nt transient that may be many orders of magnitude longer than time scales associated with instrument inertia. Intrinsic material time scales can be identified with the dynamics of the macro­ molecular chains. Shaping processes for polymeric materials are usually carried out in the liquid state, often over times that are rapid relative to those associated with molecular reorganization; the viscoelasticity is thus relevant to any understanding of flow and structure development. The distinction between the rheology and the fluid mechanics of visco­ elastic materials is vague but is worth stating. The former is concerned with constitutive relations between stress and deformation and may involve physical modeling at a molecular level. Controllability of the flow field is essential when making rheological measurements to evaluate material properties, so the kinematics are generally imposed and the momentum equation is not solved. Viscoelastic fluid mechanics, on the other hand, is the study of motions in which the kinematics cannot be established a priori, and the continuity and momentum equations must be solved together with the constitutive equation for the stress. The equations that must be solved for even the most elementary viscoelastic liquids are considerably more complex than the Navier-Stokes equations, and many unresolved issues

Issues in viscoelastic fluid mechanics

The flow of four different linear or branched silicones through thin-walled orifice dies has been visualized. The observation of the extrudate downstream of the orifice has allowed a thorough examination of the appearance and evolution of the various flow regimes. Thus it has been possible to detect very clearly a surface defect appearing in the form of scratches at the free surface, and whose appearance threshold has been thoroughly measured. Depending on the rheology of the fluids considered, these defects may evolve into more severe forms commonly designated by “loss of gloss” or “sharkskin”. Moreover, for all the silicones studied, the well-known melt fracture phenomenon has been observed. This defect first appears in the form of a regular helix, and then evolves into a chaotic regime as flow pressure increases. In other respects, the visualization of the upstream flow shows that this remains perfectly stable as long as the rupture regime has not been reached. Thus, it seems that the surface defect, even in its more severely evolved form, namely the sharkskin defect, is an exit phenomenon related to the relaxation of stretch strains at the orifice outlet. On the other hand, instabilities are generated in the upstream region for the flow regime at which melt fracture appears downstream. Consequently, it seems that this phenomenon should be attributed, at least in part, to the unstable phenomena developing in the elongational flow field upstream of the orifice die. This assumption is supported by the fact that experiments performed with various wall material have shown that wall slip was, in any case, unlikely or minor, so that it could not be responsible for the observed phenomena.

Influence of upstream instabilities and wall slip on melt fracture and sharkskin phenomena during silicones extrusion through orifice dies

This article reviews recent results on capillary melt flow anomalies. Long standing controversies and debates in this field are illustrated by summarizing previous results and clarified with an extensive discussion of the most recent results. Explicit molecular mechanisms for flow instabilities are presented in contrast to a background of 40 years’ continuous and far ranging research. New experiments show that the widely observed extrusion anomalies (including oscillating flow, discontinuous flow transition and sharkskin) of linear polyethylenes (LPE) originate from interfacial molecular transitions, which may or may not be stable depending the specific flow conditions. A global flow instability (commonly known as oscillating capillary flow) evidently arises from a time-dependent oscillation of the global hydrodynamic boundary condition (HBC) between no-slip and slip limits at the capillary die wall. Other convincing observations show that sharkskin originates from a local instability of HBC at the die exit wall. The global and local interfacial instabilities both originate from a reversible coil-stretch transition involving interfacial unbound chains that are entangled with the adsorbed chains. In other words, local and global stress oscillations result in the observed macroscopic sharkskin-like and bamboo-like extrudate distortions respectively. A second molecular mechanism for wall slip is also clearly identified, involving stress-induced chain desorption off low surface energy walls. An organic coating of capillary die walls produces massive chain desorption and a large magnitude wall slip at rather low stresses, whereas bare metallic and inorganic surfaces (e.g., steel, aluminum, and glass) usually retain sufficient chain adsorption and prevent catastrophic slip up to the critical stress for the coil-stretch transition. The intricate interfacial flow instabilities exhibited by LPE are also shared by other highly entangled melts such as polybutadienes. In contrast, monodisperse melts with high critical entanglement molecular weight (M e ) such as polystyrene of M w =106 show massive wall slip on low energy surfaces but no measurable interfacial stick-slip transition before reaching the plateau around 0.2 MPa. Tasks for future work include (i) direct molecular probe of melt chain adsorption and desorption processes at a melt/wall interface as a function of the surface condition, (ii) new theoretical studies of chain dynamics in an entangling melt/wall interfacial region as well as in bulk at high stresses, (iii) test of universality of the established physical laws governing melt/wall interfacial behavior and flow for all polymers, and (iv) development of tractable experimental and theoretical methods to study boundary discontinuities and stress singularities.

