Drops & Bubbles: From Fundamentals to Applications

Droplets and bubbles abound in nature: from drops sliding on your window on a rainy winter day, to respiratory aerosols consisting of tiny saliva and mucus droplets ejected when you sneeze or cough; from tiny bubbles agglomerated at the bottom of your heating pan, to bubbles of volcanic gas trapped in magma. And more often than not, drops and bubbles coexist, like in a glass of sparkling wine where bubbles occasionally rise to the surface, burst and produce jets which eventually disintegrate into droplets, or like in breaking waves. To comprehensively list the instances of their occurrence might require yet another thesis.

Herein, we shall review the dynamics of drops and bubbles in a multitude of physical systems, while listing some of their important applications. For instance, we discuss bubble dynamics mostly in the framework of cavitation, a phenomenon consisting of bubble nucleation, expansion and collapse, due to sudden pressure drops or to local heating. We tackle the problem of cavitation both in infinite and semi-infinite media, while developing the numerical methods that allow us to achieve a better understanding of the underlying physics. Likewise, we only discuss droplets in the context of atomization and aerosols, motivated by the recent outbreak of the Covid-19 pandemic. We study the fragmentation of thin films of liquid into droplets of different sizes, thus emulating coughing or sneezing manoeuvres, in the aim of understanding how viral loads are spread.