Leidenfrost drop dynamics: An approach to follow the complete evolution

Abstract

A new model to follow the complete evolution of a drop in Leidenfrost state is presented in this work. The main ingredients of the phenomenon were considered, including: 1) the shape and weight of a sessile drop, according to its size, compared to the capillary length, using the Young-Laplace equation; 2) the evaporation at the entire surface of the drop, due to the heat transfer across the vapor film, to the proximitiy of a hot plate and to the diffusion in air; 3) the velocity, pressure and temperature fields at the vapor film, between the drop and the hot plate, which are recovered by means of a Hankel transform method, being valid for any size of drops and any thickness of vapor films (below the vapor film stability threshold); 4) an estimation of the thermo-capillary Marangoni convection flow, without simulating numerically the flow within the drop. The aforementioned features were addressed and calculated, in order to include their effect within a single non-linear ODE, describing the temporal evolution of the size of the drop, through the Bond number. Three dimensionless parameters, relating the thermophysical properties of the drop fluid and the surrounding air, control the development of the phenomenon. All those properties were calculated according to the ideal gas approximation and to widely used empirical correlations, without any fitting parameter. The model predictions were compared against experimental results, using different organic and inorganic compounds, for which a good agreement has been found, when no bounce or rotation of the drop spontaneously occurs.