Dynamics of particle sedimentation in viscoelastic fluids: A numerical   study on particle chain in two-dimensional narrow channel
  In this article we present a numerical method for simulating the sedimentation of circular particles in two-dimensional channel filled with a viscoelastic fluid of FENE-CR type, which is generalized from a domain/distributed Lagrange multiplier method with a factorization approach for Oldroyd-B fluids developed in [J. Non-Newtonian Fluid Mech. 156 (2009) 95]. Numerical results suggest that the polymer extension limit L for the FENE-CR fluid has no effect on the final formation of vertical chain for the cases of two disks and three disks in two-dimensional narrow channel, at least for the values of L considered in this article; but the intermediate dynamics of particle interaction before having a vertical chain can be different for the smaller values of L when increasing the relaxation time. For the cases of six particles sedimenting in FENE-CR type viscoelastic fluid, the formation of chain of 4 to 6 disks does depend on the polymer extension limit L. For the smaller values of L, FENE-CR type viscoelastic fluid can not bring them together like the case of these particles settling in a vertical chain formation in Oldroyd-B fluid; but two separated chains of three disks are formed. Similar results for the case of ten disks are also obtained. The numerical results of several more particle cases suggest that for smaller values of L, the length of the vertical chain is shorter and the size of cluster is smaller. 
Tsorng-Whay Pan and Roland Glowinski
physics.flu-dyn