Comparison of hollow fiber and flat mixed-matrix membranes: theory and simulation

We extend effective medium theory (EMT) to composite hollow fiber mixed matrix membranes, considering the asymmetric filler volume fraction profile arising from finite system size. This volume fraction profile leads to strong variation of the driving force (i.e. pseudo-bulk concentration gradient) in the regions adjacent to the composite ends, and to sensitivity of the effective permeability of the composite to the geometrical configuration. The new theory is validated against rigorous simulations of the transport in mixed-matrix membranes (MMMs) using both concentration-independent and concentration-dependent diffusivities in the MMM constituent phases. Both theory and simulations show that flat mixed-matrix membranes (F-MMMs) have higher effective overall permeability than hollow fiber mixed-matrix membranes (HF-MMMs), upon comparison of systems having identical operating conditions, filler phase loading and particle size. Furthermore, we show here that the sensitivity to the geometry vanishes with increase of inner radius of the hollow fiber membrane at fixed thickness, and the effective permeability of a HF-MMM is found to asymptotically approach that of a F-MMM