Cause of decreased bubble lifetime in the hot chocolate/coffee effect

Determine the cause of the observed decrease in bubble lifetime between successive experiments when tapping the bottom of a cup containing espresso mixed with foam (the hot chocolate/coffee effect), and ascertain whether this decrease is primarily due to reduction of the foam layer at the liquid surface that diminishes the time bubbles remain trapped in the liquid.

Background

The hot chocolate/coffee effect arises when small gas bubbles entrained in a hot beverage significantly increase the compressibility of the liquid, thereby reducing the speed of sound and lowering the resonance frequency of the liquid column. As bubbles rise and escape, the resonance frequency increases over time. In this paper, the authors use Wood’s formula to relate the measured resonance frequency to the void fraction and fit the temporal evolution to an exponential law.

During repeated experiments, the authors observe that the bubble lifetime—i.e., the duration that bubbles remain within the liquid—can vary substantially, with a pronounced decrease between the first and second trials. Understanding the mechanism behind this variability is important for interpreting acoustic measurements of bubbly liquids and for applications such as BARDS, where the acoustic signature depends sensitively on bubble dynamics and retention.