Dynamics of a macroscopic elastic fibre in a polymeric cellular flow

Abstract

We study the dynamics and transport of an elastic fibre in a polymeric cellular flow. The macroscopic fibre is much larger than the infinitesimal immersed polymer coils distributed in the surrounding viscoelastic fluid. Here we consider low-Reynolds-number flow using the Navier–Stokes/Fene-P equations in a two-dimensional, doubly periodic domain. The macroscopic fibre supports both tensile and bending forces, and is fully coupled to the viscoelastic fluid using an immersed boundary framework. We examine the effects of fibre flexibility and polymeric relaxation times on fibre buckling and transport as well as the evolution of polymer stress. Non-dimensional control parameters include the Reynolds number, the Weissenberg number, and the elasto-viscous number of the macroscopic fibre. We find that large polymer stresses occur in the fluid near the ends of the fibre when it is compressed. In addition, we find that viscoelasticity hinders a fibre’s ability to traverse multiple cells in the domain.