| The hydrodynamic interactions between the dispersed and continuous phases in gas-liquid contactors are studied. A mathematical model based on the macroscopic mechanical energy balance is developed to predict liquid circulation velocity in airlift fermentors. There is a reasonably good agreement between the predicted and experimental values for three different types of airlift columns over wide ranges of operating conditions. This analysis takes into account effects of energy dissipation due to wakes behind the bubbles in the upflow zone and energy dissipation due to the upflow motion of large bubbles with respect to the liquid in the downflow zone. The results indicate that each of these modes of energy dissipation accounts for 30% to 60% of the total for the draft-tube and split-cylinder airlift columns examined. The liquid turnaround in the top and bottom regions of the airlift column and other resistance to liquid recirculation in the system account for the rest of energy dissipation.; Two phenomenological models are proposed to describe bubble breakup and coalescence in a turbulent gas-liquid dispersion. The first model, which is mainly based on probabilistic theory, gives reasonable prediction of bubble breakage frequency in terms of the liquid density, interfacial tension, bubble diameter, and the energy dissipation rate per unit mass. The second model predicts the binary bubble coalescence frequency as a function of the liquid viscosity, interfacial tension, bubble diameter, energy dissipation rate per unit mass, and the surface immobility parameter.; Finally, a generalized population continuity equation is developed for 'a priori' prediction of the distribution function of countable entities in dispersed-phase systems. The distribution function is defined by the solution of an integro-differential equation which contains detailed information of the breakage and coalescence processes. The population balance equation is then applied to the analysis of bubble size distribution for non-coalescing systems in a bench-scale airlift column by incorporating the previously developed breakage model. Favorable agreement between experimental observation and the model indicates that the model is suitable for predicting dispersion properties such as bubble size distributions, and interfacial areas. |
