A NOVEL BOUNDARY-INTEGRAL ALGORITHM FOR VISCOUS INTERACTION OF DEFORMABLE DROPS

A new three-dimensional boundary-integral algorithm for deformable dro ps moving in a viscous medium at low Reynolds numbers is developed, wh ich overcomes some familiar difficulties with boundary-integral calcul ations. The algorithm is used to simulate different modes of interacti on between drops or bubbles, primarily for buoyancy-driven motion. The present iterative method for mean curvature calculation is found to b e more robust and accurate than contour integration schemes. A novel i terative strategy based on combining biconjugate gradient and simple i terations overcomes the poor convergence of ''successive substitutions '' for drops in very close approach with extreme viscosity ratio. A su bstantially new variational method of global mesh stabilization solves the problem of mesh degradation with advantageous, soft stability con straints. A curvatureless boundary-integral formulation is also derive d and shown to provide, in principle, a more accurate description of t he drop breakup than the conventional formulation. The efficiency of t hese techniques is demonstrated by numerical examples for two drops in gravity-induced motion with high surface resolutions. The present cod e successfully simulates mutual approach of slightly deformable drops to extremely small separations, as well as their rotation when in ''ap parent contact,'' thus bridging the gap between finite deformation cal culations and a recent asymptotic theory for small capillary numbers. Also provided is a 3D simulation of the experimental phenomenon of enh anced bubble coalescence, discovered by Manga and Stone [J. Fluid Mech . 256, 647 (1993); 300, 231 (1995)]. For drops of viscosity comparable to that of the surrounding fluid, it is shown in contrast that breaku p is a typical result of hydrodynamic interaction in gravity-induced m otion for large and even moderate capillary numbers. The code is readi ly applicable to any type of an ambient flow and may be adapted to mor e than two drops. (C) 1997 American Institute of Physics.