Parameter estimation for the modelling and simulation of expanding polyurethane foams

This paper presents a numerical study and approach for estimating associated parameters resulting from the mathematical modelling of self expanding polyurethane (PU) foams. In reaction injection molding of PU foams, the reactant polymer mixture undergoes phase transition resulting from exothermic chemical reaction, evolution of gas and network formation. Thereby, exhibiting the chemorheological property of the mixture viscosity which strongly influence the final structure of the expanded foam. More so, measuring this viscosity experimentally becomes extremely difficult, hence, the resolve to numerical investigations. However, to account for this behaviour mathematically, the foam viscosity is assumed to depend on the rate of conversion of the reactants mixture (degree of cure), temperature of the system and the volume fraction of evolving gas attributed to the chemical reaction. With this form of coupling in the state variables it becomes very challenging to estimate the associated model parameters analytically. We therefore explore a purely numerical approach in estimating some of these parameters. The coupled system of time dependent PDEs governing the foam expansion process is solved on a numerical simulation platform (CoRheoS) based on finite volume method. With graphical illustrations, we discuss the influence of these parameters on the foam viscosity and then validate our results with available experimental data.