Boundary integral equations in quasisteady problems of capillary fluid mechanics. I  Application of the hydrodynamic potentials
Abstract
The motion of a viscous multiphase liquid occupying all the space under the action of surface tension is considered. Applying the quasisteady approximation (i.e., when mass forces including inertia terms are neglected), the flow is completely defined by the location of an interface for which the abstract Cauchy problem with nonlocal 'normal velocity' operator is formulated. In order to obtain this operator, a standard auxiliary problem for the Stokes system is to be solved which can be reduced to the Fredholm boundary integral equations by means of the application of the hydrodynamic potentials of simple layers. The stability problem of a spherical drop drift is investigated as an illustration of this method.
 Publication:

Meccanica
 Pub Date:
 December 1990
 Bibcode:
 1990Mecc...25..239A
 Keywords:

 Boundary Integral Method;
 Capillary Flow;
 Hydrodynamic Equations;
 Multiphase Flow;
 Potential Flow;
 Cauchy Problem;
 Interfacial Tension;
 NavierStokes Equation;
 QuasiSteady States;
 Reduced Gravity;
 Fluid Mechanics and Heat Transfer