Homogenization Theory Captures Macroscopic Flow Discontinuities Across Janus Membranes

The document discusses a study on Janus membranes, thin permeable structures with asymmetric properties used in industrial separation processes and potential applications in energy-related challenges and biomedical applications. The study develops a homogenization-based model to understand the behavior of these membranes at micro and macro levels, introducing upstream and downstream spatial averages to account for discontinuities induced by the microstructure. The model quantifies the macroscopic jump in solvent velocity, stresses, solute concentration, and fluxes across the membrane. The study found that the upward and downward averages of microscopic quantities produce different values of effective tensors only when membrane properties are not symmetric. The researchers concluded that the homogenization theory can effectively capture macroscopic flow discontinuities across Janus membranes. The model extends to a larger class of thin porous membranes, providing a rigorous foundation to quantify the effective properties of real, partially permeable membranes.