Nonlinear Flux−Pressure Behavior of Solvent Permeation through a Hydrophobic Nanofiltration Membrane.

Nonpolar solvents have been reported to exhibit a nonlinear flux−
pressure behavior in hydrophobic membranes. This study explored the flux−pressure
relationship of six nonpolar solvents in a lab-cast hydrophobic poly-
(dimethylsiloxane) (PDMS) membrane and integrated the permeance behavior in
the evaluation of the proposed transport model. The solvents exhibited a nonlinear
relationship with the applied pressure, along with the point of permeance transition
(1.5−2.5 MPa), identified as the critical pressure corresponding to membrane
compaction. Two classical transport models, the pore-flow model and solutiondiffusion
model, were evaluated for the prediction of permeance. The solutiondiffusion
model indicated a high correlation with the experimental results before the
point of transition (R2 = 0.97). After the point of transition, the compaction factor
(due to membrane compaction after the critical pressure) derived from the
permeance characteristics was included, which significantly improved the
predictability of the solution-diffusion model (R2 = 0.91). A nonlinear flux−pressure behavior was also observed in hexane−oil
miscella (a two-component system), confirming the existence of a similar phenomenon. The study revealed that a solution-diffusion
model with appropriate inclusion of compaction factor could be used as a prediction tool for solvent permeance over a wide range of
applied transmembrane pressures (0−4 MPa) in solvent-resistant nanofiltration (SRNF) membranes.