BOUNDARY-ELEMENT ANALYSIS OF PLANAR DROP DEFORMATION IN CONFINED FLOW- PART II - VISCOELASTIC FLUIDS

A boundary element formulation is presented for the general two-dimens ional simulation of confined two-phase incompressible flow of viscoela stic fluids. A boundary-only formulation is implemented for fluids obe ying the Oldroyd-B constitutive equation. Similarly to the formulation in Part I for Newtonian fluids [Khayat et al. Engng Anal Boundary Ele ments 1997;19:279], the method requires the solution of two simultaneo us integral equations on the interface between the two fluids and the confining solid boundary. Although the problem is formulated for any c onfining geometry, the method is illustrated for a deforming drop as i t is driven by the ambient flow inside a convergent channel. The accur acy and convergence of the method are assessed by comparison with the analytical solution for two-phase Taylor-Couette flow, leading to exce llent agreement. Further assessment is made by varying the time increm ent and mesh size of the discretized boundary for a drop deforming in a convergent channel. The influence of fluid elasticity is examined wh en one or both fluids are viscoelastic. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.