A spherical Leidenfrost droplet with translation and rotation

Abstract

This study presents a theoretical model for a spherical Leidenfrost droplet with rotational and translational motion. Scaling analysis is carried out to validate the lubrication approximation, from which the velocity, the pressure field, and the temperature profile in the vapor film underneath the mobile Leidenfrost droplet are solved. The velocity field in the rotating Leidenfrost droplet is measured by microscale particle image velocimetry, and used as the boundary condition. The pressure and the rotational speed is then linked by the balance of shear force at the liquid-vapor interface. For a given wall temperature and an initial radius of the Leidenfrost droplet, our model is able to determine the minimal thickness of vapor film, the rotational speed, the translational speed, the heat transfer rate, and the variation of droplet radius with time by numerical iteration. During the evaporation process, the Leidenfrost droplet spins and moves faster and faster, and droplet shrinkage also accelerates. In addition, there exists a critical radius below which the levitation of droplet reduces rapidly. As the wall temperature increases, this critical radius decreases and the speed-up of the droplet shrinkage becomes more apparent. The results also show that heat transfer of a Leidenfrost droplet is dominated by thermal conduction through the vapor film, but contribution of thermal radiation from the hot surface to the entire droplet grows as the wall temperature heightens. Due to the lower thermal conductivity of oil vapor, a mineral oil droplet leads to a heat transfer rate smaller than that of a water droplet. Comparing to the results of a stationary droplet, incorporating the droplet motion into the model is able to predict the characteristics of the Leidenfrost droplet more accurately.