(617a) Numerical Analysis of the Nonlinear Deformation and Breakup of Semi-Insulating Electrified Liquid Jets

The breakup of electrified jets is important in applications as diverse as electrospraying, electrospinning, electroseparations, electrodispersion, and electrospray mass spectrometry. Of particular interest are the fine liquid filaments that are emitted from the tips of highly-charged conical menisci in the so-called cone-jet mode of electrospraying (cf. Cloupeau and Prunet-Foch, J. Aerosol Sci., 1994). These filaments breakup to form monodisperse droplets, yielding high quality aerosols. Previous numerical studies of electrified jet breakup have either employed one-dimensional slender-jet approximations of the equations of motion (cf. Lopez-Herrera and Ganan-Calvo, J. Fluid Mech., 2004) or have been restricted to inviscid, irrotational flow (cf. Setiawan and Heister, J. Electrostatics, 1997). Further, these studies have generally treated the electrified jet as a perfect conductor. While a perfect conductor model is appropriate in many instances for describing the bulk phenomena associated with electrified jet breakup for highly conducting fluids, this model does not necessarily provide a realistic description of the actual pinch-off singularity. As pinch-off is approached, the fluid velocity in the immediate vicinity of the pinch point becomes unbounded such that the time scale for charge relaxation ceases to be small with respect to the local capillary time scale. In this work, the finite amplitude deformation and breakup of a semi-insulating, incompressible Newtonian liquid jet surrounded by a dynamically inactive, insulating gas that is stressed by a radial electric field is examined computationally by a temporal analysis. The three dimensional but axisymmetric Navier Stokes system of equations together with the Laplace equation for the electric potential and the equations governing surface charge transport are solved by a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. Finite charge relaxation is modeled using the Taylor-Melcher leaky-dielectric model (cf. Melcher and Taylor, Annu. Rev. Fluid Mech., 1969). The adaptive elliptic mesh generation technique used (cf. Christodoulou and Scriven, J. Comput. Phys., 1992) is capable of tracking the dynamics of the jet up to the incipience of pinch-off without requiring remeshing. Similar FEM algorithms have been shown to be in excellent agreement with both scaling theories and measurements in the absence of electric fields (cf. Chen, Notz, and Basaran, Phys. Rev. Lett., 2002). These techniques have been modified to allow for accurate resolution of electrostatic stresses in the spatial and temporal proximity of the pinch-off singularity without requiring a prohibitively large number of elements. The influence of electric Bond number (electric/surface tension force), Reynolds number (inertial/viscous force), disturbance wavenumber, permittivity ratio, and dimensionless conductivity on the deformation and breakup of electrified jets are examined. Further, the influence of electrostatic stresses on the local scaling laws governing pinch-off is examined, including a detailed comparison between results obtained for semi-insulating and perfectly conducting jets.