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Asymptotic modelling of symmetry-breaking Leidenfrost-drop dynamics


   Department of Mathematics

   Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

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 [1]. 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 [2]. Moreover, recent experiments have shown that Leidenfrost drops can even move spontaneously, in the absence of external gradients or imposed asymmetry [3].

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 [4] to 3D and larger drops, as well as modelling the spontaneous dynamics of so-called inverse Leidenfrost drops [5], namely drops levitating above cryogenic liquid baths, and liquid drops levitating above heated liquid baths [6].

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.


Funding Notes

Please get in touch if you are a strong student looking for a PhD project that involves interfacial fluid dynamics and asymptotic analysis. There are a variety of studentships available for Home/EU students and Overseas students, and your chance of securing one of them is greater the earlier you apply.

References

[1] A. L. Biance et al., Leidenfrost drops, Phys. Fluids, 15 6 1632-1637, 2003
[2] D. Quéré, Leidenfrost dynamics, Annual Review of Fluid Mechanics, 45, 197-215
[3] A. Bouillant et al., Leidenfrost wheels, Nat. Phys., 14 1188, 2018
[4] R. Brandão and O. Schnitzer, Spontaneous dynamics of two-dimensional Leidenfrost wheels, Phys. Rev. Fluids, 5 091601(R), 2020
[5] A. Gauthier et al., Self-propulsion of inverse Leidenfrost drops on a cryogenic bath, Proc. Natl. Acad. Sci. USA, 116 1174, 2019
[6] L. Macquet et al., Leidenfrost drops on a heated liquid pool, Phys. Rev. Fluids, 1 053902, 2016

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