Finite element modeling of internal flow and stability of droplets levitated in electric and magnetic fields

The present study presents the numerical model of the free surface deformation and oscillation, heat and mass transfer, and Marangoni flow in the electrostatically levitated droplets under microgravity conditions. The free surface deformation, heat and mass transfer, and Marangoni flow are also investigated in the electrostatically levitated droplets comprised of the immiscible liquid metals. The present study not only investigates the steady-state fluid flow and heat transfer, but also the transient fluid flow and heat transfer, which is important for the fundamental study of nucleation and crystal growth phenomena. The 3-D vertical and horizontal movement of the magnetically levitated droplet is also investigated in the present study.;The coupled boundary method is developed to predict the electric potential distribution in the electrostatically levitated droplets. The surface deformation is determined using the weighted residuals method to solve the normal stress balance equations. The complex 3-D fluid flow and heat transfer fields are solved by using the Galerkin finite element method. The computational methodology for the oscillation of the electrostatically levitated droplets entails solving the Laplace equation by the boundary element method, solving the Navier-Stokes equations by the Galerkin finite element method, and the use of deforming elements to track the oscillating free surface shapes. The coupled boundary and finite element methods with edge element algorithm are applied to the solution of the movement of the conducting droplet in the magnetic levitation mechanism. The numerical model should be a useful toolkit for developing electrostatic and magnetic levitation systems for space applications as well as for planning relevant experiments in space shuttle flights or in the International Space Station under construction.