Simulation of the Crystallinity Effect on Cell Growth in Semi-Crystalline Microcellular Foams by Semi Solid-State Batch Foaming Process

Thispaper, for the first time, reports a mathematical formulation and numerical simulation of the effect of crystallinity on cell growth in semi-crystalline microcellular foams by solid state batch foaming process at high temperature. Well-known Cell model is used to simulate the isothermalcell-growth phenomenonwith a limited dissolved gas concentration. The presence of crystalline phase in a semi-solid batch process andthe amount of fluid absorbed in the polymer, vary the properties of the polymer-fluid mixture. Therefore, the appropriate modified equationsare usedto evaluatethe system properties as functions of temperature, pressure and crystallinity.Theeffective properties such as solubility, diffusion, surface tension and viscosityof high density polyethylene and nitrogen system areevaluated.A combination of finite element and finite difference methodsare employed to numerically solve the highly nonlinear and coupled equations of cell-growth dynamics. The numerical resultsin terms of cell size agree fairly well with the experimental data. The predicted cell pressure profile, gas concentration in polymer/gas media and the effect of crystallinity on them have also been found to be in good agreement with the dynamics of the cell growth