Blood Flow in Prefractal Media: Rheological Model Approaches and Sensitivity Analysis

The development of microfluidic media supporting blood flow is significant for many applications. Prefractal models have considerable potential for contributing to the study of flow in these media, since information about scale complexity is captured by a small number of parameters. Flows of power law fluids, Bingham fluids and described by the marginal zone theory are considered. In this study, physically based models for estimating the permeability of a microfluidic porous materials are presented. Models are derived assuming that media are represented by a bundle of tortuous capillary tubes with fractal pore-size distributions. They are expressed in terms of porosity, microstructural parameters and fluid characteristics. Expressions for the flow resistance through single tortuous tubes, and the relationship between fluid velocity through tortuous tubes and through straight tubes, in terms of fractal dimensions, are also obtained.