Emptying of a bottle: How a robust pressure-driven oscillator coexists with complex two-phase flow dynamics

Abstract

The emptying of a bottle is one of the most common two-phase flows encountered in everyday’s life fluid mechanics. We report on a detailed experimental analysis of this flow configuration covering a wide range of neck-to-bottle diameter ratios, d*, and initial filling ratios, F. The joint use of a pressure sensor at the top of the bottle and a shadowgraph technique to track the evolution of the upper liquid surface allows the average gas volume fraction in the fluid column to be computed throughout the discharge. Variations of the bottle emptying time, gas content, and characteristics of the pressure signal as a function of d* and/or F are analyzed, and scaling or evolution laws are derived. A specific focus is put on the initial transient stages following the neck opening, especially on the nature and growth of the first bubble that reaches the upper free surface. Over a wide range of d*, this bubble takes the form of a large spherical cap or Taylor bubble, the rise speed of which is controlled by the bottle diameter. Such a bubble directly emerges from the neck for large enough d*, but rather results from successive coalescence of smaller bubbles for small d*. Whatever d*, the volume of this leading bubble increases over time, since a fraction of the small bubbles swarm trailed in its wake merges with its back face. This coalescence-induced growth is quantified through a simple model.