A fractal analysis of laminar flow resistance in roughened microchannels

The fractal geometry theory and method are used to simulate the rough surface topography. The pressure gradients, friction factors and Poiseuille numbers for laminar flow through microchannels with roughened surfaces are derived. The proposed fractal models for the relative increases of the pressure gradient, friction factor, and the Poiseuille numbers of laminar flow through microchannels with roughened surfaces are found to be a function of the microstructural parameters of roughness surfaces. These parameters are the fractal dimension, maximum peak, minimum peak, and the ratio of the minimum diameter to the maximum diameter of conic peaks on roughened surfaces. Moreover, every parameter in the proposed models has clear physical meaning. The model predictions are compared with those of the existing measurements. Fair agreement between the fractal model predictions and experimental data is found.