Berkeley Fluids Seminar

Skating on a thin vapour film: the inverse Leidenfrost phenomenon

Monday, April 22, 2019

12:00-13:00, 3110 Etcheverry Hall

Prof. Stephen Morris

(Mechanical Engineering)

Abstract: When placed on the surface of a volatile liquid, a sufficiently small hot sphere of denser matter skates over the surface until it cools and sinks. Surface tension sets a upper limit to the particle size which can be thus supported. In experiments, the largest particles appear to approach this limit [Hall et al. Nature 1969]. Based on their experiments, Adda–Bedia et al. [Langmuir 2016] argue that the vapour, in effect, causes a sphere to become non–wetting with respect to the liquid. In that case, neither the phenomenon of skating, nor knowledge of the precise value of the superheat, would be essential to understanding particle levitation. To test that conclusion, levitation of a stationary sphere is analysed here. The Reynolds equation governing the pressure distribution within the vapour film is coupled to the Laplace–Young equation determining the response of the pool surface to that pressure. This B.V.P. has an elementary solution describing the limit in which the sphere load vanishes compared with the surface tension force available to support it. The pool surface is then asymptotically flat, allowing film pressure and interface profile to be found as explicit functions of dimensionless load L, superheat ε, and Bond number B. For finite L, fixed ε and vanishing B, numerical solutions show that, for a given film thickness $$h₀ at the sphere bottom, two interface shapes are possible: one corresponds to a low value of the pressure $$p₀ at the sphere bottom; the other, to a higher value of $$p₀ , and to the presence at the sphere bottom of a thin bubble cap having imperfectly sealed rim, through which vapour escapes to the atmosphere. Above a certain $$p₀, there appears to be no solution to the B.V.P. When the superheat ε is reduced, this maximum $$p₀ approaches a limit, but the supportable load vanishes because the vapour bubble shrinks in angular extent. For realistic values of ε, the maximum size of a stationary particle which can be supported is small compared those found experimentally. This suggests skating is essential to the phenomenon; this might be tested by studying experimentally the behaviour of a hot bead freely sliding on a vertical wire.

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Acknowledgments

Prof. Eliot Quataert on behalf of The Theoretical Astrophysics Center and the Astronomy Department (UC Berkeley)

Prof. Philip S. Marcus on behalf of the Mechanical Engineering Department (UC Berkeley)

Prof. Michael Manga (Earth and Planetary Science, UC Berkeley)

Prof. Evan Variano (Civil and Environmental Engineering, UC Berkeley)