Study level

Master of Philosophy


Vacation research experience scheme


Topic status

We're looking for students to study this topic.


Dr Michael Dallaston
Lecturer in Applied and Computational Mathematics
Division / Faculty
Faculty of Science


One of the more challenging aspects of modelling fluid dynamics is the contact-line problem: how does a contact line (a junction between two different fluids and a solid) move over time? A variety of models exist, such as disjoining pressure models, Navier slip models, and the imposition of a prewetting film, to name a few.

In this project we will explore the behaviour of these different contact line models in the context of closing or healing liquid films. A hole in a liquid film will close due to surface tension, and the way in which models of this behave will depend strongly on the way in which the contact line is modelled. Both numerical computations and asymptotic analysis (for instance, approximations for small contact line velocity) will help illuminate the similarities and differences between these models.

For further reading, please see the following references:

  • Z. Zheng, M.A. Fontelos, S. Shin, M.C. Dallaston, D. Tseluiko, S. Kalliadasis, and H.A. Stone. Healing capillary films. J. Fluid Mech., 838:404–434, 2018.
  • D. Bonn, H. Eggers, J. Indeku, J. Meunier, and E. Rolley. Wetting and spreading. Rev. Mod. Phys., 81:739–805, 2009.

Research activities

Students will experience the techniques of mathematical modelling and asymptotic analysis of PDEs, programming (in Matlab, for example) of numerical PDE solution methods, and academic writing.


This project aims to produce mathematical working and numerical code to compare different mathematical models of contact line motion. The most ambitious outcome will be an analytically justified and numerically validated asymptotic law for the closure rate of a dry spot due to capillarity.

Skills and experience

To excel at this project you should have some knowledge of programming (e.g. in Matlab), and partial differential equations (PDEs). Knowledge of fluid mechanics principles is advantageous.



Contact the supervisor for more information.