Fractal Analysis of Power-Law Fluid in a Single Capillary

The fractal expressions for flow rate and hydraulic conductivity for power-law fluids in a single capillary are derived based on the fractal nature of tortuous capillaries. Every parameter in the proposed expressions has clear physical
meaning. The flow rate and hydraulic conductivity for power-law fluids are found to be related to the tortuosity fractal dimension and the power-law index. The flow rate for power-law fluids increases with the increasing power-law index but decreases with the increasing tortuosity fractal dimension. Good agreement between the model predictions for flow in a fractal capillary and in a converging--diverging duct is obtained. The results suggest that the
fractal capillary model can be used to model the power-law fluids with different rheological properties.