AXISYMMETRICAL NON-NEWTONIAN DROPS TREATED WITH A BOUNDARY INTEGRAL METHOD

A boundary integral method for the simulation of the time-dependent de formation of axisymmetric Newtonian or non-Newtonian drops suspended i n a Newtonian fluid subjected to an axisymmetric flow field is develop ed. The boundary integral formulation for Stokes Row is used and the n on-Newtonian stress is treated as a source term which yields an extra integral over the domain of the drop. By transforming the integral rep resentation for the velocity to cylindrical coordinates we can reduce the dimension of the computational problem. The integral equation for the velocity remains of the same form as in Cartesian coordinates, and the Green's functions are transformed explicitly to cylindrical coord inates. Besides a numerical validation of the method we present simula tion results for a Newtonian drop and a drop consisting of an Oldroyd- B fluid. The results for the Newtonian drop are consistent with result s from the literature. The deformation process of the non-Newtonian dr op for small capillary numbers appears to be governed by two relaxatio n times.