Free surface profiles and thermal convection in electrostatically levitated droplets

A mathematical model for marangoni flow and mass transfer in electrostatically positioned droplets

“…The balance of this force with others acting on the droplet determines the equilibrium shape of the droplet. [13,14] The electric surface force, however, is nonvorticial in nature and does not generate a flow in the droplet. Also, for microgravity applications, the electric forces are used to position the droplet at a fixed location.…”

“…[4] A complete description of the electrically induced surface deformation, thermally induced fluid flow phenomena in a droplet requires the solution of the coupled Maxwell and Navier-Stokes equations, along with the energy balance equation. However, the dynamic pressure and the viscous stresses together contribute less than 2 pct to the surface deformation [13] and thus may be neglected. For a metal droplet, the Maxwell equation is simplified to a partial differential equation governing the distribution of the electric field outside the droplet.…”

“…[8] [9] [10] [11] [12] [13] [14] [15] [16] [17] A simple explanation of these equations may be worthwhile. Equation [7] is the jump condition for the electric field along the droplet surface, a manifestation of a well-known fact that charges are distributed only on the surface of a conducting body.…”

“…Recently, numerical models have been developed for surface deformation and the Marangoni flows in droplets with axisymmetric heating under both earthbound and microgravity conditions. [10][11][12][13][14] These studies show that the Marangoni convection can be considerably vigorous in electrostatically levitated metallic droplets for various different heating arrangements.…”

“…[4] Previous studies on droplet deformation show that for electrostatically levitated droplets under normal conditions, the deformation is approximately axisymmetric even when the heating is not. [10][11][12][13][14] As such, an axisymmetric model may be used to represent the droplet deformation as a first approximation. The flow field is fully three-dimensional (3-D) with complex heating arrangements.…”