A property of extreme entropy values in critical regimes of two-phase flows

Abstract

In a critical regime of vertical ascending flows, a certain part of solid particles moves with the flow, while another part settles against the flow. Entropy is a key parameter in the analysis of properties of mass systems. It can be considered as consisting of two parts ― internal entropy arising during irreversible processes within the system and external entropy depending on the system correlation with the surroundings. Here a system represents the totality of all solid particles of various sizes simultaneously present in the flow. In thermodynamics, ordinary total entropy consisting of these two components has a tendency to reach the maximum when the entire system reaches equilibrium. In this case, its internal entropy always increases. In contrast to the conventional entropy, the internal entropy in the process under study can decrease due to the peculiarities of the solid phase motion and mass exchange caused by the latter. However, in a critical regime, one can always reveal a narrow size class in a mixture of particles, whose entropy tends to maximum when this class reaches a peculiar equilibrium in the flow. The peculiarity of this equilibrium consists in an equiprobable distribution of particles of this class in both directions – upwards and downwards. For other size classes participating in the process, the internal entropy does not reach the maximum, and these classes are not equally distributed between the directions of motion. The condition of optimal mass exchange of the total granulometric set of particles in specific conditions of critical flow is connected with an equilibrium size class. Ill. 1. Ref. 2.