A passive Stokes flow rectifier for Newtonian fluids

Abstract

Non-linear effects of the Navier–Stokes equations disappear under the Stokes regime of Newtonian fluid flows disallowing a flow rectification behavior. Here we show that passive flow rectification of Newtonian fluids is obtainable under the Stokes regime of both compressible and incompressible flows by introducing nonlinearity into the otherwise linear Stokes equations. Asymmetric flow resistances arise in shallow nozzle/diffuser microchannels with deformable ceiling, in which the fluid flow is governed by a non-linear coupled fluid–solid mechanics equation. The proposed model captures the unequal deflection profile of the deformable ceiling depending on the flow direction under the identical applied pressure, permitting a larger flow rate in the nozzle configuration. Ultra-low aspect ratio microchannels sealed by a flexible membrane have been fabricated to demonstrate passive flow rectification for low-Reynolds-number flows (0.001 < Re < 10) of common Newtonian fluids such as water, methanol, and isopropyl alcohol. The proposed rectification mechanism is also extended to compressible flows, leading to the first demonstration of rectifying equilibrium gas flows under the Stokes flow regime. While the maximum rectification ratio experimentally obtained in this work is limited to 1.41, a higher value up to 1.76 can be achieved by optimizing the width profile of the asymmetric microchannels.