On the dynamics of particle sedimentation in viscoelastic fluids: A numerical study on particle chaining in two-dimensional narrow channels

The main goal of this article is to generalize to two-dimensional particulate viscoelastic channel flow of the FENE-CR type, the distributed Lagrange multiplier based fictitious domain (FD/DLM) methodology the authors employed in [J. Non-Newtonian Fluid Mech. 156 (2009) 95] for the simulation of viscoelastic particulate flow of the Oldroyd-B type. As in the above reference the methodology we employ here is based on a FD/DLM technique, combined with operator-splitting, a Cholesky factorization treatment (à la Lozinski-Owens) of the conformation tensor, and with appropriate finite element approximations of the various functions contained in the flow model. In this article, N being the number of particles and L the fluid polymer extension limit, we have used the methodology briefly sketched above to investigate, both in the transient and time asymptotic regimes, the influence of N, L, and of the relaxation time, on the formation of vertical chains of particles and on the maximal number of particles these chains do contain. We have verified in particular that small values of L do not authorize long particle chains, and also that one recovers, as expected, Oldroyd-B from FENE-CR as L→+∞.