Modeling of a liquid nitrogen droplet evaporating inside an immiscible liquid pool

Evaporation of liquid nitrogen in another immiscible liquid occurs in many industrial applications. Existing oversimplified one-dimensional (1D) quasi-steady models, although can quantitatively predict the evaporation rate by introducing an empirical fitting parameter, rely on configurations inconsistent with experimental observation so more rigorous models are required to get in-depth physical insights and improve modeling capability. This study proposes a 2D quasi-steady-state theoretical model, free of fitting parameters, that predicts the bubble growth rate and estimates the heat transfer rate for a liquid nitrogen droplet evaporating inside a liquid pool within the spherical bubble regime. The droplet's shape and position within a spherical bubble are determined by the equilibrium between the gravitational force and the upward pressure force resulting from the vapor flow between the droplet and the pool. The vapor layer thickness is calculated to be on the order of 10 microns. Notably, the primary contribution to heat transfer arises from the lower portion of the droplet, leading to local heat flux values up to approximately six times higher at the bottom compared to the top. The predicted bubble growth is quantitatively consistent with experimental data within the capillary spherical bubble regime. Furthermore, the overall heat transfer rate Q exhibits a distinct scaling relationship with the volume ratio between the bubble and droplet, yielding Q∼(Vb/Vd)−0.1.