A volume averaging and overlapping domain decomposition technique to model mass transfer in textiles

A new three scale approach for textile models is suggested: a one-dimensional fiber model and a fabric model, with a meso-level in between, i.e. the yarn scale, Goessens et al. (2012). For loose textile substrates this seems appropriate as the yarn level plays an important role. This is because the saturation vapor pressure will influence the release rate from the fibers, and its value will vary over the yarn cross section. Therefore, in this work we present two upscaling techniques for the three step multiscale model. The active component is tracked in the fiber, the yarn, and finally at the fabric level. At the fiber level a one-dimensional reduction to a non-linear diffusion equation is performed, and solved on an as needed basis. The outcome is upscaled via the volume averaging method and used as an input for the yarn level. At this level a one-dimensional model can be applied to calculate the concentration, which on its turn is upscaled using the overlapping domain decomposition as an input for the fabric level model.