Fractal characteristics of surface roughness and its effect on laminar flow in microchannels

Abstract

The fractal characteristics of the surface roughness are investigated by using fractal geometry. A three-dimensional model of laminar flow in microchannels with surface roughness characterized by fractal geometry is developed and analyzed numerically. The Weierstrass-Mandelbrot function is introduced to characterize the multiscale self-affine roughness. The effects of Reynolds number Re， relative roughness， and fractal dimension on Poiseuille number are investigated and discussed. The results show that， different from the conventional channels， Poiseuille number in rough microchannels is no longer constant for different Re， but increases approximately linearly with Re， and is larger than the classical value. The flow over roughness features with high relative roughness induces recirculation and flow separation， which plays an important role in flow pressure drop. More specifically， roughness with larger fractal dimension， which yields more frequent variation in the surface profile， also results in a significant increase in pressure loss， even though at the same relative roughness. In addition， the accuracy of Poiseuille number calculated by the present model is verified by the experimental data available in the literature.