Metastability at the loss of the morphological stability of the moving boundary of a fluid

The morphological stability of the interface between two fluids has been analyzed for the case where one of them displaces the other in a radial Hele-Shaw cell. The numerical calculation has shown for the first time that the critical size of instability decreases with an increase in the perturbation amplitudes of the interface and reaches a value previously determined from independent analytical calculations of the thermodynamic entropy production and the maximum entropy production principle. This reason is important evidence for the hypothesis that the entropy production makes it possible to predict nonequilibrium phase transitions in hydrodynamic systems (i.e., it is an analog of the thermodynamic potential). In other words, the entropy production determines a kinetic binodal, i.e., the interface of a metastable region in the case of perturbations with arbitrary amplitude.