Fractal characterization of wall roughness on pressure drop in microchannels

In this paper, a fractal dimension D for wall roughness in microchannels on <110> silicon wafers is calculated. The fractal dimension of wall roughness in these microchannels fabricated at different etching conditions is found to be in the range from 1.02 to 1.69. We propose that the Darcy friction factor for laminar flow in microchannels of a specific cross-sectional area is a function of the Reynolds number Re (based on the hydraulic diameter), the ratio of the wall-roughness height to the hydraulic radius of the microchannel epsilon/r, and the fractal dimension D. A correlation equation in terms of the above parameters is obtained for pressure drop in microchannels with rough surfaces. The accuracy of this correlation is found to be very good when compared with other experimental data. (C) 2003 Elsevier Science Ltd.