A BOUNDARY INTEGRAL METHOD FOR 2-DIMENSIONAL (NON)-NEWTONIAN DROPS INSLOW VISCOUS-FLOW

A boundary integral method for the simulation of the time-dependent de formation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term whic h yields an extra integral over the domain of the drop. The implementa tion of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the diver gence theorem smoothness assumptions are made concerning the non-Newto nian stress tenser. The correctness of these assumptions in actual sim ulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second o rder accurate. Besides this validation we present simulation results f or a Newtonian drop and a drop consisting of an Oldroyd-B fluid. The r esults for Newtonian and non-Newtonian drops in two dimensions indicat e that the steady state deformation is quite independent of the drop-f luid. The deformation process, however, appears to be strongly depende nt on the drop-fluid. For the non-Newtonian drop a mechanical model is developed to describe the time-dependent deformation of the cylinder for small capillary numbers.