Stress relaxation of a polymer melt after extensional flow

The relaxation behaviour of a stretched polymer melt is described with the aid of the semi-empirical constitutive equation of Wagner. The theoretical predictions based on this model, are in fair agreement with the experimental results, as far as the period of stress decay following the stress build-up is not too long.     

Investigation of thermoplastic melt flow and dimensionless groups in 3D bioplotting

Rheologica Acta - We investigate the key 3D bioplotting processing parameters, including needle diameter and dispensing pressure, on the shear rates, shear stresses, pressure drops, and swell...     

Fingerprinting the processing behavior of polyethylenes from transient extensional flow and peel experiments in the melt state

The flow curves of linear (linear-low and high density) and branched polyethylenes are known to differ significantly. At increasing shear rates, the linear polymers exhibit a surface melt fracture or sharkskin region that is followed by an unstable oscillating or stick-slip flow regime when a constant piston speed capillary rheometer is used. At even higher shear rates, gross melt fracture appears. Unlike their linear counterparts, branched polyethylenes rarely exhibit sharkskin melt fracture and although gross melt fracture appears at high shear rates there is no discontinuity in their flow curve. The various flow regimes of these two types of polyethylenes are examined by performing experiments in the melt state using a unique extensional rheometer (the SER by Xpansion Instruments) that is capable of performing accurate extensional flow and peel experiments at very high rates not previously realized. The peel strength curves of these linear and branched polyethylenes exhibit all of the distinct flow regimes exhibited in their respective flow curves, thereby providing a fingerprint of their melt flow behavior. Moreover, these extensional flow and peel results in the melt state provide insight into the origins and mechanisms by which these melt flow phenomena may occur with regard to rapid tensile stress growth, melt rupture, and adhesive failure at the polymer wall interface.     

Hydrodynamic instability of extensional flow

The stability analysis for sheet stretching recently presented by Minoshima and White for Newtonian fluids is repeated for non-Newtonian fluids. For that purpose a constitutive law for nearly extensional flow is derived which, apart from a restriction to short memory of the fluid, is generally valid. Using this constitutive law the result found by Minoshima and White is generalized. Application of the general result to a Maxwell-type fluid shows that the elasticity of the fluid has a stabilizing influence.     

Three-dimensional presentation of extensional flow data

A proposal has been made by Ferguson and Hudson (Eur. Polym. J., 29 (1993) 141–147; J. Non-Newtonian Fluid Mech., 52 (1994) 121–135) that three-dimensional representation of extensional flow data can be used to resolve apparent disagreements among the results from a variety of extensional flow experiments. A theoretical investigation of the procedure, which involves plotting a transient extensional viscosity against strain and time is carried out in this paper. We then seek to draw some conclusions about the validity and limitations of the approach. The method does not work for purely viscous non-newtonian liquids or for simple (co-rotational and upper convected) Maxwell models. However, the failure of results to lie close to a unique surface (for any particular material) is most marked in situations where our theoretical models are least reliable. More work, both experimental and theoretical, is required.     

Uniaxial extensional flow for a viscoelastic model that displays thixotropic yield stress behavior

Homogeneous uniaxial extensional flow of a viscoelastic fluid, namely, the partially extending strand convection model combined with a Newtonian solvent, is investigated for large relaxation time. Initial value problems are addressed, for prescribed constant tensile stress. The limit of large relaxation time introduces a slow time scale of evolution, in addition to a fast time scale for flow. Numerical solutions of the original equations show distinct stages of evolution, which are mathematically analyzed with asymptotic analyses for multiple time scales. We discuss the stages of evolution from equilibrium, as well as unloading the applied stress from a yielded solution. The overall picture which emerges captures a number of features which are usually associated with thixotropic yield stress fluids, such as delayed yielding, and hysteresis for up and down stress ramping. Even at large applied tensile stress, there is persistence of an interval of parameters where the deformation rate increases quickly, only after a delayed response.     

Shear and extensional flow of polyacrylamide solutions

As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made.The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution.Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Resistance to uniaxial extensional flow of fibre suspensions

The tensile stress due to resistance to uniaxial extensional flow of fibre suspensions in Newtonian and non-Newtonian fluids has been measured using the filament stretching technique. It has been found that addition of fibres to a Newtonian fluid increases the extensional viscosity. The steady state results agree with Bachelors theory and the stress growth behaviour is qualitatively predicted by the theory of Dinh and Armstrong. Experimental results from this work have also shown that the behaviour of a fibre suspension in viscoelastic fluid is qualitatively described by Fans equation. The added fibres increase the extensional stress growth coefficient of the viscoelastic fluid at low strain but have marginal effect on the fluid after the onset of strain-hardening.     

