PhD Studentship: The effect of surfactant on liquid film flow over a corrugated wall

Supervised by Dr Anna Kalogirou

This project will be based at the University of Nottingham in the School of Mathematical Sciences.

When a thin layer of liquid flows down a wall, its surface can deform due to the action of physical forces such as gravity and surface tension, or in response to externally imposed factors such as electric fields, wall surface irregularities etc. The latter can be a useful tool to engineer desired liquid film structures (e.g. smooth or rippled films) depending on particular practical applications, for instance coating technologies or heat exchangers. Flow-manipulation techniques also include the use of chemical additives known as surfactants, which can greatly affect the behaviour of film flows, thereby providing a means of achieving appropriate surface shapes.

This project will consider a thin film flow over a patterned wall and the primary aim will be to investigate the deforming influence of surfactants on the profile of the film surface. Previous research analysed the flow of a clean (surfactant-free) liquid down a corrugated wall or surfactant-laden film flow over a smooth wall; here, the interacting effects of surfactant and bottom topography to the deformation of the free surface will be examined. The project will combine analytical and numerical techniques with aim to develop, analyse and solve appropriate mathematical models for the study of liquid film flow with surfactants over a topographically structured wall.

Relevant publications: [1] Kalliadasis, S., Bielarz, C. and Homsy, G. M. (2000) Steady free-surface thin-film flows over topography. Phys. Fluids 12 (8), 1889–1898.

[2] C. Pozrikidis (2003). Effect of surfactants on film flow down a periodic wall. J. Fluid Mech. 496, 105–127.

[3] H. Luo and C. Pozrikidis (2007) Gravity-driven film flow down an inclined wall with three-dimensional corrugations. Acta Mechanica 188, 209–225.

Subject Areas: Applied Mathematics, Fluid Dynamics

Funding Notes: Competition funded project open to European/UK students only. Tuition Fees will be paid, and a full stipend provided at the RCUK rate (£15,285 per annum for 2020/21). There will also be some funds available to support conference attendance. The scholarship length will be 3.5 years.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably at MMath/MSc level, or an equivalent overseas qualification (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

It is highly desirable that the successful applicant is familiar with one or several of the following topics: fluid mechanics, mathematical modelling, asymptotic analysis, PDEs, numerical methods. While experience with more than one of the aforementioned mathematical fields would be beneficial, the willingness to learn and engage with all of them is an absolute necessity. The project requires the student to have experience with a scientific computing software package or programming language such as MATLAB, Fortran and/or Python.

For any informal enquiries please email Anna.Kalogirou@nottingham.ac.uk.

This studentship is open until filled. Early application is strongly encouraged.