Porous media isotropic

Prager [302] examined diffusion in concentrated suspensions using the variational approach. (A discussion of the basic principles in variational theory is given in Ref. 6.) Prager s result is applicable to a very general class of isotropic porous media. Prager s solution for a limiting case of a dilute suspension of particles was... 

Equation 7.119 seems to be consistent with the flow in real life. The explanation may be extended to the difference between Eq. 7.103 and Eq. 7.118 at an arbitrary flow angle. Equation 7.118 appears to model the two-dimensional flow in a homogeneous and isotropic porous media. The trapping numbers for two-dimensional and three-dimensional heterogeneous, anisotropic porous media were also derived in Jin (1995). 

It should be noted that Ward (17) attempted to cast equation 6 into a more usable form by relating a and Q to the known porous medium properties for isotropic porous media. In a one-dimensional situation, Ward s model gave... 

The void area fraction in (21-76) is based on the fractional area in a plane at constant x that is available for diffusion into catalysts with rectangular symmetry. A rather sophisticated treatment of the effect of g 6) on tortuosity is described by Dullien (1992, pp. 311-312). The tortuosity of a porous medium is a fundamental property of the streamlines or lines of flux within the individual capillaries. Tortuosity measures the deviation of the fluid from the macroscopic flow direction at every point in a porous medium. If all pores have the same constant cross-sectional area, then tortuosity is a symmetric second-rank tensor. For isotropic porous media, the trace of the tortuosity tensor is the important quantity that appears in the expression for the effective intrapellet diffusion coefficient. Consequently, Tor 3 represents this average value (i.e., trace of the tortuosity tensor) for isotropically oriented cylindrical pores with constant cross-sectional area. Hence,... 

As an isotropic porous media, the porosity and permeability coefficient of the coal particle are not affected by the internal gas pressure change of coal particle (Zhou Shining 1957, Li Yunhao, et al. 2007). 

Because of the randomness of cave gangue and residual coal distribution, the goaf area is com-sidered as isotropic porous media. Permeability does not change with time ... 

Another attempt was made in 1941 by Leverett, who, using a semiempirical approach, proposed the following expression for the capillary pressure, applicable to isotropic porous media... 

Flow is more difficult to model in the unsaturated zone because hydraulic conductivity changes as water content changes. In unsaturated flow models, the Darcy-Richards equation, which is a more general form of Darcy s law, is used. For isotropic porous media in three dimensions. 

Millington (1959) envisioned a porous medium as consisting of solid spheres, which interpenetrate each other, separated by spherical pores that also interpenetrate. Based on his determination of the area available for flow in a given plane of a porous media, and the probability of the continuity of pores within two adjacent planes, Millington (1959) derived the following expression for diffusion in dry isotropic porous media ... 

Cirpka, O.A. and P.K. Kitanidis. 2001. Theoretical basis for the measurement of local transverse dispersion in isotropic porous media. Water Resources Research 37(2) 243-252. 

The gas diffusers, catalyst layers, and the PEM are considered each as isotropic porous media. 

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