Intrinsic Flux Inequality in Forward Osmosis (FO) and Pressure-Retarded Osmosis (PRO) Processes

In pressure-retarded osmosis (PRO) and forward osmosis (FO) processes, solvent (permeate) flux depends on which surface the draw solution faces. There are two operation modes. PRO mode indicates that the active layer faces the draw solution, and FO mode means that the porous substrate fronts the draw stream. It is often observed that the PRO mode produces higher flux than that of FO under the same operating conditions. The current work uses the method of proof by contradiction, and mathematically proves the intrinsic flux inequality between the two modes.