Dynamics of drop formation in an electric field

The effect of an electric field on the formation of a drop of an inviscid, perfectly conducting liquid from a capillary which protrudes from, the top plate of a parallel-plate capacitor into a surrounding dynamically inactive , insulating gas is studied computationally. This free boundary problem whi ch is comprised of the surface Bernoulli equation for the transient drop sh ape and the Laplace equation for the velocity potential inside the drop and the electrostatic potential outside the drop is solved by a method of line s incorporating the finite element method for spatial discretization. The f inite element algorithm employed relies on judicious use of remeshing and e lement addition to a two-region adaptive mesh to accommodate large domain d eformations, and allows the computations to proceed until the thickness of the neck connecting an about to form drop to the rest of the liquid in the capillary is less than 0.1% of the capillary radius. The accuracy of the co mputations is demonstrated by showing that in the absence of an electric fi eld predictions made with the new algorithm are in excellent agreement with boundary integral calculations (Schulkes, R M. S. M. J. Fluid Mech. 278, 8 3 (1994)) and experimental measurements on water drops (Zhang, X., and Basa ran, O. A. Phys. Fluids 7(6), 1184 (1995)). In the presence of an electric field, the algorithm predicts that as the strength of the applied held incr eases, the mode of drop formation changes from simple dripping to jetting t o so-called microdripping, in accordance with experimental observations (Cl oupeau, M., and Prunet-Foch, B. J. Aerosol Sci. 25(6), 1021 (1994); Zhang, X., and Basaran, O. A. J. Fluid Mech. 326, 239 (1996)). Computational predi ctions of the primary drop volume and drop length at breakup are reported o ver a wide range of values of the ratios of electrical, gravitational, and inertial forces to surface tension force. In contrast to previously mention ed cases where both the flow rate in the tube and the electric field streng th are nonzero, situations are also considered in which the flow rate is ze ro and the dynamics are initiated by impulsively changing the field strengt h from a certain value to a larger value. When the magnitude of the step ch ange in field strength is small, the results of the new transient calculati ons accord well with those of an earlier stability analysis (Basaran, O. A. , and Scriven, L. E. J. Colloid Interface Sci. 140(1), 10 (1990)) and there by provide yet another testament to the accuracy of the new algorithm. (C) 1999 Academic Press.