Christopher A. Bertelo

Prediction of bubble growth and size distribution in polymer foaming based on a new heterogeneous nucleation model

The cell size distribution in a thermoplastic foam to a large extent determines its mechanical and thermal properties. It is difficult to predict because of the many physical processes involved, each affected in turn by an array of factors and parameters. The two most important processes are bubble nucleation and diffusion-driven bubble growth. Neither has been thoroughly understood despite intensive and long-standing research efforts. In this work, we consider foaming by a physical blowing agent dissolved in a polymer melt that contains particulate nucleating agents. We propose a nucleation model based on the concept that heterogeneous nucleation originates from pre-existing microvoids on the solid particles. The nucleation rate is determined by a bubble detachment time. Once nucleated, the bubbles grow as the dissolved gas diffuses through the polymer melt into the bubbles, a process that couples mass and momentum transport. By using the Oldroyd-B constitutive equation, we explore the role of melt viscoelasticity in this process. Finally, we integrate the nucleation and growth models to predict the evolution of the bubble size distribution. A cell model is employed to simulate the effects of neighboring bubbles and the depletion of blowing agents. The latter also causes the nucleation rate to decline once growth of older bubbles is underway. Using the physical and operating parameters of a recent foam extrusion experiment, we are able to predict a cell size distribution in reasonable agreement with measurements.

An arbitrary Lagrangian-Eulerian method for simulating bubble growth in polymer foaming

We present a sharp-interface algorithm for simulating the diffusion-driven bubble growth in polymer foaming. A moving mesh of unstructured triangular elements tracks the expanding and deforming bubble surface. In the interior of the liquid, the mesh velocity is determined by solving a Laplace equation to ensure spatially smooth mesh movement. When mesh distortion becomes severe, remeshing and interpolation are performed. The governing equations are solved using a Galerkin finite-element formalism, with fully implicit time marching that requires iteration among the bubble and mesh deformation, gas diffusion and the flow and stress fields. Besides numerical stability, the implicit scheme also guarantees a smooth interfacial curvature as numerical disturbances on the interface are automatically relaxed through the iterations. The polymer melt is modeled as a viscoelastic Oldroyd-B fluid. First, we compute three benchmark problems to validate various aspects of the algorithm. Then we use a periodic hexagonal cell to simulate bubble growth in an isothermal two-dimensional foam, fed by a gaseous blowing agent initially dissolved in the melt to supersaturation. Results show two distinct stages: a rapid initial expansion followed by slow drainage of the liquid film between bubbles driven by capillarity. The effect of viscoelastic rheology is to enhance the speed of bubble growth in the first stage, and hinder film drainage in the second. Finally, we use axisymmetric simulations to investigate the thinning film between a bubble and a free surface. Melt viscoelasticity is shown to initially enhance film thinning but later resist it. An important insight from the simulations is that polymer strain-hardening, namely the steep increase of elongational viscosity with strain, helps stabilize the foam structure by suppressing bubble-bubble coalescence and bubble burst at the foam surface. This confirms prior observations in foam extrusion experiments.

trans-1,2-Dichloroethylene for Improving Fire Performance of Urethane Foam

In the United States, HCFC-141b was phased out of urethane foam applications on January 1, 2003. Zero ozone depletion potential (ODP) alternatives, such as hydrofluorocarbons (HFCs) and hydrocarbons (normal pentane, isopentane, and cyclopentane), have been introduced to replace HCFC-141b. However, none of these alternatives can match the performance of HCFC-141b in terms of handling, economics, and overall final product performance. In particular, the fire performance of hydrocarbons-based foams cannot reach the performance previously achieved with HCFC-141b. trans-1,2-Dichloroethylene is a liquid at room temperature (b.p. 48 C). It does not deplete the ozone layer1, and it has very low global warming potential (GWP) because it has very short atmospheric lifetime. We have recently reported that when trans-1,2-dichloroethylene is used in urethane foams with hydrocarbons, it could improve the fire performance of the foams, based on a small-scale fire test (Mobil 45). In this paper, we report physical properties of hydrocarbons/trans-1,2-dichloroethylene foams, such as dimensional stability and compressive strength. We have also extended our studies of the use of trans-1,2-dichloroethylene, and report on the fire performance of HFC-blown urethane foams incorporating trans-1,2-dichloroethylene2.