Abstract
Based on Frenkel's Newtonian viscous flow approach [1] and Mackenzie and Shuttleworth's [2] extension accounting for trapped gas, a model for the shrinkage of a gaseous pore in a viscoelastic polymer melt driven by surface tension was developed. The viscoelastic flow of polymeric materials was considered by using a simple viscoelastic model described by Bellehumeur [3]. In the simulation, the viscoelastic relaxation leads to a pronounced increase of the characteristic time of shrinkage but does not alter the final equilibrium gas sphere diameter. A first attempt at including gas diffusion into the polymer melt motivated by the works of Kontopoulou and Vlachopoulos [4] and Gogos [5] will be given. Numerical solutions of our simplified model show that gas diffusion leads to a complete collapse of the pore. The rate of diffusion can change the collapse mechanism and the time-dependence of pore radius and pressure tremendously.