Yves Demay

Stationary and stability analysis of the film casting process

Abstract Film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as a inhomogeneous decrease of the thickness. Thickness as well as width instabilities may be observed above a critical draw ratio. An isothermal and time dependent two-dimensional (2D) membrane model is proposed and compared to a non-constant width 1D model. Newtonian and viscoelastic constitutive equations have been tested. The influence of the processing parameters (draw ratio and aspect ratio) and of the rheology of the polymer (Deborah number) on the film geometry is first determined. The onset of the draw resonance instability is finally studied by linear stability analysis and through the dynamic response to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results.

A finite element method for computing the flow of multi-mode viscoelastic fluids: comparison with experiments

Abstract The numerical computation of viscoelastic fluid flows with differential constitutive equations presents various difficulties. The first one lies in the numerical convergence of the complex numerical scheme solving the non-linear set of equations. Due to the hybrid type of these equations (elliptic and hyperbolic), geometrical singularities such as reentrant corner or die induce stress singularities and hence numerical problems. Another difficulty is the choice of an appropriate constitutive equation and the determination of rheological constants. In this paper, a quasi-Newton method is developed for a fluid obeying a multi-mode Phan-Thien and Tanner constitutive equation. A confined convergent geometry followed by the extrudate swell has been considered. Numerical results obtained for two-dimensional or axisymmetric flows are compared to experimental results (birefringence patterns or extrudate swell) for a linear low density polyethylene (LLDPE) and a low density polyethylene (LDPE).

Linear stability of multilayer plane Poiseuille flows of Oldroyd B fluids

Abstract The linear stability of plane Poiseuille flows of two and three-symmetrical layers is studied by using both longwave and moderate wavelength analysis. The considered fluids follow Oldroyd-B constitutive equations and hence the stability is controlled by the viscous and elastic stratifications and the layer thicknesses. For the three symmetrical-layer Poiseuille flow, competition between varicose (symmetrical) and sinuous (antisymmetrical) mode is considered. In both cases (two and three symmetrical layers), the additive character of the longwave formula with respect to viscous and elastic terms is largely used to determine stable arrangements at vanishing Reynolds number. It is found that if the stability of such arrangements is due simultaneously to viscous and elastic stratification (the flow is stable for longwave disturbance and the Poiseuille velocity profile is convex), then the Poiseuille flow is also stable with respect to moderate wavelength disturbances and the critical thickness ratio around which the configurations becomes unstable is given by longwave analysis. Note that a convex velocity profile means a positive jump of shear rate at the interface. Finally, the destabilization due to a moderate increase in the Reynolds number is considered and two distinct behaviors are pointed according to the convexity of the Poiseuille velocity profile. Moreover, an important influence of the thickness ratio on the critical wavenumber is found for three symmetrical layer case (for two layer case, the critical wave number is of order one and depends weakly on the thickness ratio).

Flow birefringence study of the stick–slip instability during extrusion of high-density polyethylenes

Abstract The flow behavior of two molten linear high-density polyethylenes (HDPE) is carefully studied using a single screw extruder equipped with a transparent slit die. Flow curves are drawn for both resins and compared. Slit die experiments are performed using birefringence technique to obtain stress fields, and image analysis is developed to visualize the stress transients during the instability. At low flow rate, the extrusion is stable. At more important flow rate, the so-called spurt or stick–slip instability appears. During the instability, periodic birefringence fringes pulsations are observed, synchronized with pressure oscillations, suggesting a periodic stick–slip transition mechanism. Correlation with velocity oscillations is discussed.

