A 2D boundary element method for simulating the deformation of axisymmetric compound non-Newtonian drops

The boundary integral formulation of the solution to the Stokes equations i s used to describe the deformation of small compound non-Newtonian axisymme tric drops suspended in a Newtonian fluid that is subjected to an axisymmet ric flow field. The non-Newtonian stress is treated as a source term in the Stokes equations, which yields an extra integral over the domains containi ng non-Newtonian material. By transforming the integral representation for the velocity to cylindrical co-ordinates and performing the integration ove r the azimuthal direction analytically, the dimension of the problem can be reduced from three to two. A boundary element method for the remaining two -dimensional problem aimed at the simulation of the deformation of such axi symmetric compound non-Newtonian drops is developed. Apart from a numerical validation of the method, simulation results for a drop consisting of an O ldroyd-B fluid and a viscoelastic material are presented. Moreover, the met hod is extended to compound drops that are composed of a viscous inner core encapsulated by a viscoelastic material. The simulation results for these drops are verified against theoretical results from literature. Moreover, i t is shown that the method can be used to identify the dominant break-up me chanism of compound drops in relation to the specific non-Newtonian charact er of the membrane. Copyright (C) 1999 John Wiley & Sons, Ltd.