Modeling the Liquid Volume Flux in Bubbly Jets Using a Simple Integral Approach

This study presents a simple model to predict the liquid volume flux induced by round bubbly jets. The model is based on the classical integral equations for bubble plumes, but also accounts for the momentum at the source by including new conditions for the initial liquid jet velocity and radius. Moreover, an exponential functional relationship is used to relate the entrainment coefficient to a densimetric Froude number. The model predicts well the experimental results available in the literature for bubbly jets. Model simulations plotted together with experimental data for both bubbly jets and bubble plumes also reveals a clear jet/plume transition, resulting in entrainment rates in the bubbly jet zone larger than those in the bubble plume zone. Finally, potential applications of the model in aeration/mixing systems are presented.