Glancing out a window on a rainy day, your eyes are accidentally caught by a small droplet rolling down the glass, where its “other half” is awaiting… Now, the “dating” is about to begin and the droplet reaches out to another. The moment they touch, a connecting liquid bridge forms and quickly grows – the two droplets then coalesce into a bigger one before you could see clearly what has happened. While you are still wondering why it was so fast, another coalescence has just flashed by…

Droplet-droplet coalescence is of essence to numerous natural and industrial processes, for example, rain clouds formation and fuel spray in rocket engines. Nowadays, with the help of high-speed cameras, many experimental scientists have successfully captured the transient coalescence of liquid droplets that cannot be perceived by naked eyes. They discovered that, as the two droplets merge into one, the connecting liquid bridge grows by obeying two distinct rules: it either grows linearly with time when the droplets are smaller (or more viscous) or grows with the square-root of time when the droplets are bigger (or less viscous).

To unveil the secret of the different rules governing droplet coalescence, Dr Xi Xia, former research fellow (now Associate Professor of Shanghai Jiaotong University), Mr Chengming He, PhD student, and Dr Peng Zhang, Associate Professor of the PolyU Department of Mechanical Engineering, established a theory that unifies the dynamics of liquid bridge growth. The theory is amazingly simple but innovatively integrates some mathematical techniques, such as integral equation and asymptotic analysis, with some physical insights, such as flow self-similarity and interfacial vortex. This work has been recently published online on PNAS (Proceedings of National Academy of Sciences). [X. Xia, C. He and P. Zhang, “Universality in the viscous-to-inertial coalescence of liquid droplets”, http://www.pnas.org/cgi/doi/10.1073/pnas.1910711116]