Characterization of Surface Roughness Effects on Laminar Flow in Microchannels by Using Fractal Cantor Structures

Abstract

The fractal characterization of surface topography by using Cantor set structures is introduced to quantify the microchannel surface. Based on this fractal characterization of surface, a model of laminar flow in rough microchannels is developed and numerically analyzed in this paper. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all discussed. The results indicate that the presence of roughness leads to the form of detachment, and the eddy generation is observed at the shadow of the roughness elements. The pressure drop in the rough microchannels along the flow direction is larger than that in the smooth channel. It is no longer in a linear fashion and the fluctuation in pressure drop along the stream due to the vortex near the wall is found. Differing from the smooth channel, the Poiseuille number for laminar flow in rough microchannels is no longer only dependent on the cross-sectional shape of the channel, but also strongly influenced by the Reynolds number, roughness height, and fractal dimension (spectrum) of the surface.