A model for tracheolar flow in insects

Abstract eng:
Inspired by some of the fundamental features of insect respiratory systems, we investigate the effects of rarefaction on lowReynolds number, collapse-driven flow through a microtube. The Navier-Stokes equations are linearized, a periodic wall collapse motion is prescribed at two sites along the tube, and physiologically realistic pressure boundary conditions are applied along with first-order slip boundary conditions. The axial and radial velocities, axial pressure gradient, and time averaged flow rate in the tube are found as a function of the phase lag between the two contraction sites, with and without slip. Unlike for purely pressure- or collapse-driven flows, when slip is added, this flow is highly sensitive to the phase lag parameter, and the flow can be accelerated, decelerated, or reversed, depending on its value, resulting in a multi-functional microfluidic system that can acccelerate or decelerate flow as needed with slight changes in the timing of its wall collapses.

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