Air entrainment by a viscous jet plunging into a bath

A liquid jet plunging into a container of liquid often entrains a thin film of air with it, producing bubbles. This bubble production is detrimental to many industrial processes, such as filling a container with a molten glass or polymer, or in coating processes. Conversely, in making a foam, one uses this effect; hence it is important to control the rate of bubble production. Here, we measure the amount of air entrained by a viscous jet over a wide range of parameters and explain the phenomenon theoretically. Simple scaling arguments are shown to predict entrainment rates over 4 orders of magnitude in the dimensionless jet speed.