A Baseline Model for the Simulation of Polyurethane Foams via the Population Balance Equation

In this work a novel modeling approach, based on the solution of the population balance equation (PBE), is presented and applied for the first time to the simulation of expanding polyurethane foams. The solution of the PBE allows to determine the evolution of the bubble (or cell) size distribution (BSD) of the foam, which in turn defines the final foam mechanical and thermal properties. The approach includes a simple kinetic model for the polymerization reaction, between isocyanate and polyol, and for the blowing reaction, between isocyanate and water. The presence of a physical blowing agent is also accounted for and the model is completed by the enthalpy balance that allows to update the system temperature. Model predictions are compared with experiments from the literature for 12 different chemical recipes, highlighting very good agreement, and showing the promising potential of the method