Homogeneous–heterogeneous regime transition in bubble columns

Abstract

A simple physical model for homogeneous–heterogeneous regime transition in bubble columns is developed. The model is based on hydrodynamic coupling between gas and liquid phases. For the homogeneous regime, the coupling is made via bubble drift concept (Darwin, Proc. Camb. Phil. Soc. 49 (1953) 342). As a byproduct, a novel non-empirical formula for bubble slip velocity results, u/ w=1− ae/(1− e). For the heterogeneous regime, the coupling is obtained in a simple formal way, recovering the classical result of Zuber and Findlay. The regime transition is considered as a smooth and gradual process characterized by a transition function. The model has five parameters: two terminal bubble velocities, bubble drift coefficient, Zuber–Findlay constant, and intermittency factor. All have clear physical meaning and are extractable from experimental data. The model gives formulas for the voidage-gas flow rate dependence separately for the homogeneous regime, heterogeneous regime and transition regime. The model gives a kinematic stability condition for the homogeneous regime and predicts the critical gas flow rate where the transition begins. It also predicts the maximum possible gas holdup in bubble columns. The model is verified by experiments with four different air–water bubble columns. Good agreement is found. Our results are compared with results of other authors. The model agrees with the drift-flux concept developed by Wallis (One-dimensional Two-phase, Flow, McGraw-Hill, New York, 1969) and with the stability theory of Shnip et al. (Int. J. Multiphase Flow 18 (1992) 705).