Bubbly barriers


Buoyancy-driven currents, caused by horizontal density stratifications in fluids, occur in different industrial and natural settings over a wide range of spatial and temporal scales. The exchange of flows between two zones at different densities is associated with various phenomena, including advective transport of mass and biological substances. An example of a problematic buoyancy-driven flow through doorways of buildings arises when the exchange flow is driven by the temperature differences between two adjacent rooms. In this situation, shutting the doors is not always a viable solution for preventing these buoyancy-driven exchange flows since it will obstruct the movement of people or vehicles. Therefore, alternative mitigation strategies such as aerodynamical sealing by means of air curtains have been developed for reducing buoyancy-driven exchange flows.

In a similar scenario,  multiphase line plumes, also known as bubble curtains, are a promising strategy for reducing buoyancy-driven flows between two water zones at different densities, that, for example, exist in ship locks. This is analogous to fitting air curtain devices across doorways in buildings to serve as a separation barrier between two climatically different environments. While bubble curtains have been in use for decades, there are still limited experimental data on their performance as separation barriers when installed across horizontal density stratifications. Similarly, there is a lack of consensus on the appropriate optimum parameters for the bubble  curtain operation.

Furthermore, despite the physical similarity between the use of bubble curtains and air curtains for reducing buoyancy-driven exchange flows, the two research directions involving these both strategies have been completely detached. In fact, two different theoretical frameworks and sets of parameters have been used to describe the performance of air curtains and bubble curtains as separation barriers. To address the above research limitations, Dr. Daria Frank and Professor Paul Linden from the University of Cambridge with Alexis Bacot from École Polytechnique investigated the application of bubble curtains as a separation barrier across horizontal density stratifications. The research is currently published in the peer-reviewed Journal of Fluid Mechanics.

In brief, the authors started their investigation by establishing a formal analogy between air curtains and bubble curtains and proposed a unifying framework for their description. A series of small-scale laboratory experiments was conducted in a channel with brine solutions and freshwater to study the effectiveness of bubble curtains in reducing saltwater intrusions into the freshwater zone for a wide range of water depths, air fluxes and density differences.

The authors identified two operating regimes of the bubble curtain: the breakthrough regime characterized by a very weak bubble curtain unsuitable for preventing the buoyancy-driven exchange flow and the curtain-driven regime in which the bubble curtain successfully interrupts the buoyancy-driven current. In the curtain-driven regime, the infiltration flux of dense fluid was attributed to the self-induced bubble curtain mixing. Based on the theoretical considerations and quantitative measurements, the optimal operating conditions were determined at the non-dimensional parameters, the so-called deflection modulus, Dm,b ≈0.12 or the air Froude number, Frair ≈0.93 , which correspond to the transition values between the two regimes.

Building upon experimental observations and insights from the air curtain theory, the authors proposed a theoretical model to predict the infiltration flux of dense fluid across the bubble curtain into the freshwater zone in the curtain-driven regime. The theoretical predictions agreed well with the experimental measurements, allowing the determination of the upper limit on the effectiveness of the bubble curtain in the curtain-driven regime. Scaling laws for the horizontal extent of the zones of mixed fluid around the bubble curtain were provided and the water density in the mixed zones could be predicted.

In summary, the bubble curtain performance in separating two water zones at different densities was investigated theoretically and experimentally. The application of the derived theoretical models to the real-scale bubble curtains was discussed. The bubble curtain achieved an optimal effectiveness value of up to 80% in preventing the saltwater intrusion into the freshwater zone. In a statement to Advances in Engineering, Dr. Daria Frank, the corresponding author explained that their findings will help in developing effective strategies involving bubble curtains for preventing buoyancy-driven exchange flows across horizontal density stratifications.

Bubbly barriers - Advances in Engineering

About the author

Daria Frank is currently a Sultan Qaboos Early-Career Research Fellow and College Lecturer in Mathematics at Corpus Christi College, University of Cambridge, UK. She conducts her research in the G. K. Batchelor Laboratory at the Department of Applied Mathematics and Theoretical Physics (DAMTP) of the University of Cambridge.

Daria is an Applied Mathematician working on fundamental fluid dynamical questions related to turbulent single- and multiphase jets and plumes, that are ubiquitous in nature and industry. Her work combines small-scale laboratory experiments with theoretical and numerical modelling. Her research interests address pressing societal issues such as the reduction of urban energy consumption and creating a healthy indoor environment by optimising the ventilation of buildings, mitigation of consequences of large-scale oil spills such as the Deepwater Horizon Oil Spill and, more recently, the risks associated with musical performances with regard to the airborne pathogens.

Daria obtained a Diploma in Mathematics from the Friedrich-Alexander University Erlangen-Nürnberg in Germany and a Master of Advanced Study (MASt) from the University of Cambridge. She completed her PhD studies under the supervision of Prof. Paul F. Linden. Daria is also the recipient of the prestigious 2021 L’Oréal-UNESCO For Women In Science Rising Talent Award for Mathematics and Computer Science.


Bacot, A., Frank, D., & Linden, P. (2022). Bubble curtains used as barriers across horizontal density stratifications. Journal of Fluid Mechanics, 941.

Go To Journal of Fluid Mechanics

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