Role of surface roughness characterized by fractal geometry on laminar flow in microchannels

A three-dimensional model of laminar flow in microchannels is numerically analyzed incorporating surface roughness effects as characterized by fractal geometry. The Weierstrass-Mandelbrot function is proposed to characterize the multiscale self-affine roughness. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all investigated and discussed. The results indicate that unlike flow in smooth microchannels, the Poiseuille number in rough microchannels increases linearly with the Reynolds number, Re, and is larger than what is typically observed in smooth channels. For these situations, the flow over surfaces with high relative roughness induces recirculation and flow separation, which play an important role in single-phase pressure drop. More specifically, surfaces with the larger fractal dimensions yield more frequent variations in the surface profile, which result in a significantly larger incremental pressure loss, even though at the same relative roughness. The accuracy of the predicted Poiseuille number as calculated by the present model is verified using experimental data available in the literature.