Fluid-structure interaction effects in the sedimentation of thin elastic sheets

There is much current interest in so-called two-dimensional materials because of their unusual and attractive mechanical and electrical properties. Much of their processing is performed in a fluid environment, e.g. during the size selection of dispersed graphene flakes by centrifugation, or their deposition by ink-jet printing. The flakes’ large aspect ratio implies that despite their impressive in-plane stiffness they have a very small bending stiffness and are therefore easily deformed by the traction that the surrounding fluid exerts on them. The resulting strong fluid-structure interaction affects not only the dynamics of individual flakes but also their collective behaviour.

The aim of this project is to perform a systematic study of the behaviour of thin elastic sheets in a viscous fluid. Specifically, we wish to establish how the flow-induced deformation affects the sedimentation of such sheets, paying particular attention to

- the effect of the sheets’ aspect ratio; long narrow sheets are likely to behave in a manner similar to elastic rods: at which point does their finite aspect ratio become significant?

- the effect of wrinkling instabilities and the development of symmetry-breaking frustrated patterns: how do they arise in sheets of canonical shapes (circular, rectangular, polygonal,...) and how do they affect the sheets’ sedimentation?

The focus of this specific project is on computational/semi-analytical approaches and would suit a student with a good background in Applied Mathematics (especially fluid and solid mechanics) and Scientific Computing. There is an opportunity for hands-on involvement in an associated experimental study in the School of Physics and Astronomy.