PhD in Mathematics and Statistics: Viscous fingering instabilities: control and flow-structure interaction (mathematical modelling, theory, and computation)

The interface between two fluids can be made morphologically unstable, resulting in complex pattern formation frequently encountered in porous media and biological systems. Such phenomena are widespread in nature and industry, ranging from crude oil recovery, hydrology, and filtration, to the self-organisation of collective biological systems and medical applications. In most cases, these instabilities occur when a less viscous fluid displaces a more viscous one, for example water displacing syrup, either by injection or by gravity when the interface separates two fluids of different densities. Initially small disturbances to the liquid-liquid interface may result in the formation of a single finger or multiple fingers that can undergo successive tip-splitting, and may involve complex, multiple finger interactions resulting in interesting fluid-dynamical patterns. In industrial processes, it is often desirable to suppress these instabilities and to control their late-time dynamics.

The aim of the project is to investigate suppression techniques involving flow-structure interaction. The project involves mathematical modelling and numerical computation.

Informal enquiries: katarzyna.kowal@glasgow.ac.uk / nigel.mottram@glasgow.ac.uk

How to Apply:

Please refer to the following website for details on how to apply:

http://www.gla.ac.uk/research/opportunities/howtoapplyforaresearchdegree/

and select “Mathematics”