Transport Coherence Loss in Heterogeneous Forward Osmosis Membranes: A Hierarchical Diagnostic Framework.

Forward osmosis (FO) membranes are commonly evaluated through macroscopic observables such as water flux and reverse solute flux. However, these quantities do not necessarily reveal whether water permeation and solute leakage remain governed by the same dominant transport pathways, particularly in heterogeneous nanostructured membranes where selective nanochannels and defect-mediated pores can contribute differently to solvent and solute transport. Here, we introduce a hierarchical diagnostic framework to assess transport coherence loss in heterogeneous FO membranes. The framework comprises a baseline model (BM), an extended model (EM) including chemistry-geometry coupling through accessibility loss, and a full model (FM) incorporating selective pore-size heterogeneity. The ratio of reverse solute flux to water flux RJ=Js/Jw is used as a regime-based diagnostic descriptor of transport organisation, while its normalised form maps coherence variations across the state-space defined by structural selectivity and nanochemical state. The results show that chemistry-geometry coupling produces the first clear reorganisation of the coherence landscape, whereas pore-size heterogeneity mainly broadens the response while preserving its dominant topology. Simulations based on both Monte Carlo and experimentally derived pore-size distributions show consistent trends. Overall, the BM-EM-FM hierarchy offers an interpretable framework for describing transport coherence loss and the emergence of leakage-prone regimes in heterogeneous FO membranes.