Molecular Transitions and Dynamics at Polymer / Wall Interfaces: Origins of Flow Instabilities and Wall Slip

Polymers, melted at room temperature, have been extruded through capillary dies using either a controlled pressure system or an automatic capillary rheometer in which the rate of flow is controlled. When the polymer is highly entangled, macroscopic slip is observed at the wall. However, flow curves differ: for controlled pressure conditions, slip appears simultaneously with a sudden increase in the rate of flow, an dflow curves exhibit a hysteretic regime. For controlled flow conditions, slip is accompanied by oscillations of the rate of flow and pressure head around a mean value, as a result of polymer compressibility. The succession and evolution of the different flow defects are clearly identified. As the flow regime increases, scratches appear first. Then, beyond a critical value of wall shear stress in the exit region, cracks are formed just at the exit of the capillary die. These cracks are accompanied by the formation of “rings”, which are more easily observed as the molecular weight increases. At high flow rates, when macroscopic slip appears at the wall, the aspect of the extrudate depends on the system used. For controlled pressure conditions, the polymer is ejected in the form of an opaque, irregular jet, where swelling is quasi-non-existent. For controlled flow conditions, cork flow is observed. At higher flow regimes the extrudate becomes chaotic. The existence of a master curve was also shown for variations in average velocity vs. wall stress, during flow with macroscopic slip at the wall. It is important to note that this curve represents the sliding friction properties of the polymer under consideration.

The different capillary flow regimes of entangled polydimethylsiloxane polymers : macroscopic slip at the wall, hysteresis and cork flow

Film blowing of linear low-density polyethylene blended with a novel hyperbranched polymer processing aid

The sharkskin defect in linear low density polyethylene has been studied using both flow birefringence and roughness measurements. Roughness measurements allow us to detect accurately the onset of the defect and to quantify its amplitude. With increasing flowrate, the sharkskin defect appears at a critical value of the flowrate and then grows. This critical value and the maximum amplitude of the defect increase with temperature. Birefringence patterns give information on the stress distribution at the die entrance. At the appearance of the sharkskin defect, all birefringence patterns are identical and independent of the flowrate and the temperature. The influence of die geometry and the addition of lubricant to the polymer were investigated.

Experimental study of the sharkskin defect in linear low density polyethylene

A theoretical study has been carried out of the two directional isothermal flow of two molten polymers in a flat die. The viscous behavior of each fluid is described by a power-law. Using an iterative finite difference method, a numerical program predicts the influence of geometrical and Theological parameters on the variations of the interface position. Theoretical values are in good agreement with experimental results obtained on a fish-tail die. In the case of a coat hanger-die, the mean value of the interface position is correct, but the general shape may be quite different.

Two directional coextrusion flow of two molten polymers in flat dies

A theoretical study of the one-directional coextrusion flow of two molten polymers between parallel plates has been carried out using a non-isothermal power-law model. A numerical method has been used to solve simultaneously the momentum and energy balance equations, in order to obtain the evolutions of the interface position, the pressure gradient, and the temperature profiles all along the flow. The theoretical results are in good agreement with experimental values measured on an industrial coextrusion line.

G. Sornberger

Papers

Experimental study of the sharkskin defect in linear low density polyethylene

Two directional coextrusion flow of two molten polymers in flat dies

Coextrusion flow of two molten polymers between parallel plates: non isothermal computation and experimental study