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We give a general phenomenological description of the steady state 1D frontpropagation problem in two cases: the solidification of a pure material and theisothermal solidification of two component dilute alloys.  The solidification of a pure material is controlled by the heat transport inthe bulk and the interface kinetics.  The isothermal solidification of two component alloys is controlled by thediffusion in the bulk and the interface kinetics.  We find that the condition of positive-definiteness of the symmetric Onsagermatrix of interface kinetic coefficients still allows an arbitrary sign of theslope of the velocity-concentration line near the solidus in the alloy problemor of the velocity-temperature line in the case of solidification of a purematerial. This result offers a very simple and elegant way to describe theinteresting phenomenon of a possible non-single-value behavior of velocityversus concentration which has previously been discussed by differentapproaches. We also discuss the relation of this Onsager approach to the thininterface limit of the phase field description.

Onsager approach to 1D solidification problem and its relation to phase field description