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Fluid flow and heat transfer in levitated droplets were numericallyinvestigated. Three levitation methods: electro-magnetic levitation (EML),aerodynamic levitation (ADL), and electro-static levitation (ESL) wereconsidered, and conservative laws of mass, momentum, and energy were applied ascommon models. The Marangoni effect was applied as a velocity boundarycondition, whereas heat transfer and radiation heat loss were considered asthermal boundary conditions. As specific models to EML, the Lorentz force, andJoule heat were calculated based on the analytical solution of theelectromagnetic field. For the ADL model, besides the Marangoni effect, theflow driven by the surface shear force was considered. For ADL and ESL models,the effect of laser heating was introduced as a boundary condition. All theequations were nondimensionalized using common scales for all threelevitations. Numerical simulations were performed for several materials anddroplet sizes, and the results were evaluated in terms of the Reynolds numberbased on the maximum velocity of the flow in the droplet. The order ofmagnitude of Reynolds numbers was evaluated as $\text{Re} \sim 10^4$ for EML,$\text{Re} \sim 10^3$ for ADL, and $\text{Re} \sim 10^1$ for ESL. Based on thesimulation results, we proposed simple formulas for predicting the Reynoldsnumber of droplet internal convection using combinations of nondimensionalnumbers determined from the physical properties of the material and the drivingconditions. The proposed formulas can be used as surrogate models to predictthe Reynolds numbers, even for materials other than those used in this study.

Surrogate models for the magnitude of convection in droplets levitated through EML, ADL, and ESL methods