Effect of surface roughness on laminar liquid flow in micro-channels

There are three prominent theories with regard to the effects of surface roughness on the pressure drop of laminar liquid flow in micro-channels, the original constricted flow model, the constricted model containing roughness distribution and the roughness–viscosity model. However, they have only been validated with very limited data by the authors. To provide a more reliable guide for various micro-channel applications, a review of these theories was conducted based upon the broad experimental data in literature. It is found that all the normalized data of fRe can be predicted by the original constricted flow model within an error of about ±15%. It is possible that the constricted model containing roughness distribution and the roughness–viscosity model can be further improved for easier use. However, the data, which support these two theories, can also be predicted well by the original constricted flow model with similar accuracy. Furthermore, the dependence of the critical Reynolds number (transition to turbulent flow) on the relative roughness of micro-channels was examined based upon the broad and much scattered experimental data. It is interesting to find that the effects of large discrete roughness on the side walls of shallow micro-channels follow the roughness correlation of macro-channels. The critical Reynolds numbers for different kinds of rough micro-channels were correlated respectively.