Two particle interactions in a confined viscoelastic fluid under shear

Abstract

Numerical simulations of the interaction between two non-Brownian isotropic particles in a shear flow confined between two sliding plates in two and three dimensions are presented. The suspending fluid is modelled using the Oldroyd-B constitutive equation and so incorporates the effects of viscoelasticity and first normal stress difference, but not shear-thinning. The particles are treated as a separate phase within the simulation with automated adaptive mesh refinement used to increase the resolution near the particle boundaries. The finite element method is used to discretise the spatial domain with a discontinuous Galerkin approximation for polymer stress and is implemented using the deal.II object oriented library. We identify three distinct types of interaction in two-dimensional systems: pass, return and tumble. We also show that the interactions between two spheres in a three-dimensional shear flow is qualitatively similar to the interaction between two circular particles, for particles in the same vorticity plane. For oblique interactions we find a further type of behaviour, similar to the Jeffery orbits of rigid rods.