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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.
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Yun et al. (2008) studied this question.
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