(473i) Bubble-Size Experiments and Predictions for Polyurethane Foam Using a Population Balance Equation

Polyurethane foams are widely used in manufacturing in part due to their ease of use and beneficial material properties, such as low thermal conductivity, stress and shock cushioning, and tunable density. Our goal is to develop computational models to predict these properties as a function of precursor formulations and processing conditions to aid in the manufacturing of polyurethane products. In this presentation, we focus on PMDI polyurethane foams, which are chemically blown foams used for electronic encapsulation and lightweight structural parts. A recently published kinetic model [1] is extended with a population balance equation using the Quadrature Method of Moments (QMOM) [2] in order to predict bubble size evolution as well as density variations during mold filling. We use a stabilized finite element method to solve the conservation equations; equations of motion, energy balance equation, species conservation with reaction, and transport of moments for QMOM. We combine these equations with the level set method in order to track the free surface between the foam and the surrounding gas. This model is used to predict final foam properties including density, thermal conductivity, and bubble size evolution in a three-dimensional foam bar geometry. Results for final densities are compared to experimental X-ray CT data. Bubble size evolution and final distributions are compared to experimental optical and SEM data.

References

[1] Rao, Rekha, et al. "Density predictions using a finite element/level set model of polyurethane foam expansion and polymerization." Computers & Fluids 175 (2018): 20-35.

[2] Karimi, Mohsen, Hermes Droghetti, and Daniele L. Marchisio. "Multiscale modeling of expanding polyurethane foams via computational fluid dynamics and population balance equation." Macromolecular Symposia. Vol. 360. No. 1. 2016.