par Sobac, Benjamin 
;Rednikov, Alexei ;Colinet, Pierre
Référence Journal of fluid mechanics, 1010, A47
Publication Publié, 2025-06-01
;Rednikov, Alexei ;Colinet, Pierre Référence Journal of fluid mechanics, 1010, A47
Publication Publié, 2025-06-01
Article révisé par les pairs
| Résumé : | An isolated Leidenfrost droplet levitating over its own vapour above a superheatedflat substrate is considered theoretically, the superheating for water being up to severalhundred degrees above the boiling temperature. The focus is on the limit of small,practically spherical droplets of several tens of micrometres or less. This may occurwhen the liquid is sprayed over a hot substrate, or just be a late life stage of an initiallylarge Leidenfrost droplet. A rigorous numerically assisted analysis is carried out withinverifiable assumptions such as quasi-stationarities and small Reynolds/Péclet numbers.It is considered that the droplet is surrounded by its pure vapour. Simple formulaeapproximating our numerical data for the forces and evaporation rates are preliminarilyobtained, all respecting the asymptotic behaviours (also investigated) in the limits of smalland large levitation heights. They are subsequently used within a system of ordinarydifferential equations to study the droplet dynamics and take-off (drastic height increase asthe droplet vapourises). A previously known quasi-stationary inverse-square-root law forthe droplet height as a function of its radius (at the root of the take-off) is recovered,although we point out different prefactors in the two limits. Deviations of a dynamicnature therefrom are uncovered as the droplet radius further decreases due to evaporation,improving the agreement with experiment. Furthermore, we reveal that, if initially largeenough, the droplets vanish at a universal finite height (just dependent on the superheatand fluid properties). Scalings in various distinguished cases are obtained along the way. |
