Mathematical Model for Fluid Flow in Artificially Roughened Microchannels

Two dimensional lubrication approximation is applied to the analysis of fluid flow in a rectangular microchannel with structured roughness. Each of two major walls is composed of designed microscale transverse ribs, modeled by two-dimensional functions. A pressure drop correlation is formed as a direct function of these surface equations and the resultant velocity profile is incorporated into boundary layer analysis. Friction factors are calculated based on the obtained pressure drop values for comparison with conventional theory. The method presented here is consistent with conventional correlations in the case of hydraulically smooth channels, and is a stronger function of structured roughness geometry than the existing methods.