On Laminar Flow in Microfabricated Channels with Partial Semi-Circular Profiles

Abstract

Soft and hard micromachining techniques used to develop microfluidic devices can yield microchannels of many different cross-sectional profiles. For semi-circular microchannels, these techniques often produce only partialsemicircular (PSC) cross-sections. This study investigated fully developed laminar flow in PSC microchannels as a function of a circularity index, κ, defined as the ratio of the radiuses along the curved and flat surfaces of the PSC profile. A correction factor, K, to the Hagen-Poiseuille relation was determined and was well-fitted by the power-law relationship K=5.299/κ2.56. Actual correction factors were compared to estimates based on several hydraulic models for flow in microchannels of arbitrary cross-section, as well as the half-ellipsoid cross-section. The level of wall shear stress, when normalized by the pressure drop per unit length, increased approximately linearly with increase in the circularity index, κ.