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Mathematical Modelling and Analysis of Sessile Droplets

   Department of Mathematics & Statistics

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  Prof S K Wilson, Dr A Wray  No more applications being accepted  Funded PhD Project (European/UK Students Only)

About the Project

The behaviour of evaporating sessile droplets is an area of very active international research, with new publications appearing on an almost daily basis and entire conferences now dedicated to the topic.

In recent years, the first supervisor Professor Stephen Wilson has collaborated very successfully with Professor Khellil Sefiane from the School of Engineering at the University of Edinburgh (a Visiting Professor at the University of Strathclyde who will be closely involved with the present project) on a variety of practically important fluid-dynamical problems, including evaporating droplets, bubble dynamics, self-rewetting fluids, and anti-surfactants, and the second supervisor Dr Alexander Wray has rapidly established a reputation for cutting-edge analytical and numerical research in a wide range of fluid dynamics problems (including both thin-film and thick-film flows).

The aim of the present project is to build on the supervisors’ previous work on evaporating sessile droplets to explore two exciting new aspects of this scientifically and practically important problem.

Firstly, recent work by Sefiane and his collaborators [1] has provided the first comprehensive experimental investigation of vapour absorption by sessile droplets of a desiccant liquid (i.e. one which draws moisture from the air). The mathematical modelling and analysis of such systems is an exciting and challenging open problem.

Secondly, in practice, droplets almost never occur singly, but, due to the inherent complexity of the multiple-droplet problem, very little work has so far been done regarding the interactions between evaporating droplets. This conspicuous omission in the literature was very recently rectified by the supervisors and their collaborators [2,3] who demonstrated how to accurately model arrays of droplets in two and three dimensions. The aim of the proposed work is to investigate the fascinating, but otherwise virtually unexplored, subject of the collective behaviour of large arrays of small sessile droplets. Interactions between the droplets (in particular, so-called "shielding" effects) are expected to lead to very different collective behaviour compared to that of isolated droplets.

The student will join a lively and mutually supportive cohort of fellow PhD students within the Continuum Mechanics and Industrial Mathematics (CMIM) research group.

You should have (or expect to have) a UK Honours Degree (or equivalent) at 2.1 or above in Mathematics, Mathematics and Physics, Physics or a closely related discipline with a high mathematical content. Knowledge of Continuum Mechanics and mathematical methods (such as asymptotic methods) for the solution of partial differential equations is desirable (but not essential, particularly for overseas applicants).

This project is available now (but the actual start date is flexible and can be as late as Autumn 2020) and applications will be considered as they are received up to the closing date of 28th February 2020. Early application is strongly encouraged.

Informal enquiries can be made to the lead supervisor, Professor Stephen K. Wilson, Department of Mathematics and Statistics, University of Strathclyde, Glasgow at [Email Address Removed] and/or +44(0)141 548 3820. However, formal applications must be made via the online application procedure which can be found at

remembering to list the title of the project as “Mathematical Modelling and Analysis of Sessile Droplets” and Professor Stephen K. Wilson as the first supervisor. There is no need to include a detailed research plan, but a brief outline of your relevant experience (if any) and your motivation for choosing this project would assist with the selection procedure.

Funding Notes

This project will be supported by a Research Excellence Award (REA) Studentship funded by the University of Strathclyde with the support of the University of Edinburgh.

Unfortunately, funding rules mean that this studentship is only open to UK and EU students, and not to EEA or International students. Moreover, EU students are only eligible for the stipend element of the studentship if they have been resident in the UK for 3 years, including for study purposes, immediately prior to starting their PhD.


[1] Wang, Z., Orejon, D., Sefiane, K., Takata, Y., "Water vapor uptake into hygroscopic lithium bromide desiccant droplets: mechanisms of droplet growth and spreading", Phys. Chem. Chem. Phys. 21 (3) 1046-1058 (2019)

[2] Wray, A.W., Duffy, B.R., Wilson, S.K., "Competitive evaporation of multiple sessile droplets", J. Fluid Mech. 884 45 (2020)

[3] Schofield, F.G.H., Wray, A.W., Pritchard, D., Wilson, S.K., "The shielding effect extends the lifetimes of two-dimensional sessile droplets", to appear in J. Eng. Maths. (2020)
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