Gibbs Duhem vector

Let us now introduce the Gibbs-Duhem (GD) vector of extensive values for each phase A =1,2,...,/ ... 

In this case, (12.68) merely recovers the vector form of the Gibbs-Duhem equation for the single phase (cf. Section 10.3), as we should anticipate. 

Furthermore, it is noted that the first three terms in the brackets on the RHS of (2.452) are similar to the terms in the Gibbs-Duhem relation (2.451). However, two of these three terms do not contribute to the sum. The pressure term vanishes because js = 0. The two enthalpy terms obviously cancel because they are identical with opposite signs. Moreover, the last term in the brackets on the RHS of (2.452), involving the sum of external forces, is zero = 0- Oue of the two remaining terms, i.e., the one containing the enthalpy, we combine with the q term. Hence, the modified entropy flux vector (1.171) and production terms (1.172) become ... 

Let us find the vector Xjj orthogonal to the hypersurface of the phase transition at point D in the space of the ehemieal potentials. The Gibbs-Duhem relations (32) at constant temperature, on the gas and on the liquid sides of the phase transition, may be expressed as follows ... 

The starting point for the rigorous derivation of the diffusive fluxes in terms of the activity is the entropy equation as given by (1.174), wherein the entropy flux vector is deflned by (1.175) and the rate of entropy production per unit volume is written (1.176) as discussed in Sect. 1.2.4. To eliminate S from the Gibbs-Duhem relation formulated in terms of specific quantities (2.324) we need the definitions of H = mH and G = mG ... 

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