A model to predict the cell density and cell size distribution in nano-cellular foams

A numerical model is developed to simulate the simultaneous bubble nucleation and growth during depressurization of thermoplastic polymers saturated with supercritical blowing agents. Of particular importance is the ability of the model to predict the formation of nano-cellular foams, including the cell size distribution within the foam, based on the specific process conditions and polymer properties. Additionally the model differentiates between the Free and Limited expansion phases in the growth of a single bubble. Classical nucleation theory is used to predict nucleation rate and the popular Influence Volume Approach is used to determine the end of nucleation phase. By solving the mass, momentum and species conservation equations for each bubble, the model is capable of predicting bubble size distribution and bulk porosity. It is found that by accurately capturing the concentration gradient of the blowing agent in the boundary layer surrounding the bubble and applying appropriate boundary conditions at different stages of bubble growth, the model is able to accurately predict the conditions for making nano-cellular foams. Unlike micro-cellular foams the diffusion controlled period is short and the viscosity-controlled period is crucial to generating maximum nuclei density. Experimental data obtained by foaming acrylate copolymers with CO2 as the blowing agent compare well with model predictions of average cell size and porosity as well as cell size distribution. Furthermore, the effect of depressurization curve on the average cell size and cell size distribution are delineated. (C) 2015 Elsevier Ltd. All rights reserved.