ECM Seminar: Collision of liquid drops - bounce or merge?
In the latest run of the Early Career Mathematicians Seminar Series, we will be joined by the winner of the 2025 Lighthill-Thwaites Prize.

In the latest run of the Early Career Mathematicians Seminar Series we will be joined by the winner of the 2025 Lighthill-Thwaites Prize. The Lighthill-Thwaites Prize is awarded biennial to Early Career Mathematicians for outstanding work, that is published or original, in the field of applied mathematics, and is awarded at the British Applied Mathematics Colloquium where the finalists all present their work for the prize. The prize is named after the IMA's first two presidents, Professor Sir James Lighthill and Professor Sir Bryan Thwaites, to honour their contribution to the IMA and mathematics more widely. It was their mutual interest in the education and training of young people, as much as their involvement in applied mathematics, that has shaped the conditions of the prize. More details on the Lighthill-Thwaites prize can be found here: https://ima.org.uk/awards-medals/ima-lighthill-thwaites-prize/.

In 2025, the winner was Peter Lewin-Jones (Warwick) for his work published in the Journal of Fluid Mechanics, which can be found here: https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/collision-of-liquid-drops-bounce-or-merge/A968B4EFF54F5C130069E52CFD2A73D5.

Abstract

Collisions and impacts of drops are critical to numerous processes, including raindrop formation, inkjet printing, food manufacturing and spray cooling. For drop-drop collisions, increasing the relative speed leads to multiple transitions: from merging to bouncing and then back to merging - transitions which were recently discovered to be sensitive to the drops' radii as well as the ambient gas pressure. To provide new insight into the physical mechanisms involved and as an important predictive tool, we have developed a novel, open-source computational model for both drop-drop collisions, using the finite element package oomph-lib. This uses a lubrication framework for the gas film and incorporates fully, for the first time, the crucial micro- and nano-scale influences of gas kinetic effects and disjoining pressure. Our simulations show strong agreement with experiments for the transitions between merging and bouncing, but can also go beyond these regimes to make new experimentally-verifiable predictions. We will show how our model enables us to explore the parameter space and discover the regimes of contact (that are inaccessible to experiments). Finally, we will overview the impact of drops onto liquid baths, where for a fixed impact speed, the collision outcome can go from merging to bouncing to merging and back to bouncing with increasing bath depth. Our lubrication equation must be modified to capture the curvature of the trapped gas film, and our resulting simulations are the first to successfully predict the transitions between bouncing and merging in drop-bath impacts.

Bio

Peter is a Senior Research Associate in the School of Engineering Mathematics and Technology, University of Bristol, and is the winner of the 2025 IMA Lighthill-Thwaites Prize. He completed his PhD at the University of Warwick in January 2025, under the supervision of James Sprittles and Duncan Lockerby. He is interested in mathematical and computational modelling of fluids and solids, in particular the incorporation of micro- and nano-scale effects into continuum-scale models, and is currently working on modelling polyelectrolyte gels.