Modeling permeate pH in RO membranes by the extended Donnan steric model

We investigate permeate pH across an RO membrane by modeling transport of ions including protons and hydroxide ions using the extended Donnan steric partitioning pore model (ext-DSP model). We show that membrane charge density plays an important role in determining permeate pH, while the effect of flow rate and salt concentration are less significant. Depending on the polarity of the membrane charge, permeate pH may be lower or higher than feed pH, which indicates the necessity of a reliable membrane charging model. A general multi-site Langmuir charging model is formulated to characterize the membrane charging mechanism and constrain the model parameters. Besides, a simple formula of permeate pH based on the trans-membrane electrostatic potential difference is shown to be a good approximation to the full model prediction.