Numerical simulation of the film casting process

The film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as an inhomogeneous decrease of the thickness. An isothermal and Newtonian membrane model, constituted of an elastic-like equation for velocity coupled to a transport equation for thickness and a free surface computation, is used. These equations are solved via the finite element method (continuous Galerkin for velocity and discontinuous Galerkin for thickness). Both tracking and capturing strategies are used to determine the position of the free surface (lateral neck-in). The influence of the processing parameters (Draw ratio and Aspect ratio) on the film geometry is first determined. The onset of the Draw Resonance instability is then studied through the dynamic response of the process to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown, consistently, with results of a 1D model, that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results. The film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as an inhomogeneous decrease of the thickness. An isothermal and Newtonian membrane model, constituted of an elastic-like equation for velocity coupled to a transport equation for thickness and a free surface computation, is used. These equations are solved via the finite element method (continuous Galerkin for velocity and discontinuous Galerkin for thickness). Both tracking and capturing strategies are used to determine the position of the free surface (lateral neck-in). The influence of the processing parameters (Draw ratio and Aspect ratio) on the film geometry is first determined. The onset of the Draw Resonance instability is then studied through the dynamic response of the process to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown, consistently, with results of a 1D model, that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results.

A Two-dimensional Numerical Method for the Deformation of Drops with Surface Tension

Abstract This paper is concerned with the development of a numerical method for the computation of two-dimensional time-dependent free-surface problems where surface tension cannot be neglected. The imposition of a surface tension force in a finite element method requires the evaluation of a line integral where the curvature R of the interface has to be accurately evaluated. In this paper, we demonstrate how this line integral can be replaced by a volume integral over the entire domain avoiding the explicit computation of R. The proposed method is then applied to the computation of the complex deformation of a drop of a viscous fluid immersed in another fluid and submitted to a shearing flow field.

Steady flow of a White-Metzner fluid in a 2-D abrupt contraction : computation and experiments

Abstract The flow of a White-Metzner fluid in a 2-D abrupt contraction was computed, using a decoupled finite-element method, previously developed for an upper-convected Maxwell model. The convergence of the algorithm was carefully studied, including the influence of the mesh size and of the rheological parameters. Experiments were carried out on a transparent slit die, in order to observe birefringence patterns in various flow conditions. These patterns were expressed in terms of stress distribution and compared to the computations. The agreement is generally satisfactory but exposed the inadequacy of the White-Metzner model at low shear rates.

Experimental study of the draw resonance in fiber spinning

Abstract An experimental fiber-spinning device has been built in order to study the draw-resonance phenomenon in nearly isothermal conditions. The influence of the output rate, of the take-up speed and of the spinning length was studied for four different polyesters. The experimental results are in accordance with non-isothermal and viscoelastic computations.

Experimental Investigation of the Development of Interfacial Instabilities in Two Layer Coextrusion Dies

Abstract The stability of two-layer flow of polyethylene and polystyrene is experimentally studied in different flow geometries and for various flow rate ratios. A first coextrusion device allows to stop the coextrusion flow in a very long slit channel, to cool down the polymer sample and to dismantle the die in order to extract extrudate which is then carefully analyzed. A second device allows to observe the whole slit flow through transparent lateral walls and to record the interfacial waves in both spontaneous and controlled unstable conditions. Both devices point clearly out that the interfacial defect begins to grow after a specific flow distance and is then quickly amplified. This demonstrates the convective character of interfacial wave. Controlled unstable processing conditions in transparent die allow to measure accurately growth rate of defect in the linear regime and show quick occurrence of non linear regime.

Investigation of Polymer Stretching Instabilities: Application to Film Blowing

Abstract Film blowing, as other elongational polymer forming processes, may present marked drawing instabilities leading to unacceptable products. But in film blowing, these instabilities are much more complex than for example in fibre spinning: there is no stabilizing effect of the polymer cooling, and the symmetry of the process may be broken, leading in some processing conditions to so called helical instabilities. Stability of the process has been investigated using a strategy inspired from shell or homogeneisation theory: as the classical approach uses a frame locally affixed to the membrane, the equations of the problem are now written in the cartesian laboratory frame. Making the equations dimensionless introduces naturally a small parameter defined as an aspect ratio (ratio of the film thickness to the bubble radius). Kinematic and stress variables are expanded as a function of this small parameter and introduced in the equations. It leads classically to a sequence of equations at successive orders. This strategy is used to obtain a time dependent membrane model. The stationary solution is equivalent to the one obtained using the classical approach. This model allows to develop a stability analysis, first in the axisymmetric case and then in the non axisymmetric one. Even a crude Newtonian temperature dependent rheology allows to capture qualitatively the observed instability phenomena.