Quantifying the dynamic spreading of a molten sand droplet using multiphase mesoscopic simulations
RB Koneru and A Flatau and Z Li and L Bravo and M Murugan and A Ghoshal and GE Karniadakis, PHYSICAL REVIEW FLUIDS, 7, 103602 (2022).
Upon coming into contact with a solid surface, a liquid droplet spreads rapidly during the early moments due to inertial/capillary effects before the viscous dissipation slows it down. The temporal evolution of the spreading radius depends on the viscosity of the liquid drop. For low-viscosity liquids, the spreading radius follows a power-law, whereas for higher viscosity liquids it scales linearly with time with additional logarithmic corrections. In this work, the spreading dynamics of molten sand is investigated at isothermal conditions. The molten sand is a mixture of Calcia, Magnesia, Alumina, and Silicate, commonly referred to as CMAS, and is characterized by large viscosity, density, and surface tension. The multiphase many-body dissipative particle dynamics (mDPD) model is carefully parame-terized to simulate a highly viscous molten CMAS droplet at 1260 oC. Three-dimensional (3D) simulations were carried out at different initial drop sizes and equilibrium contact angles. Despite its unique properties, the spreading behavior of molten CMAS is in good agreement with theory and experiments of viscous coalescence of drops. Importantly, the two distinct spreading regimes are observed in the mDPD simulations. Due to the large vis- cosity, a slower but a nonunique spreading rate is observed in the inertial regime. However, the spreading rate in the viscous regime is in agreement with Tanner's law. The spreading radius remains unaffected by the initial drop size and collapses onto a master curve under viscous time scaling in agreement with theory and experiments. For different equilibrium angles, the spreading rate is observed to be nearly identical in the inertial regime. This indicates a universal spreading behavior during the early stages of spreading unaffected by both the initial drop size and the equilibrium contact angle. The contact line velocity was also computed to assess its relation with the dynamic contact angle. The dynamic contact angle data collapse when plotted as a function of the capillary number, displaying a remarkable agreement with Hoffman's description of dynamic contact angle evolution.
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