AXISYMMETRICAL SHAPES AND STABILITY OF PENDANT AND SESSILE DROPS IN AN ELECTRIC-FIELD

The equilibrium shapes and stability of an axisymmetric conducting drop of fixed volume that is surrounded by a fluid insulator and is pendant or sessile on a face of a parallel-plate capacitor are governed by electrical and gravitational Bond numbers, Ne and G. These measure, respectively, the relative importances of electrical and gravitational forces compared to surface tension forces. When both Ne and G vanish, equilibrium drop shapes are sections of a sphere and are stable with respect to all perturbations having an infinitesimal amplitude. When Ne and G are nonzero, drop shape and stability can be found by solving simultaneously, by Galerkin's method with finite element basis functions, the free boundary problem composed of the augmented Young-Laplace equation for surface shape and the Laplace equation for electric field. Asymptotic analysis for small values of Ne, when G = 0, agrees well with numerical calculations and predicts that drops that are hemispherical in the absence of electric field evolve into a family of spheroidal shapes when the contact angle is prescribed and a family of conical shapes when the contact line is fixed. The locus of singular points marking the loss of existence of static drops is determined. The theoretical results are found to be in excellent agreement with available experiments. As expected, the results show that drops with their contact lines fixed are more stable than ones whose contact angles are prescribed. © 1990.