Model Based on the Balance and Maximum Production of Entropy

Model Based on the Balance and Maximum Production of Entropy 

While analyzing the above-presented models, one realizes that the problem of mode choice cannot be unambiguously solved within the solution of mass transfer equation. This makes it necessary to consider thermodynamic or kinetic approaches to the analysis of transformation front stability and to choose a certain contact zone morphology. From the point of view of kinetics, the interphase boundary instability may be caused either by instabihty with respect to fluctuations of the boundary shape [15-17] or by the failure of balance equations for fluxes at the moving boundaries [16]. From a thermodynamic viewpoint, the problem of choice of one kinetically allowed mode can be solved using the variation principles of nonequilibrium thermodynamics [18-29], 

Both the entropy production and the divergence of entropy fluxes are functions of two variables (say, interlameUar distance and I). Each of these functions independently has no maximum. Yet, at the subset of variables corresponding to the constraint of steady-state balance of entropy, the maximum of entropy production does exist and should correspond to the most probable evolution path. 

We described the model for independent determination of the main parameters Az and L at known thermodynamic parameters of the system, triple product sDh for the interphase boundary, and initial concentration Cq of the supersaturated solution. The employed approach allows us to find the concentration distribution c(z) along the a-phase lamella and, therefore, the averaged concentration inside the a-phase lamella. The main approximation is that we assume diffusion 

Let us assume that a change in the entropy d S during the elementary time interval dt due to the phase transformation in the region R shifting by its width is equal to the change in the entropy diS due to the diffusive redistribution of components in the same region R. We consider a steady-state process obeying the condition [18] 

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