Phase Transitions in Convection

Abstract

The paper presents the results of the study of the models of convective instability near its threshold of thin layers of liquid and gas bounded by poorly conducting walls. These models single out one spatial scale of interaction, leaving the possibility for the evolution of the system to choose the symmetry character. This is due to the fact that the conditions for the realization of the modes of convective instability near the threshold are chosen. All spatial perturbations of the same spatial scale, but of different orientations, interact with each other. It turned out that the presence of minima of the interaction potential of the Proctor-Sivashinsky equation modes, the absolute value of the wave number vectors of which is unchanged, determines the choice of symmetry and, accordingly, the characteristics of the spatial structure. In the case of a more realistic model of convection described by the Proctor-Sivashinsky equation, it was possible to observe both the first-order phase transition and the second-order phase transition and detect the form of the state function, which is responsible for the topology of the resulting convective structures: metastable rolls and stable square cells. In this paper, it is shown that the nature of the structural-phase transition in a liquid when taking into account the dependence of viscosity on temperature in the Proctor-Sivashinsky model is similar to the case of the absence of such a dependence. The transition time turns out to be the same, despite the fact that a different structure is formed -hexagonal convective cells. As in the Swift-Hohenberg model, a hard mode for the formation of hexagonal cells in a gas medium is possible only for a sufficiently noticeable dependence of its viscosity on temperature. The phase transition times are inversely proportional to the difference in the values of this function for two consecutive states. A similar description of phase transitions did not use phenomenological approaches and various speculative considerations, which allows for a closer look at the nature of transients.

A Demonstration Bench for Representing the Character of Phase Transitions of the First and Second Kind

“…By the way, the equations of the Proctor Sivashinsky model, after the instability of the primary structure -convective rolls, formed a system of square convective cells The question of the appearance of a phase transition of the first kind did not need to be discussed, but it remained unclear what the instability of the primary structure of convective shafts is and whether this process is a phase transition of the second kind. This is exactly what was found out later in [6][7][8][9][10][11][12][13], where the state function whose values determined the type of topology of emerging spatial structures was found and verified, the process of their formation was shown and thus it was proved that the that transition is nothing but a phase transition of the second kind (see also [14], which results in the formation of a more stable field of convective square cells [15][16][17][18][19]).…”

“…Defects occur mostly on the boundaries of homogeneous areas -domains. There is a correlation between the relative proportion of visually observed (geometrically) structure defects and the defectiveness value, defined as the ratio of the squares of the amplitudes of the spectrum modes that do not correspond to the square cell system to the total sum of the squares of amplitudes (see [12,13]).…”