A self-consistent physical model of the bubbles in a gas solid two-phase flow

In this work, we develop a self-consistent physical model of bubbles in a gas solid two-phase 1 flow. Using the Peng-Robonson state equation and a detailed specific heat ratio equation of bubbles, 2 we obtain the kinetic equations of the bubbles on the basis of the Ergun equation, thermodynamic 3 equations, and kinetic equations. It is found that the specific heat ratio of bubbles in such systems 4 strongly depends on bubble pressures and temperatures, which play an important role in the 5 characteristics of the bubbles. The theoretical studies show that with increasing height in the systems, 6 the gas flow rate shows a downward trend. Moreover, the larger particles in the gas solid flows are, 7 the greater the gas velocity is. The bubble sizes increase with the increasing heights of the gas solid 8 systems, and then decrease. The bubble velocity is affected by the gas velocity and the bubble size, 9 which gradually increase and eventually quasi-stabilize. This shows that gas and solid phases in a 10 gas solid two-phase flow interact with each other and a self-consistent system comes into being. The 11 theoretical results have exhibited important value as a guide for understanding the properties and 12 effects of bubbles in gas solid two-phase flows. 13