Dynamics of a viscoelastic thread surrounded by a Newtonian viscous fluid inside a cylindrical tube

A viscoelastic thread in vacuum is known to evolve into a beads-on-a-string structure at large deformations. If the thread is immersed in another fluid, the surrounding medium may influence the topological structure of it, which remains unexplored. To get some insights into the nonlinear behaviour of a viscoelastic thread in a two-phase flow system, a one-dimensional model is developed under the slender body approximation, in which the thread of a highly viscoelastic fluid described by the Oldroyd-B or Giesekus constitutive equation is immersed in a Newtonian viscous fluid of much smaller density and viscosity inside a cylindrical tube. The effect of the outer viscous fluid layer and the confinement of the tube is examined. It is found that the outer fluid may change substantially the beads-on-a-string structure of the viscoelastic thread. Particularly, it may induce the formation of secondary droplets on the filament between adjacent primary droplets, even for large wavenumbers. The outer fluid exerts a resistance force on the extensional flow in the filament, but the necking of the thread is slightly accelerated, due to the redistribution of capillary and elastic forces along the filament accompanied by the formation of secondary droplets. Decreasing the tube radius leads to an increase in secondary droplet size but affects little the morphology of the thread. The non-uniformity of the filament between droplets is more pronounced for a Giesekus viscoelastic thread, and pinch-off of a Giesekus thread always occurs in the neck region connecting the filament to the primary droplet in the presence of the outer viscous fluid.