A one-dimensional model for compressible fluid flows through deformable microchannels

Abstract

Fluid-structure interactions in low-Reynolds-number flows have received an increasing interest due to emerging bio-applications of deformable microfluidics. We utilize the lubrication theory and wide-beam framework to develop a one-dimensional coupled fluid-solid-mechanics model for the prediction of the characteristic behavior of compressible fluid flows through deformable microchannels. An explicit relationship is extracted for the mass flow rate as a function of pressure difference across a microchannel, undeformed channel dimensions, and properties of channel’s ceiling such as thickness, modulus of elasticity, and Poisson’s ratio. The resulting fifth-order algebraic equation is also solved numerically to obtain the pressure distribution within the microchannel. As a special case for compressible fluid flows, the characteristics of ideal gas flows are extracted from the general model. Rigid and deformable microchannels are fabricated, and the mass flow rates of air through the channels are measured under various pressure differences across the channels. The proposed model predicts the mass flow rate with an acceptable accuracy. Our experimental and theoretical results highlight the importance of fluid compressibility and microchannel deformability, demonstrating that neglecting either of them under sufficiently large pressure differences can lead to erroneous results. To the best of the authors’ knowledge, this is the first theoretical model simultaneously addressing both fluid compressibility and microchannel deformability for an equilibrium pressure-driven compressible fluid flow in microscale.