Nonlinear Interactions of Evaporating Droplets

This exciting new project builds on the proposed first supervisor's highly successful collaboration with Professor Khellil Sefiane (School of Engineering, University of Edinburgh and Visiting Professor at the International Institute for Carbon-Neutral Energy Research, Kyushu University, Japan) on the popular and highly-topical problem of droplet evaporation. This collaboration has previously led to two excellent PhD theses by Gavin Dunn (2009), with whom we won the Institute of Physics Printing and Graphics Science Group Prize in 2009, and Jutta Stauber (2015), associated publications in top international journals (see, for example, [1]-[5] below), and invitations to give plenary talks at a number of international meetings (most recently at "Droplets 2015" in Twente in October 2015). We will build on the considerable body of previous work by ourselves and others on single droplets to tackle the challenging problem of the nonlinear interactions between multiple evaporating droplets. There are various physical mechanisms by which two or more evaporating droplets can interact, but the most important in practice are expected to be through the atmosphere via the vapour they emit [2], and through the substrate via the evaporative cooling they cause [1]. We will use a combined theoretical and experimental approach to formulate and analyse new mathematical models that capture and elucidate the key physical mechanisms at play when multiple droplets evaporate simultaneously incorporating both of these effects. We will begin be investigating a number of idealised geometries (e.g. pairs of droplets and a long line of equally spaced droplets) before tackling the typical experimental situation of a three-dimensional array of droplets (both regularly and randomly arranged). Since in practice droplets almost never occur singly, this problem is of enormous practical importance but, due to its inherent complexity, little is understood about theoretically about the role that the nonlinear interactions between the individual droplets has on the global properties of the system. We believe that with an excellent student like Lauren keen to begin work on this challenging problem, we have the experience and skills to make rapid and substantial progress on this problem, and to produce results which will be of wide interest to the many mathematicians, physicists and chemists working in the rapidly-growing field of droplet evaporation.

[1] Dunn, Wilson, Duffy, David and Sefiane,
The strong influence of substrate conductivity on droplet evaporation,
J. Fluid Mech. 623 329-351 (2009)

[2] Sefiane, Wilson, David, Dunn and Duffy,
On the effect of the atmosphere on the evaporation of sessile droplets of water,
Phys. Fluids 21 06210 (2009)

[3] Stauber, Wilson, Duffy and Sefiane,
On the lifetimes of evaporating droplets,
J. Fluid Mech. 744 R2 (2014)

[4] Stauber, Wilson, Duffy and Sefiane,
Evaporation of droplets on strongly hydrophobic substrates,
Langmuir 31 3653-3660 (2015)

[5] Stauber, Wilson, Duffy and Sefiane,
On the lifetimes of evaporating droplets with related initial and receding contact angles,
Phys. Fluids 27 122101 (2015)