A liquid drop can levitate on a thin film of its own vapour above a sufficiently hot substrate. This classical effect, named after J. G. Leidenfrost who first described it in 1756, is associated with a sharp transition from nucleate to film boiling with increasing substrate temperature . In the absence of direct contact between the drop and substrate, friction is virtually eliminated, resulting in high mobility and a wide range of fascinating oscillatory and instability-driven dynamical phenomena . Moreover, recent experiments have shown that Leidenfrost drops can even move spontaneously, in the absence of external gradients or imposed asymmetry .
The goal of this project is to use mathematical modelling and asymptotic analysis to study the dynamics of Leidenfrost drops and especially the symmetry-breaking fluid-dynamical instabilities underpinning their spontaneous motion. Specific goals include extending the 2D small-drop model in  to 3D and larger drops, as well as modelling the spontaneous dynamics of so-called inverse Leidenfrost drops , namely drops levitating above cryogenic liquid baths, and liquid drops levitating above heated liquid baths .
This PhD project will contribute to the Leverhulme Trust Research Grant project titled "Asymptotic modelling of symmetry breaking Leidenfrost flows," see https://www.leverhulme.ac.uk/research-project-grants/asymptotic-modelling-symmetry-breaking-leidenfrost-flows.
Essential: A strong background in applied mathematics, fluid dynamics and modelling. Desirable: Background in and experience using singular perturbation techniques, such as matched asymptotic expansions, and familiarity with wetting phenomena.