A nitrogen Leidenfrost droplet on a water pool: Experiments, theory and simulations of droplet shrinkage and ice formation

The cooling capabilities of liquid nitrogen are exploited in various fields, where the liquid is often in apparent contact with a soft or even liquid partner. Even though the heat transfer between the partners is mostly of actual concern for the given application, it is not yet fully described. In the present work, the shrinkage of a nitrogen Leidenfrost droplet on a water pool and the resulting formation of ice inside the pool are examined experimentally, theoretically and numerically. Experiments are performed using nitrogen droplets of varying size, deposited onto a water pool which is initially always at its melting temperature. Droplet shrinkage and ice formation are captured using a high-speed video camera providing a synchronized top and side-view on the scene. An existing analytical model for the interface shape of the droplet and the pool in the given situation is extended to enable theoretical prediction of the temporal evolution of the droplet size and the volume of ice formed inside the pool. While only heat transfer at the droplet bottom is considered in the original model, in the present work also the major contributions to the heat transfer at the droplet top and at the pool meniscus are accounted for. Additionally, numerical simulations of droplet shrinkage are performed using a commercial finite-element simulation software (COMSOL Multiphysics). For both the theoretical model and the numerical simulations, the droplet and the pool are assumed isothermal and heat transfer is only considered in the gaseous ambient. Finally, both the theoretical predictions and numerical results generally well resemble the experimental findings for droplet shrinkage, where the numerical simulations show a slightly better agreement. Also the theoretical predictions for the ice volume forming inside the pool are in good agreement with the experimental results, confirming the good predictive capabilities of the theoretical model for the present situation.