Modeling and simulation of liquid-liquid droplet heating in a laminar boundary layer

Asymmetric liquid-liquid droplet heating mechanisms differ from the more commonly studied and better understood symmetric liquid-gas mechanisms. In this work, we simulate two-dimensional low Weber number droplet heating in developing low Reynolds number liquid boundary layers. Of particular interest are the influences of Weber, Prandtl, and Reynolds number magnitudes on the system evolution. We perform simulations with a coupled Eulerian-Lagrangian interface capturing methodology - the Lagrangian volume of fluid - alongside an Eulerian solver for the Navier-Stokes equations that provides the spatial and temporal evolution of the temperature and velocity fields for the droplet and the surrounding fluid. Our results show droplet rolling induced by the velocity boundary layer modifies the temperature field in and around the droplet. Conduction negates the thermal influence of rolling in low Prandtl number droplets, but modifies the continuous phase temperature field. The Magnus force separates the droplets from the heated surface, decreasing their heating rate. These results establish the fundamentals of asymmetric liquid-liquid droplet heating in developing boundary layers: it is necessary to include the Magnus force in physically representative near-wall droplet heating models, and resolution of near-droplet temperature gradients may be necessary in situations with temperature dependent interface processes.