Flow in a Microchannel with Propagative-Rhythmic Membrane Contraction: A Novel Insect-Inspired Micropumping Model

A newly derived micropumping mathematical model for the flow in a microchannel with propagative-rhythmic membrane contraction is given in this study. The model is inspired by the microscale flow transport phenomena in the network architecture of tracheal tubes found in most insect respiratory systems. The lubrication theory is used to approximate the induced flow field in a microchannel with a single membrane site at low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. The model accounted for the coupling between the induced flow in the channel and propagative membrane deformation. We compare the pressure, axial pressure gradient, and axial and radial velocities in the channel, and the volumetric flow rate through the channel for propagative and non-propagative mode of membrane contractions. Unlike our previously derived pumping model "non-propagative" 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 working as micropumping mechanism.