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.
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.