Modeling of diffusion in closed cell polymeric foams
Closed-cell foams made of polymers have the lowest thermal conductivity of any currently available insulation material other than vacuum insulation systems. The increase of foam conductivity with age occurs as air diffuses into the foam while the blowing agent diffuses out, thus modifying the cell gas composition. Also, the change in cell gas composition influences the dimensional stability of the foams. To predict the long term aging behavior and dimensional stability of these foams, the diffusion characteristics of the different components need to be known. Several models exist in the literature which describe diffusion in foams. The most popular of these models are reviewed, and effective diffusivities predicted from one model are compared with experimental data. An unsteady state model is then proposed and solved numerically using a finite difference scheme. The numerical solution algorithm is developed to efficiently solve the large number of coupled equations resulting from this model. The uptake curves predicted from both the unsteady-state model and a discrete model (Bart and Du Cauze De Nazelle, 1993) are compared with available experimental data for the polystyrene-nitrogen system. From the analysis of uptake curves generated for different numbers of cells, the effective diffusivity of the PS/N2 system is predicted. Also, the effect of initial cell gas composition and cell size on both the long term aging profile and dimensional stability of polyurethane foam is considered. The proposed model can easily be extended to include the influence of blowing agent concentration on diffusivity in the polymer phase and the isotherm describing the distribution of blowing agent between the gas and polymer phases.