Free surface profiles and thermal convection in electrostatically levitated droplets

A numerical analysis is presented of free surface profiles, Marangoni conve ction and the temperature distribution in electrostatically levitated dropl ets. The analysis is based on the boundary element solution of electric pot ential outside the droplet, the weighted residuals formulation of the free surface balance equation involving electrostatic stresses, surface tension and gravity, and the finite element solution of the internal fluid flow and temperature distribution in the electrostatically deformed droplets. Numer ical simulations are carried out for several different materials and variou s operating conditions. Results show that an applied electrostatic field ge nerates a normal stress distribution along the droplet surface, which, comb ined with surface tension, causes the droplet to deform into an ellipsoidal shape in microgravity and into the shape of a blob with the lower side bei ng flatter under terrestrial conditions. Laser heating induces a non-unifor m temperature distribution in the droplet, which in turn produces recircula ting convection in the droplet. For the cases studied, Marangoni convection is the predominant mode and buoyancy effects are negligible. It is found t hat there is a higher temperature gradient and hence stronger Marangoni con vection in droplets with higher melting points which require more laser pow er. The internal recirculating flow may be reduced by more uniform laser he ating. During undercooling of the droplet with heating turned off, both tem perature and fluid flow fields evolve in time, such that the temperature gr adient and the tangential velocities along the droplet surface subside in m agnitude and reverse their directions. (C) 2000 Elsevier Science Ltd. All r ights reserved.