Three-dimensional boundary element analysis of drop deformation in confined flow for Newtonian and viscoelastic systems

An adaptive (Lagrangian) boundary element approach is proposed for the gene ral three-dimensional drop deformation in confined flow. The adaptive metho d is stable as it includes remeshing capabilities of the deforming interfac e between drop and suspending fluid, and thus can handle large deformations . Both drop and surrounding fluid are viscous incompressible and can be New tonian or viscoelastic. A boundary-only formulation is implemented for flui ds obeying the linear Jeffrey's constitutive equation. Similarly to the for mulation for two-dimensional Newtonian fluids (Khayat RE, Luciani A, Utrack i LA. Boundary element analysis of planar drop deformation in confined flow . Part I. Newtonian fluids. Engineering Analysis of Boundary Elements 1997; 19: 279), the method requires the solution of two simultaneous integral eq uations on the interface between the two fluids and the confining solid bou ndary. Although the problem is formulated for any confining geometry, the m ethod is illustrated for a deforming drop as it is driven by the ambient fl ow inside a cylindrical tube. The accuracy of the method is assessed by com parison with the analytical solution for two-phase radial spherical flow, l eading to good agreement. The influence of mesh refinement is examined for a drop in simple shear flow. Copyright (C) 2000 John Wiley & Sons, Ltd.