Explorations on the multi-scale flow structure and stability condition in bubble columns

Physical understanding of heterogeneous flow structure is of crucial importance for modelling and simulation of gas–liquid systems. This article presents a review and report of recent progress in our group on exploratory application of the variational (analytical) multi-scale approach to gas–liquid systems. The work features the closure of a hydrodynamic model with the incorporation of a stability condition reflecting the compromise between the dominant mechanisms in the system. A dual-bubble-size (DBS) model is proposed to approximate the heterogeneous structure of gas–liquid systems based on a single-bubble-size (SBS) model previously established. Reasonable variation of the gas holdup and the composition of the two bubble species with operating conditions have been calculated and the regime transition can therefore be reasonably predicted for air-water system, suggesting that stability condition may provide an insightful concept to explain the general tendencies in gas–liquid systems out of their hydrodynamic complexity, and to give simple models of their overall behaviors. Of course, the diversity of the correlations for drag force and minimum bubble size and the sensitivity of the model predictions to these correlations may suggest the necessity to clarify further the essential and robust results in the current model and to reduce the uncertainties involved.