ALBERT

Description: The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions are measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar, et al. The solutions are polystyrene-based (PS) Boger fluids that are stretched at constant strain rates ranging from 0.6 less than or equal to epsilon(0) less than or equal to 4s(exp -1) and to Hencky strains of epsilon greater than 4. The test fluids all strain harden and Trouton ratios exceeding 1000 are obtained at high strains. The experimental data strain hardens at lower strain levels than predicted by bead-spring FENE models. In addition to measuring the transient tensile stress growth, we also monitor the decay of the tensile viscoelastic stress difference in the fluid column following cessation of uniaxial elongation as a function of the total imposed Hencky strain and the strain rate. The extensional stresses initially decay very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation, and deviate significantly from FENE relaxation predictions. The relaxation at long times t is greater than or equal to 5 s, is compromised by gravitational draining leading to non-uniform filament profiles. For the most elastic fluids, partial decohension of the fluid filament from the endplates of the rheometer is observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. Flow visualization experiments using a modified stretching device show that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the nonhomogeneous region of highly deformed fluid near the rigid endplate.

Description: We analyze the onset of "necking" and subsequent filament failure during the transient uniaxial elongation of viscoelastic fluid samples in extensional rheometers. In the limit of rapid elongation (such that no molecular relaxation occurs), the external work applied is all stored elastically and the Considere criterion originally developed in solid mechanics can be used to quantitatively predict the critical Hencky strain to failure. By comparing the predictions of the Doi-Edwards model for linear homopolymer melts with those of the "Pom-Pom" model for prototypical branched melts we show that the critical strain to failure in rapid elongation of a rubbery material is intimately linked to the molecular topology of the chain, especially the degree of chain branching. The onset of necking instability is monotonically shifted to larger Hencky strains as the number of branches is increased. Numerical computations at finite Deborah numbers also show that there is an optimal range of deformation rates over which homogeneous extensions can be maintained to large strain. We also consider other rapid homogeneous stretching deformations, such as biaxial and planar stretching, and show that the degree of stabilization afforded by inclusion of material with long-chain branching is a sensitive function of the imposed mode of deformation.