A hybrid boundary/finite element method for simulating viscous flows and shapes of droplets in electric fields

A mixed boundary element and finite element numerical algorithm for the sim ultaneous prediction of the electric fields, viscous flow fields, thermal f ields and surface deformation of electrically conducting droplets in an ele ctrostatic field is described in this paper. The boundary element method is used for the computation of the electric potential distribution. This allo ws the boundary conditions at infinity to be directly incorporated into the boundary integral formulation, thereby obviating the need for discretizati on at infinity. The surface deformation is determined by solving the normal stress balance equation using the weighted residuals method. The fluid flo w and thermal fields are calculated using the mixed finite element method. The computational algorithm for the simultaneous prediction of surface defo rmation and fluid flow involves two iterative loops, one for the electric f ield and surface deformation and the other for the surface tension driven v iscous flows. The two loops are coupled through the droplet surface shapes for viscous fluid flow calculations and viscous stresses for updating the d roplet shapes. Computing the surface deformation in a separate loop permits the freedom of applying different types of elements without complicating p rocedures for the internal flow and thermal calculations. Tests indicate th at the quadratic, cubic spline and spectral boundary elements all give appr oximately the same accuracy for free surface calculations; however, the qua dratic elements are preferred as they are easier to implement and also requ ire less computing time. Linear elements, however, are less accurate. Numer ical simulations are carried out for the simultaneous solution of free surf ace shapes and internal fluid flow and temperature distributions in droplet s in electric fields under both microgravity and earthbound conditions. Res ults show that laser heating may induce a non-uniform temperature distribut ion in the droplets. This non-uniform thermal field results in a variation of surface tension along the surface of the droplet, which in turn produces a recirculating fluid flow in the droplet. The viscous stresses cause addi tional surface deformation by squeezing the surface areas above and below t he equator plane.