Analyses of Liquid Flow in Micro-Conduits

Abstract

Experimental observations of liquid microchannel flow are reviewed and results of computer experiments concerning channel entrance, wall slip, non-Newtonian fluid, surface roughness, viscous dissipation and flow instability effects on the friction factor are discussed Specifically, based on numerical friction factor analyses, the entrance effect should be taken into account for any microfluidic system. It is a function of channel length, aspect ratio and the Reynolds number. Non-Newtonian fluid flow effects are expected to be important for polymeric liquids and dense particle suspension flows. The wall-slip effect is negligible for liquid flows. For relatively low Reynolds numbers, i.e., Re > 1,200, onset to instabilities may have to be considered because of possible geometric non-uniformities, including a contraction and/or bend at the microchannel inlet as well as substantial surface roughness. Significant roughness effects, described with a new porous medium layer (PML) model, are a function of the Darcy number, the Reynolds number and cross-sectional configurations. This model was applied to micro-scale liquid flows in straight channels, tubes and rotating cylinders, and validated with experimental data sets. In contrast to published models, PML model simulations yield both an increase and decrease of the friction factor depending on the Darcy number. Viscous dissipation in microchannels is a strong function of the channel aspect ratio, Reynolds number, Eckert number, Prandtl number, and conduit hydraulic diameter. Specifically, viscous dissipation effects are quite important for fluids with low specific heat capacities and high viscosities, even for very low Reynolds numbers, i.e., ReD < 1. The viscous dissipation effect was found to decrease as the fluid temperature increases. As the aspect ratio deviates from unity, the viscous dissipation effect increases. It was found that ignoring the viscous dissipation effect could ultimately affect friction factor measurements for flows in micro-conduits. This could imply a significant amount of viscous heat generation and, for example, may diminish a projected micro-heat-exchanger performance.