  We give a general phenomenological description of the steady state 1D front
propagation problem in two cases: the solidification of a pure material and the
isothermal solidification of two component dilute alloys.
  The solidification of a pure material is controlled by the heat transport in
the bulk and the interface kinetics.
  The isothermal solidification of two component alloys is controlled by the
diffusion in the bulk and the interface kinetics.
  We find that the condition of positive-definiteness of the symmetric Onsager
matrix of interface kinetic coefficients still allows an arbitrary sign of the
slope of the velocity-concentration line near the solidus in the alloy problem
or of the velocity-temperature line in the case of solidification of a pure
material. This result offers a very simple and elegant way to describe the
interesting phenomenon of a possible non-single-value behavior of velocity
versus concentration which has previously been discussed by different
approaches. We also discuss the relation of this Onsager approach to the thin
interface limit of the phase field description.