Miniature universal testing platform: from extensional melt rheology to solid-state deformation behavior

Described is a detachable fixture for a rotational rheometer, the Sentmanat Extensional Rheometer Universal Testing Platform, which incorporates dual wind-up drums to ensure a truly uniform extensional deformation during uniaxial extension experiments on polymers melts and elastomers. Although originally developed as an extensional rheometer, this highly versatile miniature test platform is capable of converting a conventional rotational rheometer host system into a single universal testing station able to characterize a host of physical properties on a variety of polymer melts and solid-state materials over a very wide range of temperatures and kinematic deformations and rates. Experimental results demonstrating these various testing capabilities are presented for a series of polymers of varying macrostructure and physical states.     

The rheology of polymer solution elastic strands in extensional flow

We apply micro-oscillatory cross-slot extensional flow to a semi-dilute poly(ethylene oxide) solution. Micro-particle image velocimetry (μPIV) is used to probe the real local flow field. Extreme flow perturbation is observed, where birefringent strands of extended polymer originate from the stagnation point. This coincides with a large increase in the extensional viscosity. The combination of stagnation point flow and μPIV enables us to investigate directly the stress and strain rates in the strand and so determine the true extensional viscosity of the localised strand alone. The Trouton ratio in the strand is found to be ~4000, amongst the highest values of Trouton ratio ever reported. Consideration of the flow in the exit channels surrounding the highly elastic strand suggests a maximum limit for the pressure drop across the device and the apparent extensional viscosity. This has implications for the understanding of high Deborah number extensional thinning reported in other stagnation point flow situations.     

Extensional flow of polystyrene melt

Summary The extensional flow of molten polystyrene was studied in the strain rate range of 7.8×10^–4 sec^–1 to 2.2×10^–2 sec^–1 at a test temperature of 300F (149 C) Extensional viscosity was compared to shear viscosity measured at the same degree of stress and temperature and found to be from 3 to 350 times greater in magnitude but much less stress dependent.     

Non-isothermal polymer melt flow in sudden expansions

This paper presents numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The mathematical model includes the mass, momentum and energy conservation laws within the framework of a generalized Newtonian formulation. Two constitutive relations are adopted to describe the non-Newtonian behavior of the flow, namely Cross and Modified Arrhenius Power-Law models. The governing equations are discretized using the finite difference method based on central, second-order accurate formulas for both convective and diffusive terms. The pressure–velocity coupling is treated by solving a Poisson equation for pressure. The results are presented for two commercial polymers and demonstrate that important flow parameters, such as pressure drop and viscosity distribution, are strongly affected by heat transfer features.     

A simple extensional viscometer

An extensional viscometer is described in which the liquid filament leaving a capillary is subjected to a stretching deformation. In order to keep the flow rate through the capillary unaltered upon inception of stretching, the pressure head at the capillary entrance has to be reduced by an amount equal to the extensional viscoelastic stress at the capillary exit. This affords a simple means of measuring small fluid forces such as those that occur in the stretching of dilute polymer solutions. Since stretch rates can be obtained from a knowledge of the mass flow rate and the filament diameter profile, extensional viscosities can be computed. The efficacy of the technique is demonstrated by obtaining the anticipated results for Newtonian liquids.     

Generation of sub-micron-sized droplets,by continuous extensional flow

A method is devised to generate sub-micron-sized droplets without surfactants by using a continuous extensional flow. By using the extensional flow judiciously the physical limits on the viscosity ratio of the dispersed and dispersing media could be overcome. The strain hardening behavior of the Boger fluid under the extensional flow gave a synergic effect to generate the smaller droplets. It was shown that the drop size could be decreased to a sub-micron scale and the droplet size distribution was much narrower compared to the case of the conventional shear (stirring) method. This method is also applicable when the two phases are compatible.     

Birefringence measurements in extensional flow of polyisobutylene around an expanding bubble

Birefringence in liquid polymers offers the possibility of obtaining information about stress in complex flows. In this work, this is done for extensional flows of polyisobutylene in a “breathing bubble” rheometer. In this type of rheometer, a bubble consisting of an incompressible, low-viscosity fluid (usually water) is injected into the sample with a nozzle. Expanding or collapsing the bubble by adding or removing water induces biaxial or uniaxial extension in the surrounding sample. The pressure difference between the bubble and the surroundings can be measured and compared to the predictions of constitutive equations. This measurement only gives one integral value for a complex flow history. In this paper, the birefringence around the bubble is measured in order to learn more about the flow. This is done by comparing pressure and birefringence results to those of standard constitutive equations for a polyisobutylene sample. A good agreement between the pressure and optical measurements and the theory is found with a single value of the stress-optical constant. Received: 25 June 1997 Accepted: 12 November 1997