Fountain entrainment in a filling box at low Reynolds numbers

Pouring a lighter liquid into a container filled with a denser liquid creates a downward jet. The penetration of this jet into the tank is opposed by buoyancy, thus a return flow towards the upper surface occurs and forms a fountain. In such a condition, due to entrainment, a mixed layer of the two liquids is created in the upper part of the tank, whilst the lower section is only filled with the original denser liquid. In this experimental study, we characterize the behavior of fountains in bounded containers based on the Reynolds Re and Froude Fr numbers. Unlike a conventional turbulent fountain, we focus on the regime at lower Reynolds numbers Re < 500. We measure the fountain entrainment coefficient B by modeling this configuration as a filling box problem. We then show that B is a function of both Re and Fr, in contrast to the turbulent regime where B remains constant. For a given Fr, the fountain entrainment reaches a local peak at an intermediate Reynolds number Re ～ 200. We reason that this local peak of entrainment occurs due to the enhanced penetration of the downward jet and the moderate fountain entrainment coefficient at intermediate Reynolds numbers. Results of this study provide guidelines to achieve effective jet-driven mixing of two miscible liquids.