Dear colleagues,
Permit me to make the small addition to question touched in discussion. Maxwell-Stefan multicomponent diffusion theory cannot be used for mathematical description heat- and mass transfer in continuous stationary rectification processes with counter-current flow of phases, proceeding in columns with adiabatic walls. In mentioned conditions the use for calculation equations, following from this theory, leads to unpredictable errors.
This assertion is justified because, that the sequence of composition of liquid throughout height of column (or trajectory of mentioned rectifications process) in these conditions is uniquely determined by variational principles of nonequilibrium thermodynamics.
Pursuant to these principles stationary process, proceeding in phase space of concentration on true trajectory at other equal conditions mast be accompanied by the minimum speed of generation entropy on comparison with any other theoretically possible trajectory, passing in this space through common point. In this case it is the same, as stating that in this process should be made the maximal useful work of division.
§In its turn from theorem, established by Nobel premium winner L.Onsager follows, that the speed of generation entropy, is identical equal to sum of products of independent(!!) flows of components and warm into thermodynamics driving forces, conjugated with they.
In considered case due to existence uniquely determined trajectory, sizes of all component's flows have been linearly dependent. The same is true concerning to flow of warm, as at P=cons. enthalpies and temperature of liquid heated up to boiling are uniquely determined by its composition. In these conditions the equation, describing kinetics of process (in the most general(common) appearance - the speed of movement of figurative point on trajectory of process) should establish the dependence between size of one independent flow and one generalized thermodynamics driving force with help of one independent phenomenological coefficient(factor).
In more detail see in articles, translated into English:
1. Vigdorov A.S. Mathematical Description of Kinetics of Binary Mixture Continuous Rectification basing on the Laws of Nonequilibrium Thermodynamics, Khim. Prom., 1981, No. 8, p. 487 (in English translation: The Soviet Chemical Industry, p. 1057).
2. Vigdorov A.S. Thermodynamic (Mathematical) Errors in Film
Model for Describing Heat and Mass Transfer in Fraction Processes.
Mendeleev Chemistry Journal, Vol. 36, No. 1, pp. 59 - 66. (Zhurnal
Vses. Khim. Ob-va).
16.02.1998