Analytical and Numerical Investigations of Friction Number for Laminar Flow in Microchannels

Abstract

Analytical and computational fluid dynamics (CFD) analyses confirmed the presence of apparent slip for water flow in microchannels with equivalent hydraulic diameter, Dh < 103μm, markedly decreasing the friction number, fRein. The determined values of the slip length, β, from reported measurements of pressure losses in microchannels with aspect ratio, α = 1, 1.74, 2, and 40, are 0.9, 3.5, 1.6, and 0.125 μm, respectively. For Dh > 103μm, the apparent slip in microchannels diminishes, and the friction number approaches the theoretical Hagen–Poiseuille with no slip. The analytical solution for fully developed flow successfully benchmarked the CFD approach, which is subsequently used to investigate fRein and the flow development length, Le, for uniform inlet velocity in microchannels. For fully developed flow, the analytical and CFD values of fRein are in excellent agreement. For microchannels with Dh < 103μm, fRein decreases below that of the theoretical Hagen–Poiseuille with no slip, almost exponentially with decreased Dh. The difference increases with decreased Dh, but increased α and β. The friction number for uniform inlet velocity is identical to that for fully developed flow when Dh ≤ 100 μm, but is as much as 9% higher for larger Dh. For uniform inlet velocity, Le negligibly depends on α and β, but increases with increased Rein. The obtained values are correlated as: Le/Dh = 0.068 Rein.