The Critical Conditions of Filtration Flow Blocking in a Porous Channel with Phase Transitions

The paper studies the occurrence of kinetic phase transitions in porous media with thermodynamic phase transitions, which affect filtration flow through permeability or viscosity: in the simplest case, permeability is a step function of local temperature. The dependence of phase boundary under stationary heating and cooling processes has features that are concerned with the non-linearity of Stefan condition. These features result in limited stability of filtration flow. Calculations show that there exist critical temperatures in the vicinity of those stationary filtration flow becomes impossible due to the thermal interaction of phase transition and advection processes. The solutions form two branches; one of those is stable, and the other is unstable; the connection between the branches is a critical point. Several different setups are considered: flat and cylindrical channels, melting of the porous carcass, and crystallization of flowing liquid. Critical conditions for these cases are obtained in the form of approximate formulas that can be used to calculate heat transfer in thermal engineering units, including heat accumulators.