Instability of the phase front in the soils freezing process

An analytical criterion for the stability of the freezing phase front in porous media is investigated theoretically. The criterion is derived using the perturbation method for a two-dimensional, coupled heat and mass transfer model. This model assumes that the non-instantaneous crystallization process occurs in the kinetic zone, and the rate of crystallization is a function of supercooling, which corresponds to the Arrhenius form equation and agrees with experimental investigations. The perturbation analysis of the freezing front shows that the stability criterion depends on dimensionless parameters—Lewis and Stefan numbers and on a parameter that characteristics the phase transition kinetics. Employing Fourier synthesis, actual front shape evolution is calculated. It is seen that the front displays a periodic morphology whose scale is essentially unrelated to that of the starting perturbation. An effect of kinetics on the size of the stability area and on front shape evolution is also shown. The theoretical stability/instability conditions as predicted from the derived criterion were found to be in agreement with experimental investigations on the formation of soil cryogenic structure in the freezing process.