Theories linear driving force approximation

Chapter 1 introduced the reader to the notion of a mass transfer coefficient and has shown the connechon to what is termed film theory. In essence, this approach assumes the resistance to mass transfer to be confined to a thin film in the vicinity of an interface in which the actual concentration gradient is replaced by a linear approximation. The result is that the rate of mass transport can be represented as the product of a mass transfer coefficient and a linear concentration difference, or concentration driving force. Thus,... 

For dilute gases, the generalized multicomponent Fickian diffusion coefficients are strongly composition dependent. It follows that these diffusion coefficients do not correspond to the approximately concentration independent binary difffisivities, Dsr, which are available from binary diffusion experiments or kinetic theory since Dgr Dsr. In response to this Fickian model limitation it has been proposed to transform the Fickian diffusion flux model, in which the mass-flux vector, jj, is expressed in terms of the driving force, dj, into the corresponding Maxwell-Stefan form [95, 97, 142, 143] where d is given as a linear function of jj. The key idea is to rewrite the Fickian diffusion flux in terms of an alternative set of difffisivities (i.e., preferably the known binary difffisivities) which are less concentration dependent than the Fickian difffisivities. 

The result given by Eq. (411) for Spit) is the expression assumed for the errtropy entropy production and thermodynamic driving forces. On the basis of the statistical mechanical treatment of nonequihbrium systems, we find that this approximate approach is not required. 

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