A simple model of heating and evaporation of droplets on a superhydrophobic surface. (February 2023) - Antonov, D.V.; Fedorenko, R.M.; Strizhak, P.A.; Sazhin, S.S.
Highlights: A new mathematical model for droplet heating on a superhydrophobic surface. An analytical solution to the transfer equation with a source term. The analytical solution to this equation is implemented into the numerical code. Heat supplied by conduction from the substrate to the droplet is small. The model is validated against in-house and available experimental data. Abstract: A new model for heating and evaporation of a droplet on a superhydrophobic surface is proposed. The model uses the analytical solution to the spherically symmetric heat transfer equation with the source term which is implemented in the numerical code and used at each time step of the calculations. It is assumed that heat supplied by conduction and radiation from the substrate to the droplet is instantaneously and homogeneously distributed throughout the whole droplet volume. Both these assumptions are acceptable only in the case when these heats are much smaller than heat supplied to the droplet from ambient gas by convection. It is shown that in some cases heat supplied to the droplet by conduction is comparable or greater than that supplied to the droplet by convection. This happens predominantly at the final stages of droplet evaporation and in this case the model cannot be used. Another assumption on which the model is based is that the effects of the ambient gas temperature gradient on convection droplet heating can be ignored and that this heating can be considered assuming that the temperature of the ambient gas around the droplet is homogeneous. The model is validated using in-house experimental data and experimental data available from the literature. Good agreement between modelling and experimental results is demonstrated when the assumptions on which the model is based are satisfied.