Bubble formation in a coflowing air–water stream

Abstract

In this work, we present a detailed experimental study of the periodic formation of bubbles in an air–water coflowing stream, as well as a simple model to describe the process. The frequency of formation of bubbles was measured analysing a large number of images recorded with a high-speed camera for a wide range of experimental conditions and air-injection needle geometries. The analysis of the images indicated that the bubble-formation process consisted of two distinct stages, namely the ligament expansion stage, characterized by the radial growth of an air ligament left attached to the injection needle after the pinch-off of a bubble, and the ligament collapse stage, characterized by the formation of a neck at the tip of the injection needle which propagates downstream, at a velocity which is nearly the liquid velocity, until it collapses generating a new bubble. A simplified model, based on the Rayleigh–Plesset equation for a cylindrical geometry to determine the dynamics of the liquid stream and on Bernoulli's equation to determine the air pressure near the neck, has been proposed to estimate the duration of the ligament collapse stage, $t_{col}$. The experimental bubble-formation frequency, properly scaled with the breakup time given by the model, is shown to collapse onto the same curve for all the experimental conditions used here, indicating that our simple model seems to retain the main physical aspects of the process.