Laminar,transitional and turbulent friction factors for gas flows in smooth and rough microtubes

Theoretical and experimental works on microscale transport phenomena have been carried out in the past decade in the attempt to analyze possible new effects and to assess the influence of downscaling on the classical correlations which are used in macro-scale heat and fluid flow, following the need to supply engineers with reliable tools to be used in the design of micro-scale devices. These results were sometimes in mutual contrast, as is the case for the determination of the friction factor, which has been found to be lower, higher or comparable to that for macroscopic channels, depending on the researchers. In this work the compressible flow of nitrogen inside circular microchannels from 26 μm to 508 μm in diameter and with different surface roughness is investigated for the whole range of flow conditions: laminar, transitional and turbulent. Over 5000 experimental data have been collected and analysed. The data confirmed that in the laminar regime the agreement with the conventional theory is very good in terms of friction factors both for rough and smooth microtubes. For the smaller microchannels (<100 μm) when Re is greater than 1300 the friction factor tends to deviate from the Poiseuille law because the flow acceleration due to compressibility effects gains in importance. The transitional regime was found to start no earlier than at values of the Reynolds number around 1800. Both smooth and sudden changes in the flow regime have been found, as reported for conventional tubes. Fully developed turbulent flow was attained with both smooth and rough tubes, and the results for smooth tubes seem to confirm Blasius' relation, while for rough tubes the Colebrook–White correlation is found to be only partially in agreement with the experimental friction factors. In the turbulent regime the dependence of the friction factor on the Reynolds number is less pronounced for microtubes than the prediction of the Colebrook–White correlation and the friction factor depends only on the microtube “relative roughness”.