A non-instantaneous kinetic model for freezing in porous media

A solution is presented for the moving boundary problem that arises during heat and moisture transfer, when freezing fine-grained porous media under phase transition conditions. It is based upon a quasi-heterogeneous scheme. This scheme assumes the existence of an infinitely thin front and is based upon a hypothesis concerning the finite rate of the crystallization process. Non-instantaneous kinetics is considered and consequently there is no “jump at the front” for ice content and total moisture. The freezing zone is defined as the region between the frozen front and the point at which ice content vanishes. In the solution of the equations, temperature, moisture (liquid water) and ice distribution are influenced by the values of these factors at the front and its velocity. For determination of these values, the system of equations is obtained and solved by an iteration method that readily converges on the solution. The time-dependent influence of these characteristics is presented. The analysis of the freezing process for loamy soils was carried out on variations of the characteristic parameters—Stefan and Lewis numbers. As the level of phase transition increases, the frozen zone decreases, while the values for ice distribution become larger. With the increase of the Lewis number, the ice content and, consequently, total moisture get larger. In the case where water migration is absent, the solution to the equations corresponds to the classical solution with ice “jump at the front”. It is shown that the decrease of the crystallization time in a non-instantaneous kinetic model leads to the flattening of ice content and total moisture profiles at a vertical surface, and the process approaches the crystallization stage when “jump at the front” conditions occur. The theoretical concepts and results obtained from the analytical solution are in agreement with experimental investigations. The model presented predicts the freezing process in porous media and satisfactorily reflects observed phenomena.