Modeling of bubble-size distribution in free rise polyurethane foams

Abstract

The existing models of the foaming process in reaction injection molding are inadequate for predicting the bubble-size distribution, which influences many properties of interest. This work attempts to develop a model for the bubble-size distribution under conditions of free rise. The population balance equation for bubbles, coupled with the system of energy balance and reaction kinetics equations through the blowing agent evaporation rate expression, is solved to obtain the bubble-size distribution. A simple mass-transfer coefficient approach for expressing growth rate of bubbles is used, although various growth laws can be accommodated without affecting the solution procedure. Determining factors for the bubble size and its distribution are the foaming period and the growth law. With increase in initial blowing agent concentration, the foaming period increases and bigger bubbles are obtained. The bubble-size distribution becomes broader as the foaming period increases.