Bubble curtains used as barriers across horizontal density stratifications

Bubble curtains are multiphase line plumes that are used to reduce buoyancy-driven flows between two water zones at different densities. They are similar to air curtains, plane turbulent jets, that are installed in doorways of buildings between two climatically different environments. In this study, we establish a formal analogy between bubble curtains and air curtains and unify the two frameworks for their description that had previously been used. By means of small-scale laboratory experiments conducted in a channel with freshwater and brine solutions, we study how effectively a bubble curtain acts as a separation barrier for a wide range of density differences as well as different air fluxes and water depths. Qualitatively, two regimes of operation of a bubble curtain are identified and we establish the optimum operating conditions on the basis of quantitative measurements and theoretical considerations. We develop a theoretical model to calculate the infiltration flux of dense water across the bubble curtain that is in very good agreement with experimental measurements and yields a theoretical upper limit on the effectiveness of the bubble curtain. We also study the zones of mixed fluid around the bubble curtain, provide a scaling law for their horizontal extent as well as theoretically predict the water density inside these mixed zones. We discuss how the theoretical models derived from our small-scale experiments apply to real-scale bubble curtains that are, for example, used in ship locks.