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 1 two-phase flow. Based on PR state equation, and a detailed specific heat ratio equation of bubbles, 2 we self-consistently evaluate kinetic equations of the bubbles on the basis of Ergun equation, 3 thermodynamic equation and kinetic equations. It is found that the specific heat ratio of bubbles in 4 such systems strongly depends on the bubble pressures and temperatures, which play an important 5 role on the characteristics of the bubbles. The theoretical studies show that with a increasing of the 6 height in the systems, the gas flow rate shows a downward trend. Moreover, the larger particles in 7 the gas-solid flows are, the greater the gas velocity is. With a increasing the height, bubble sizes show 8 a variation of first decreasing and then increasing (U type). The bubble velocity is affected by the 9 gas velocity and the bubble size, which gradually declined and eventually stabilized. It shows that 10 gas phases and solid phases in a gas-solid two-phase flow interact with each other and come into 11 being a self-consistent system. The theoretical results have exhibited important guiding value for 12 understanding the properties and effects of bubbles in the gas-solid two-phase flows. 13