Non-conforming finite elements for axisymmetric charged droplet deformation dynamics and Coulomb explosions

摘要

The deformations of both electrically charged and uncharged incompressible axisymmetric Newtonian viscous liquid droplets acting under the effects of surface tension (but not gravity) are studied using a non-conforming, discontinuous Galerkin finite element procedure with moving meshes. The full Navier-Stokes equations are discretized and solved in an Eulerian manner with a simple predictor-corrector Lagrangian updating of the free boundary location coincident with the droplet surface at each solution iteration. By using linear Crouzeix-Raviart basis functions for the velocity and piecewise constant pressures, results are presented both for the simple (oscillatory) relaxation of elongated electrically charged/uncharged droplets to a sphere and for the deformation to steady state/Coulomb explosions of initially slightly oblate/prolate spheroidal droplets charged beyond/to the Rayleigh limit.