Abstract
In this paper, the complete double layer boundary integral equation formulation for Stokes flows is extended to viscoelastic fluids to solve the mobility problem for a particle in an unbounded body of fluid, where the non-linearity is handled by using particular solutions of the Stokes inhomogeneous equation. Some meshless techniques are employed and a point-wise solver is used to solve the viscoelastic constitutive equation, avoiding volume meshing. The method is tested against the numerical solution for a sphere settling in an unbounded Oldroyd-B fluid. Some results on a prolate motion in shear flow for the Oldroyd-B fluid are reported and compared qualitatively with some theoretical and experimental results.
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