Numerical simulation of levitating liquid drops using the dynamic van der Waals theory

Liquid drops under gravity can levitate on a vapor cushion which is either sourced at the liquid-vapor interface from evaporation caused by the hot substrate below - the Leidenfrost effect, or supplied by an upward flow injected from beneath. The lubrication approximation has been fruitfully applied to analyze the thin vapor layer between the liquid drop and the solid substrate. In the present work, we investigate the validity of the lubrication approximation for the vapor layer under the Leidenfrost drops. This is carried out by numerically simulating systems of liquid and vapor using the recently developed dynamic van der Waals theory, in which the two-phase hydrodynamics is coupled with liquid-vapor transition. We find that the solutions derived from the lubrication approximation generally compare well to our simulation results, and the shape of the vapor layer shows good agreement. The robustness of the lubrication approximation is attributed to the common features found in the pressure variation through the vapor layer, resulting from an accumulation of vapor in the central cavity region before an abrupt escape at the thin neck region. We also find that under the drop, the pressure profile remains nearly independent of the vertical distance away from the substrate, in agreement with the lubrication approximation. However, as the evaporative region is approached near the liquid-vapor interface, appreciable deviations show up. Furthermore, by simulating isothermal drops levitating on a cushion of vapor injected from beneath, the phenomenon is found to be reasonably insensitive to the specifics of injected flow. This is still attributed to the accumulation of vapor in the central cavity region before the abrupt escape at the neck region. One of the challenging aspects of the Leidenfrost effect is the vapor layer dynamics coupled with strong evaporation. Therefore, the insensitivity observed in our simulations, which agrees with previous analytical and experimental results, can be taken as a relief for a general understanding of the Leidenfrost effect.