Numerical Analysis of the 3D Flow Induced by Propagation of Plane-Wave Deformations on Thin Membranes Inside Microchannels

Propulsion mechanisms of microorganisms are based on either beating or screw-like motion of thin elastic biopolymers. Arguably, this motion is optimal for propulsion at very low Reynolds numbers. Similar actuation mechanisms can be utilized in the design of an autonomous microswimmer or even a micropump. In principle, propagation of plane-wave deformations on a thin-membrane placed inside a channel can lead to a net flow in the direction of the wave propagation. In this study we present effects of the amplitude, frequency, and the width of the membrane on the time-averaged flow rate and the rate of work done on the fluid by the membrane by means of three-dimensional transient simulations of flows induced by plane-wave deformations on membranes. Navier-Stokes and continuity equations are used to model the flow on a time-varying domain, which is prescribed with respect to the motion of the membrane. Third party commercial software, COMSOL, is used in to solve the finite-element representation of the 3D time-dependent flow on moving mesh. Numerical simulations show that the flow inside the microchannel depends on the square of the amplitude and is proportional to the excitation frequency. Lastly, characteristic flow rate vs. pressure head curve and efficiency of a typical pump are obtained from 3D transient simulations, and presented here.