Stability analysis of a polymer film casting problem

This is the accepted version of the following article: Kallel, A, Hachem, E, Rapetti, F, Demay, Y, and Agassant, JF (2015), Stability analysis of a polymer film casting problem. Int. J. Numer. Meth. Fluids, 78, 436–454. doi: 10.1002/fld.4024, which has been published in final form at http://dx.doi.org/10.1002/fld.4024International audienceThe polymer cast film process consists of stretching a molten polymer film between a flat die and a drawing roll. Drawing instabilities are often encountered and represent a drastic limitation to the process. Newtonian fluid film stretching stability is investigated using two numerical strategies. The first one is a ‘tracking’ method, which consists of solving Stokes equations in the whole fluid area (extrusion die and stretching path) by finite elements. The interface is determined to satisfy a kinematic equation. A domain decomposition meshing technique is used in order to account for a flow singularity resulting from the change in the boundary conditions between the die flow region and the stretching path region. A linear stability method is then applied to this transient kinematic equation in order to investigate the stability of the stationary solution. The second method is a direct finite element simulation in an extended area including the fluid and the surrounding air. The time-dependent interface is captured by solving an appropriate level-set function. The agreement between the two methods is fair. The influence of the stretching parameters (Draw ratio and drawing length) is investigated. For a long stretching distance, a critical Draw ratio around 20 delimitating stable and unstable drawing conditions is obtained, and this agrees well with the standard membrane models, which have been developed 40 years ago. When decreasing the stretching distance, the membrane model is no longer valid. The 2D models presented here point out a significant increase of the critical Draw ratio, and this is consistent with experimental results

Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence

We perform a direct numerical simulation (DNS) of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers \mbox{Re}, the film attains a steady state that is a square lattice of vortices and anti-vortices. We find that, as we increase the Weissenberg number \mbox{Wi}, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low \mbox{Wi}, and quasiperiodically, for slightly larger \mbox{Wi}. Finally, the system becomes disordered and displays spatiotemporal chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the \mbox{Wi} - \Omega plane, where \Omega \propto {\mbox{Re}}, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter $\Lambda$ provides us with a natural measure for characterizing the phases and transitions in this diagram.Comment: 16 pages, 17 figure

Oscillatory fracture path in thin elastic sheet

We report a novel mode of oscillatory crack propagation when a cutting tip is driven through a thin brittle polymer film. The phenomenon is so robust that it can easily be reproduced at hand (using CD packaging material for example). Careful experiments show that the amplitude and wavelength of the oscillatory crack path scale lineraly with the width of the cutting tip over a wide range of lenghtscales but are independant of the width of thje sheet and the cutting speed. A simple geometric model is presented, which provides a simple but thorough interpretation of the oscillations.Comment: 6 pages, submitted to Comptes Rendus Academie des Sciences. Movies available at http://www.lmm.jussieu.fr/platefractur

In situ observations on deformation behavior and stretching-induced failure of fine pitch stretchable interconnect

Electronic devices capable of performing in extreme mechanical conditions such as stretching, bending, or twisting will improve biomedical and wearable systems. The required capabilities cannot be achieved with conventional building geometries, because of structural rigidity and lack of mechanical stretchability. In this article, a zigzag-patterned structure representing a stretchable interconnect is presented as a promising type of building block. In situ experimental observations on the deformed interconnect are correlated with numerical analysis, providing an understanding of the deformation and failure mechanisms. The experimental results demonstrate that the zigzag-patterned interconnect enables stretchability up to 60% without rupture. This stretchability is accommodated by in-plane rotation of arms and out-of-plane deformation of crests. Numerical analysis shows that the dominating failure cause is interfacial in-plane shear stress. The plastic strain concentration at the arms close to the crests, obtained by numerical simulation, agrees well with the failure location observed in the experiment

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations

Elasticity of semiflexible polymers with and without self-interactions

A {\it new} formula for the force vs extension relation is derived from the discrete version of the so called {\it worm like chain} model. This formula correctly fits some recent experimental data on polymer stretching and some numerical simulations with pairwise repulsive potentials. For a more realistic Lennard-Jones potential the agreement with simulations is found to be good when the temperature is above the $\theta$ temperature. For lower temperatures a plateau emerges, as predicted by some recent experimental and theoretical results, and our formula gives good results only in the high force regime. We briefly discuss how other kinds of self-interactions are expected to affect the elasticity of the polymer.Comment: 8 pages, 10 figure

An Overview of Molten Polymer Drawing Instabilities

International audienceDrawing instabilities and rupture are a serious limitation in polymer fibre and film processing. Draw resonance and fibre or film rupture depend on the processing conditions, heat transfer and on the rheology of the polymer and some of these defects may also be encountered for Newtonian fluids. This paper reviews the different instabilities observed in fibre spinning, cast-film and film blowing. The time dependent equations are presented for the simplified situation of constant width cast-film and two modelling strategies, linear stability analysis and direct simulation, are proposed and then applied to the different fibre and film processes. Read More: http://www.hanser-elibrary.com/doi/abs/10.3139/217.283

The conformational evolution of elongated polymer solutions tailors the polarization of light-emission from organic nanofibers

Polymer fibers are currently exploited in tremendously important technologies. Their innovative properties are mainly determined by the behavior of the polymer macromolecules under the elongation induced by external mechanical or electrostatic forces, characterizing the fiber drawing process. Although enhanced physical properties were observed in polymer fibers produced under strong stretching conditions, studies of the process-induced nanoscale organization of the polymer molecules are not available, and most of fiber properties are still obtained on an empirical basis. Here we reveal the orientational properties of semiflexible polymers in electrospun nanofibers, which allow the polarization properties of active fibers to be finely controlled. Modeling and simulations of the conformational evolution of the polymer chains during electrostatic elongation of semidilute solutions demonstrate that the molecules stretch almost fully within less than 1 mm from jet start, increasing polymer axial orientation at the jet center. The nanoscale mapping of the local dichroism of individual fibers by polarized near-field optical microscopy unveils for the first time the presence of an internal spatial variation of the molecular order, namely the presence of a core with axially aligned molecules and a sheath with almost radially oriented molecules. These results allow important and specific fiber properties to be manipulated and tailored, as here demonstrated for the polarization of emitted light.Comment: 45 pages, 10 figures, Macromolecules (2014