Effects of random defect distributions in the barrier coating on the gas permeability of multilayer films

The influence of barrier coating defectiveness on the overall permeating flux through a bilayer film is considered with particular attention to the effect of spatial defect distribution. To that aim, the diffusion equations for the permeating species have been solved in a large number of 3D geometries, built to simulate a bilayer structure with defects randomly distributed on the coating surface. A numerical approach based on finite volume method was used and, for each value of defectiveness considered, ranging from 0.25 to 10%, a minimum number of 200 different geometries were analyzed, in order to obtain statistically meaningful results.The numerical simulations results, which for regular arrays of defects also compares rather well with data available in the open literature, showed that the average flux obtained for each different defectiveness is not a fixed value, but rather shows substantial variations due to the randomness of the defect distribution. In particular, when few defects are present on the surface, differences higher than 10% have been observed in the flux calculated, while deviation lower than 3% with respect to the average value were obtained when the defects fraction on the surface was about 10%.Interestingly, the random distribution of defects on the surface gives average flux which are always smaller than the corresponding ordered geometry and does not result in a Gaussian distribution of the permeate flux. Distributions close to the normal one were indeed observed only for higher defectiveness while, for lower defect fractions, flux distributions with a clear tail towards the lower permeation rates were obtained.