Patrick Bourgin

Lubricating films of a viscoelastic fluid, including fluid inertia, studied by a linearization method

Abstract This study is concerned with the influence of fluid inertia in thin laminar transient or steady flows of a second order Rivlin-Ericksen fluid, predicting the combined effects of inertia and viscoelasticity. In the present study, a linearized approximation for both the convective inertia terms and the nonlinear terms involved in the fluid constitutive law is used. The problem is transformed to a coordinate system in such a way as to result in a linear diffusion-type equation for the vorticity in the Newtonian case, and for the vorticity Laplacian in the viscoelastic case. Having prescribed adequate initial or entrance conditions, closed-form solutions are obtained and tested in three cases for which solutions exist in the literature and excellent agreement is found. In the viscoelastic fluid case three examples are presented showing: 1) The influence of weak inertia effects on the steady flow of a second-order fluid. 2) The behavior in squeezing flow of a slightly viscoelastic fluid. 3) The behavior of a viscoelastic fluid undergoing large amplitude oscillatory squeezing in the presence of weak inertia effects.

Competition of Flow and Thermal Effects During Crystallization of Polymers: Influence on Morphology

It is well known that the properties of polymer products are strongly dependent on the thermo‐mechanical history experienced by the material during processing. In the particular case of semicrystalline polymers, flow‐induced crystallization is known to have a major effect on crystalline morphology and consequently on structural heterogeneities such as shrinkage. In that context, a model based on the assumption that flow‐induced nucleation is linked to the trace of the deviatoric stress tensor was developed to represent both the effects of thermal‐ and flow‐induced nucleation on the polymer final crystallinity. In the present work, this model is applied to an isotactic polypropylene (iPP) in isothermal and non‐isothermal Couette flow configurations. We focus on the competition between thermal and flow effects on the crystallization rate. We study the influence of the competition on morphology for different processing conditions. We obtain in each case the crystalline fraction due to thermal and flow effect...

Simulation of Polymer Crystallization: Role of the Visco-Elasticity

In polymer processing, it is established that the flow causes the polymer chains to stretch and store the energy, by changing their quiescent state free energy. Koscher et al. [1] presented in 2002 an experimental work concerning the flow induced crystallization. They made the assumption that the polymer melt elasticity, quantified by the first normal stress difference, is the driving force of flow-induced extra nucleation. In their work, a constant shear stress is considered, and the first normal stress difference agrees with the use of the trace of the stress tensor. The stored energy due to the flow “Δ Ge” is commonly called elastic free energy and associated to the change in conformational tensor due to flow. By extending the Marrucci theory [2], several studies link this Δ Ge to the trace of the deviatoric stress tensor (first invariant). In this paper, a numerical model able to simulate polymer crystallization is developed. It is based on the assumption that flow induced extra nucleation is linked to the trace of the deviatoric stress tensor. Thus a viscoelastic constitutive equation, the multimode Upper Convected Maxwell (UCM) model, is used to express the viscoelastic extra-stress tensor τVE , and a damping function is introduced in order to take into account the nonlinear viscoelasticity of the material. In Koscher’s work [1], the integral formulation of the Upper Convected Maxwell (UCM) model is used too, but without any damping function, i.e. they assume that the polymer behaves as linear viscoelastic. As an application, a 2D isothermal flow configuration between two plates is simulated. A comparison between the proposed model and the Koscher’s one is then performed, and interesting resultes are pesented: without introducing a damping function, the two models give similar results in the same configurations, but the introduction of a damping function leads to important discrepancies between the two models, seeming that the assumption of a linear viscoelastic behavior is not realistic when the fluid strain and/or stresses are greater than a given values.Copyright

Simulation of the Cooling of a Semi‐Crystalline Polymer in the Injection Molding Process Including PVT Behavior

Accurate numerical simulation of the injection molding process requires a good comprehension of the cooling and solidification phase. In the case of semi‐crystalline polymers, this task is complicated because of a strong coupling between heat transfer, crystallization and material compressibility effects. In this work, we carry out the thermophysical characterization of a semi‐crystalline polymer (isotactic polypropylene), including the pressure‐volume‐temperature (PVT) behavior. Then we present a model of the isochoric cooling of this polymer, taking into account these couplings. This model enables us to compute the evolution of pressure, temperature, relative crystallinity and local specific volume in the mold cavity from high initial pressure down to atmospheric pressure and shrinkage onset.

Heat Transfer and Air Diffusion Phenomena in a Bed of Polymer Powder Using Apparent Heat Capacity Method: Application to the Rotational Molding Process

The process of rotational moulding consists in manufacturing plastic parts by heating a polymer powder in a biaxial rotating mould. In order to optimise the production cycle of this process, a complete simulation model has to be used. This model should describe the phenomena of heat and mass transfer in a moving granular media with phase change, coalescence, sintering, air evacuation and crystallization during the cooling stage. This paper focus on the study of heat and mass transfer in a quiescent polymer powder during the heating stage. An experimental device has been built. It consists in an open plane static mold on which an initial thickness, e, of a polymer powder is deposited. This powder is then heated until it melts. An inverse heat conduction method is used to determine the heat flux and temperature at the interface between the mold and the powder. This interfacial heat flux is taken as a boundary condition in a numerical heat transfer model witch takes into account the heat transfer in granular media with phase change, coalescence, sintering, air bubbles evacuation and rheological behaviour of the polymer. For the numerical simulation of the heat transfer, the apparent specific heat method is used. This approach allows to solve the same energy equation for all the material phases, so one do not have to calculate the melting front evolution. This fine modelling, close to the real physical phenomena makes it possible to estimate the temperature profile and the evolution of the polymer powder characteristics (phase change, air diffusion, viscosity, evolution of the thermophysical properties of the equivalent homogeneous medium, thickness reduction, air volume fraction...). Several results are then presented, and the influence of different parameters, like the thermal contact resistance, the process initial conditions and the polymer’s rheological characteristics are studied and commented. Indeed the predictions of the temperature rises in the polymer bed, agree well with the experimental measurements.Copyright