Modeling of the evolution with length of bubble size distributions in bubble columns

Many of the existing methods, for the determination of the specific interfacial area in bubble columns, consider the column in a dynamic equilibrium between bubble coalescence and breaking-up. The aim of this work is to study if this consideration can be considered true for low superficial gas velocities. Two existing models have been chosen from literature in order to predict the break-up [Wang, T., Wang, J., Jin, Y., 2003. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science 58, 4629–4637] and the coalescence [Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426] rates. In order to confirm the validity of the models, predictions were compared with experimental results obtained by image analysis. Several simulations were performed for different superficial gas velocities and initial bubble size distributions. The column length needed to reach dynamic equilibrium was calculated for each simulation. The results show that the necessary length to reach the dynamic equilibrium does not depend on the shape of the initial distribution, but essentially on its Sauter mean diameter. The necessary length to reach the dynamic equilibrium is very important for low superficial gas velocities. The assumption that the entire column is in dynamic equilibrium is in general not valid. Therefore, the initial Sauter mean diameter and the total column length are important parameters for the determination of the specific interfacial area.