a micropump. The model can be used to understand flow transport in many biological systems including but not limited to insect respiration, urine flow, and fluid dynamics of duodenum and intestine. The present pumping paradigm is relatively easy to fabricate and is expected to be useful in many biomedical applications.