Classical Nucleation Theory Applied to Homogeneous Bubble Nucleation in the Continuous Microcellular Foaming of the Polystyrene−CO2 System

In the continuous production of microcellular thermoplastic foam, a polymer−physical foaming agent (PFA) solution is subjected to a rapid pressure drop through an extrusion foaming die. Simulations were run for the flow of a polymer−PFA solution through an extrusion foaming die with an abrupt axisymmetric contraction. The pressure drops across the die obtained through the simulations showed good qualitative agreement with experimental pressure drop measurements on the foaming extrusion die obtained in our laboratory. Field values of pressure, temperature, and velocity were obtained at each point in the foaming die. Once the values of pressure and temperature were obtained along each point in the foaming die, classical nucleation theory for bubble nucleation was invoked to predict the local bubble nucleation rate downstream of the saturation surface. The hydrodynamic constraints to the nucleation rate were calculated by using a modified form of the classical nucleation theory that accounted for the diffusional and viscosity constraints to the rate of homogeneous nucleation. The capillarity approximation was found not to be valid for bubble nucleation of CO 2 in polymers; a correction accounting for the curvature dependence of surface tension was applied to get nonzero nucleation rates for the system to reconcile theoretically predicted rates with experimental observations.