A bioinspired pumping model for flow in a microtube with rhythmic wall contractions

Inspired by respiratory system in insects, in particular the rhythmic wall contractions found in insect's tracheal tubes, we propose a bioinspired pumping model that can work particularly well in the low Reynolds number flow regime. Incompressible, viscous flow transport in a fluid-filled axisymmetric, inelastic tube with rhythmic wall contractions is modeled using the lubrication theory. The wall contractions are prescribed via a tube profile with two indentation sites that can move with time lags with respect to each other. The analytical model is validated using the method of fundamental solutions based on the Stokeslets-meshfree computational method. The velocity field, pressure and time averaged net flow rate induced in a complete contraction cycle are calculated. Results demonstrate that an inelastic tube with at least two contracting spots can produce unidirectional flow and working as pumping mechanism. The physical insight of this pumping model can be explained as follows: when the first constriction starts to increase with time while second constriction is slight, the resulting flow is distributed almost equally up and downstream. Now, if second constriction becomes large, then the flow resistance on the downstream side is larger during the decreasing phase of the first constriction, so less flow is drawn back upstream. Therefore, a unidirectional flow with net flow transport is produced.