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Continuum Modeling and Flow Visualization of Blown Foams

Rekha R. Rao1, Lisa A. Mondy1, Veena Tikare1, Edward M. Russick1, P. Randall Schunk1, Andrew M. Kraynik1, Douglas B. Adolf1, Thomas A. Baer2, Stephen A. Altobelli3, and Raymond Cote1. (1) Sandia National Laboratories, PO Box 5800, Albuquerque, NM 87185-0834, (2) Gram Inc., 8500 Menaul Blvd NE, Suite B-335, Albuquerque, NM 87112, (3) New Mexico Resonance, Yale Center, Suite C1, Albuquerque, NM 87108

Foams are ubiquitous low density materials used for a variety of applications including shock, thermal, and vibration isolation, disposable containers, energy production, and anti-terrorism operations to mitigate the dispersal of toxins. Despite their many uses, foams are still not well understood at a fundamental level. In order to better understand the processing of physically blown foams, we combine experimental observations with finite element model development to help understand the manufacture of physically blown, thermosetting foam. The precursor foam starts off as a liquid phase emulsion of blowing agent in a thermosetting polymer. As the material is heated either by an external oven or by the exothermic reaction from internal polymerization of the suspending fluid, the blowing agent boils to produce gas bubbles and a foamy material.

A series of experiments have been performed to allow observation of the foaming process in a variety of geometries. The process is very sensitive to geometry, which affects the heat transfer from the oven and the amount of heat produced by the exothermic polymerization reaction. In conjunction with the visual observations, nuclear magnetic resonance (NMR) is used to determine the distribution of the 19F in the volatile blowing agent. The difference in the NMR properties T1 and T2 gives information about the physical state (gas or liquid) of the blowing agent. Properties of the components and the kinetics of the polymerization are also determined as input to the continuum model.

The continuum-modeling capability is based on a finite element discretization of the self-expansion that occurs during foam blowing. The continuum-level model has been developed with the help of three types of mesoscale modeling. First, we use a single bubble ordinary differential equation model of blowing agent nucleation and growth to better understand the mass transfer between the liquid and gas phases. Second, we use Pott's modeling to elucidate changes in microstructure as bubbles expand and rearrange while ignoring the fluid mechanics. Third, we use an overset grid finite element approach to formulate a model for bubble-bubble interactions. Different methods of coupling the mesoscale modeling with the continuum modeling will be discussed. The final resulting model is compared to the experiments in thin vessels where the foam is relatively isothermal and in cylindrical geometries where exotherms from the polymerization reaction dominate the physics.

1Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.