(175j) Modeling Polyurethane Foam Expansion and Cure
We are developing computational models to elucidate the dynamic filling of a mold with a polyurethane foam. Polyurethane foam is created through two primary reactions that compete for isocyanate monomer. In the first, isocyanate reacts with polyol to produce polymer, eventually creating a rigid solid. In the second, isocyanate reacts with water to produce CO2 gas that drives foam expansion. The kinetics of the resin polymerization was evaluated using infrared spectrophotometry on both wet and dry polyurethane precursor, in order to attempt to separate the curing and blowing reactions. The kinetics of the gas generating reaction was measured by tracking volume evolution with time in the curing system while simultaneously measuring the system temperature and pressure. As the material polymerizes, it becomes both more viscous and viscoelastic, hindering expansion; hence, gas bubbles become pressurized, since there is no change in volume though more gas has been created. Results show that the foaming reaction continues even after foam expansion has stopped. However, the curing reaction continues for some time after the gas generating reaction is complete. Because the isocyanate is in excess during the expansion stages of the foam formation, we treat the competing reactions as separable primary reactions. Both reactions show Arrhenius-type temperature dependence. The rheology of polyurethane, again both wet and dry, during reaction is examined through steady-shear and oscillatory tests. The rheological measurements are combined with the kinetic equations to estimate the effect of gas fraction and extent of polymerization on the viscosity. A finite element model was developed combining the equations of motion, an energy balance, and two rate equations for the polymerization and foaming reactions. This was joined with a level set method to track the location of the free surface as it evolves in time. The model predicts the evolution of the foam-gas interface and density of the foam. It is compared to experimental flow visualization data, temperature measurements, and x-ray images of density.
*This research is supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.