Owing to a small cell size, high cell population density and uniform cell size distribution, microcellular polymeric foams have a variety of industrial applications. To develop innovative foaming technologies, a fundamental understanding of expansion and collapse of extruded filamentary foam is essential. Since computer simulation is capable of uncovering intrinsic details which are hard to acquire either experimentally or analytically, this thesis developed a theoretical model to simulate foam expansion and collapse outside a filamentary extrusion die.

This model consists of three stages. In the first stage, foam expansion was made up of polymer swelling and expansion of bubbles. The polymer swelling was characterized experimentally whereas the expansion of bubbles was acquired by integrating growth of each cell. The growth of a single cell was simulated using cell model. In the second stage, a layer-to-layer model was established. It separated the circular extrudate into many concentric cell bands. Each band was made of a transformed gas layer and the surrounding polymer layers. After a set of governing equations were solved, the foam expansion could be estimated. The third stage emerged once the extrudate reached its maximum expansion. In this stage, all the blowing agents within polymer matrix had been depleted. But the blowing agents kept escaping into the surroundings, leading to foam contraction. Consequently, the mechanism of foam expansion and collapse was comprehended. As well, experimental research was implemented to validate the developed model.

Meanwhile, to understand cell-to-cell diffusion fundamentally, this thesis undertook a finite element analysis to investigate cell coarsening between two micro-cells and among nine nano-cells, respectively. The effects of system parameters on cell-to-cell diffusion were examined.

Furthermore, this thesis used cell-to-cell diffusion concept to predict long-term thermal insulation performance of polystyrene foam boards. The Mie Theory was utilized to calculate radiative conductivity. A transient cell-to-cell diffusion model was employed to describe the decay of blowing agents. A cubic-parallel-series approach was applied to determine thermal conductivity of the gaseous phase and polymer matrix. Effects of foam geometry and blowing agents on thermal insulation capacity were analyzed.

Finally, concluding remarks were presented and future work was recommended.