Maximum entropy production principle and morphological selection in hydrodynamic systems

In recent decades an idea has emerged that the maximum entropy production principle can be used to select from the different regimes of development of nonequilibrium systems. According to this principle, the process with maximum entropy production is most preferred among the possible non-equilibrium processes. As a consequence, entropy production can be used to find an actually observed pattern formation among the hypothetical ones. The entropy production is calculated for distorted and undistorted evolving phase interface and the process with the largest entropy production is assumed to be nonlinearly stable. A hypothesis is introduced that the role of entropy production for morphological transitions is similar to the role of chemical potential for equilibrium phase transitions, i.e. it can be used to find a boundary (binodal) dividing the region of absolutely stable growth from the region of growth which is unstable (metastable) with regard to arbitrary amplitude distortions. This principle has been successfully applied to analyze the interfacial morphological stability during crystallization.

The objective of this study is application of described principle in two cases. The first problem is the stability analysis of the displacement front of two immiscible fluids, where more viscous one is displaced by the less viscous one in the radial Hele–Shaw cell. Together with linear stability analysis (which describes the stability to infinitesimal distortions, i.e. gives the spinodal) entropy production approach allows to determinate the region of different interface forms coexistence. These boundaries are analyzed depending on the cell size, the injected flow rate, and the ratio of the fluid viscosities.

The second problem is the stability of a spherical surface of a vapor bubble growing under inertia control. In this case we obtain that the entropy production in the vicinity of the bubble's distorted surface is always greater than that of the undistorted surface. Such a result indicates that the morphological phase with a distorted surface is more preferable and consequently should be observable in a real system where arbitrary perturbations occur. This allows explaining the experimentally observed roughness of the bubble surface during explosive vaporization.

The reported study was funded by RFBR according to the research project
No.16-31-00255 мол_а and scientific project № 1.4539.2017/8.9