Understanding the merging of liquid drops is a problem of practical interest for natural (e.g. clouds) and technological processes (e.g. chemical engineering) as well as being of fundamental interest. From a modelling perspective, the problem is particularly interesting, as the classical equations result in a singularity at the start of the motion.
Our initial intention was to study this singularity using molecular dynamics (MD), but our eventual findings involved entirely different physics, showing that the classical picture of ‘spherical drops touching at a point’ is not observed at the nanoscale, and instead one observes multiple off-centre contacts.
We showed that the off-centre contacts were caused by waves on the drop’s boundary that deform it away from its usual spherical shape. These waves are driven by thermal fluctuations that become prominent at the nanoscale, where they balance with the restoring force of surface tension to create nanometric amplitude disturbances. Thus, in the light of ‘experimental findings’ from MD our research changed direction towards trying to characterise these waves.
A new theory was developed to characterise these waves, both for spheres (practical case of interest) and after a number of large MD simulations using the national supercomputer (ARCHER) the theory was validated. Most importantly, the theory can now be used to make predictions for larger droplets where MD is computationally intractable.
Remarkably, due to the cusp-like geometry of the gap between two approaching droplets, the nanoscale effects discovered are predicted to be dominant even for much larger micron-sized droplets. This calls into question existing theories and computations which focus on a classical model that does not contains any information about thermal fluctuations and opens up exciting new directions of research.
I would like to mention that this was my first publication with Jason Reese who passed away just a week before this work was published. His recent funeral made clear the depth of affection for him and the many people, myself included, who have admired and learnt from him. I think he would have been very proud of this work as it captures everything he was about: working across traditionally distinct fields, collaborating with other disciplines, encouraging young researchers, publishing in the top journals and publicising findings in an accessible manner (current Altmetric score of 80).