Identifiability Limits of Forward-Osmosis Membrane Transport from Water and Reverse-Solute Flux Observations

Forward osmosis (FO) membrane performance is commonly described through water flux J_w, reverse-solute flux J_s, and the specific reverse-solute ratio R_J = J_s/J_w. These observables provide a low-dimensional projection of a coupled transport system where selective-layer permeability, support resistance, concentration polarization, and defect-mediated leakage interact, producing non-unique links between membrane organization and measured performance. The objective of this study is to determine to what extent the commonly reported FO observables J_w, J_s, and R_J can constrain the underlying transport mechanisms, and to quantify the residual ambiguity when different combinations of selective-layer permeability, support resistance, concentration polarization, and defect-mediated leakage remain compatible with the same measured response. To address this objective, the study develops an admissible-inference framework in the experimentally accessible (J_w, R_J) plane, where published FO measurements are analyzed through observable-space mapping, concentration-polarization amplification, covariance-rank analysis, Fisher/SVD sensitivity diagnostics, and admissible-volume mapping. The resulting framework determines which transport interpretations remain compatible with the observations and which mechanistic directions require additional independent measurements to be resolved.