Shallow Deformable Microfluidics: A passive Stokes flow rectifier for Newtonian fluids

Directional dependence of hydrodynamic resistance in asymmetrically-shaped microchannels results in fluid flow rectification. Rigid nozzle/diffuser microchannels are widely used to rectify a fluid flow at sufficiently high Reynolds numbers (Re >>1), wherein the underlying mechanism is directional dependence of the hydrodynamic resistance due to the non-linear nature of the Navier-Stokes equations. Under the Stokes flow regime (Re << 1), however, the inertial terms forming the non-linear behavior of the governing equations diminish, causing the Newtonian fluid flow through a rigid nozzle/diffuser microchannel to exhibit a direction-independent hydrodynamic resistance disallowing the fluid flow rectification. In this work, we present an alternative approach to introducing nonlinear effects to the equations of motion for Stokes flow of Newtonian fluids by using the framework of deformable microchannels. The proposed nonlinearity stems from the coupled fluid-solid mechanics of the flow behavior in an asymmetrically-shaped microchannel with deformable ceiling. The flow rectification ratio of ∼ 1.4 has been theoretically and experimentally demonstrated for common Newtonian fluids like water and alcohol.