Advances in Continuum Modeling of Gas Permeation in Mixed-Matrix Membranes

Membrane-based gas separation technologies potentially offer energy-efficient and scalable solutions for various clean energy systems, carbon management, and industrial processing. As an alternative to conventional polymeric membranes that exhibit the traditional permeability-selectivity trade-off, mixed-matrix membranes (MMMs) have emerged as a promising class that combines polymer processability with enhanced transport properties of porous materials, referred to as fillers. The fundamental design principles of MMMs are centered on tailoring transport properties to improve permeability-selectivity performance. However, in practice, MMM fabrication and optimization still rely heavily on simplified permeation predictions or modeling approaches that fail to capture the complex heterogeneous structures of these membranes. In this review, we aim to establish a continuum-scale framework for modeling gas permeation in MMMs by critically examining existing permeation models and presenting a unified description of transport mechanisms and their mathematical formulations. We highlight recent advances in transport modeling and discuss the role of microstructural representation in complementing these approaches, including advances in experimental imaging techniques and synthetic microstructure generation. We then identify key phenomena often simplified or overlooked in transport modeling development. Finally, we outline future perspectives for developing more predictive and physically grounded approaches to MMM design and material selection, while promoting a deeper mechanistic understanding of gas transport in complex MMM systems.