Application of Lubrication Theory and Study of Roughness Pitch During Laminar, Transition, and Low Reynolds Number Turbulent Flow at Microscale

Abstract

This work aims to experimentally examine the effects of different roughness structures on internal flows in high-aspect-ratio rectangular microchannels. Additionally, a model based on lubrication theory is compared to these results. In total, four experiments were designed to test samples with different relative roughness and pitch placed on the opposite sides forming the long faces of a rectangular channel. The experiments were conducted to study (i) sawtooth roughness effects in laminar flow, (ii) uniform roughness effects in laminar flow, (iii) sawtooth roughness effects in turbulent flow, and (iv) varying-pitch sawtooth roughness effects in laminar flow. The Reynolds number was varied from 30 to 15,000 with degassed, deionized water as the working fluid. An estimate of the experimental uncertainty in the experimental data is 7.6% for friction factor and 2.7% for Reynolds number. Roughness structures varied from a lapped smooth surface with 0.2 μ m roughness height to sawtooth ridges of height 117 μ m. Hydraulic diameters tested varied from 198 μ m to 2,349 μ m. The highest relative roughness tested was 25%. The lubrication theory predictions were good for low relative roughness values. Earlier transition to turbulent flow was observed with roughness structures. Friction factors were predictable by the constricted flow model for lower pitch/height ratios. Increasing this ratio systematically shifted the results from the constricted-flow models to smooth-tube predictions. In the turbulent region, different relative roughness values converged on a single line at higher Reynolds numbers on an f–Re plot, but the converged value was dependent on the pitch of the roughness elements.