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Download Advances in Transport Phenomena in Porous Media by Yehuda Bachmat, Jacob Bear (auth.), Jacob Bear, M. Yavuz PDF

By Yehuda Bachmat, Jacob Bear (auth.), Jacob Bear, M. Yavuz Corapcioglu (eds.)

This quantity includes the lectures offered on the NATO complicated examine INSTITUTE that came about at Newark, Delaware, U. S. A. , July 14-23, 1985. the target of this assembly was once to provide and talk about chosen issues linked to shipping phenomena in porous media. by means of their very nature, porous media and phenomena of shipping of in depth amounts that occur in them, are very advanced. the cast matrix might be inflexible, or deformable (elastically, or following another constitutive relation), the void house should be occupied via a number of fluid stages. every one fluid section should be composed of multiple part, with a number of the elements able to interacting between themselves and/or with the cast matrix. The shipping approach will be isothermal or non-isothermal, without or with part alterations. Porous medium domain names within which huge amounts, akin to mass of a fluid section, portion of a fluid section, or warmth of the porous medium as an entire, are being transported ensue within the perform in quite a few disciplines.

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The coefficient k ujm - a second rank symmetric tensor - is called the Permeability of the porous medium. by Eq. 15). We recall that r* "U is defined Eq. 29) is the basic form of the motion equation for saturated flow in an anisotropic porous medium at low Reynolds numbers(defined by NRe = qp~~/~u). b) When the inertial effects are negligible, but we do wish to include the effects of internal friction, then Eq. 28) reduces to 33 + -a Clz) Pa g Clx. J o For an isotropic porous medium, rna = 0, Eq.

Hence, making use of Eq. 11), the macroscopic flux in this case takes the form d d d--a J-ay =-D ay Vc ay = - nDroy VC roy ........ 7) where n is porosity and D~~ = D~yr~ , a second rank symmetric tensor, is the coefficient of molecular diffusion in a porous medium. The coefficient r~ is defined and discussed in Appendix B. We have thus achieved our objective of replacing the missing microscopic information by a macroscopic coefficient that represents it. In a multiphase system, the fluid a-phase occupies only part of the void space.

1) to average Eq. 14), we obtain --a + de a V~a J ) dX i + ]la U0 f (S as ) ) (V~av . + Vrna J' v al. 15) where ]la is assumed constant within the REV. As a special case of interest, let us assume that (a) the fluid (that occupies the entire void space) adheres to the solid (= no slip m --a -s . , the Sas -s Sas -ssolid is approximately rigid, and, therefore, its averaged velocity on (Sas) is equal to its average over (Uos)' Then Eq. et J dX i - ), - s (v-: Sl dn dX j = + - - s dn } ) Vsj dX i 28 l1 a { --a rna Cln(V i -s Vsi ) Clx j --a rna -s -s -s ClV .

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