A depth-averaged model for Newtonian fluid flows in shallow microchannels

Abstract

Pressure-driven flow has been widely used in microfluidic devices to pump fluids and particles through planar microchannels for various applications. The variation in channel geometry (e.g., contraction or expansion) may lead to complex flow phenomena (e.g., recirculations) useful for microfluidic sampling, such as fluid mixing and particle focusing. In this work, we develop a depth-averaged inertial flow model for Newtonian fluids in shallow microchannels based on an asymptotic analysis of the continuity and momentum equations. The validity and accuracy of this two-dimensional model are assessed through comparisons with the experimental measurements and three-dimensional numerical simulations for water flow through contraction–expansion microchannels of varying depths. Our proposed depth-averaged model provides the accuracy of three-dimensional modeling if the channel depth-to-width ratio remains small (specifically, at ∼0.1 or less).