Tortuosity tensor

Symbols for Chemical Mass Transfer and Reaction Rates f tortuosity tensor... 

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,... 

It is important to remember that this analysis has been simplified on the basis of equation 1.101 which is equivalent to treating Cy as a constant as indicated in equation 1.102. For a porous medium that is isotropic in the volume-averaged sense, the tortuosity tensor takes the classical form... 

Here e(r) is the measured void fraction in pores of radii less than r. The permeability B and the tortuosity K(r) are symmetric second-order tensors according to the preceding two equations they can be predicted as integrals over r and f but are better obtained by fitting Eq. (3.4-11) to material flux measurements for the given porous solid. 

Standard deviation Stress tensor Time, tortuosity Viscous stress tensor Wall shear stress Variable... 

In the last expression, tortuosity t > 1 was added as a generalized factor to allow for a correction factor if the capillaries are not straight. Then, Th should be used instead of h [19]. Obviously, the other approach exploiting the permeability tensor offers better opportunity to account for the internal geometry of the porous medium because many theoretical predictions are... 

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