Mass transport anisotropic diffusion

The phenomenological coefficients are important in defining the coupled phenomena. For example, the coupled processes of heat and mass transport give rise to the Soret effect (which is the mass diffusion due to heat transfer), and the Dufour effect (which is the heat transport due to mass diffusion). We can identify the cross coefficients of the coupling between the mass diffusion (vectorial process) and chemical reaction (scalar process) in an anisotropic membrane wall. Therefore, the linear nonequilibrium thermodynamics theory provides a unifying approach to examining various processes usually studied under separate disciplines. 

Note that, in contrast to hydrodynamic processes, there is no mass transport during the diffusion process, the mass velocity x,y,z) = 0 and the mass density is constant. For this reason, the diffusion in anisotropic media is described by a simplest second rank tensor D,y ... 

Eq. 2.18) and Ohm s law for electrical conduction (where the electrical conductivity is also always positive, according to Exercise 2.1 s solution). However, this is not necessarily the case for the cross-effect tensors /3 and 7. For example, in mass diffusion in a thermal gradient, the heat of transport can be either positive or negative the direction of the atom flux in a temperature gradient can then be in either direction. The anisotropic equivalent to the heat of transport relates the direction of the mass diffusion to the direction of the temperature gradient. There is no physical requirement that these quantities could not be in reversed directions, and indeed, sometimes they are. 

Transport inside the zeolite crystals occurs through diffusion inside the zeolite pores. Although it is known that diffusion in zeoHtes is generally anisotropic [40], the random orientation of the crystals inside the reactor justifies the approximation that micropore diffusion can be described as an isotropic process. A mass balance for the zeohte crystals yields for the adsorbed phase concentration Cx in the crystals... 

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