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Abstract
Fractal expressions for flow rate, velocity and effective permeability of Rabinowitch fluid flow in porous media are derived based on the fractal properties of porous media and capillary model. Each parameter in the proposed expressions does not contain any empirical constant and has clear physical meaning and the proposed fractal models relate the flow properties of Rabinowitch fluid with the structural parameters of porous media. The presented analytical expressions help to understand the physical principles of Rabinowitch fluid through porous media.
Highlights
The Rabinowitch fluid is one of non-Newtonian fluids and its constitutive equation is Chen (1992): (1)where, = Shear rate= Shear stress and a = Material constants that describe the properties of fluids The Rabinowitch fluid model may be reduced to the Newtonian fluid model when a = 0
It has been shown that the pore size distribution in porous media follows the fractal power law, so, the total flow rate Q through a cross-section can be obtained by integrating Eq (7) over the entire range of pore sizes from the minimum pore size to the maximum pore size:
It is seen from Eq (9) and (13) that the flow rate Q and average velocity V for Rabinowitch fluid in porous media are related to the structural parameters of porous media and to the fluid characteristic parameters (μ and a)
Summary
= Shear stress and a = Material constants that describe the properties of fluids The Rabinowitch fluid model may be reduced to the Newtonian fluid model when a = 0. Fractal model for Rabinowitch fluid is derived based on the fractal characters of porous media. The cumulative size distribution of pores in porous media follows the fractal scaling law (Yu and Cheng, 2002): N (L r) ( rmax )D f
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