title: Modeling pH variation in reverse osmosis.
abstract: The transport of hydronium and hydroxide ions through reverse osmosis membranes constitutes a unique case of ionic species characterized by uncommonly high permeabilities. Combined with electromigration, this leads to complex behavior of permeate pH, e.g., negative rejection, as often observed for monovalent ions in nanofiltration of salt mixtures. In this work we employed a rigorous phenomenological approach combined with chemical equilibrium to describe the trans-membrane transport of hydronium and hydroxide ions along with salt transport and calculate the resulting permeate pH. Starting from the Nernst-Planck equation, a full non-linear transport equation was derived, for which an approximate solution was proposed based on the analytical solution previously developed for trace ions in a dominant salt. Using the developed approximate equation, transport coefficients were deduced from experimental results obtained using a spiral wound reverse osmosis module operated under varying permeate flux (2-11 μm/s), NaCl feed concentrations (0.04-0.18 M) and feed pH values (5.5-9.0). The approximate equation agreed well with the experimental results, corroborating the finding that diffusion and electromigration, rather than a priori neglected convection, were the major contributors to the transport of hydronium and hydroxide. The approach presented here has the potential to improve the predictive capacity of reverse osmosis transport models for acid-base species, thereby improving process design/control.
authors.affiliation: Faculty of Civil and Environmental Engineering, Technion - IIT, Haifa, 32000, Israel.
authors.forename: Oded
authors.initials: O
authors.lastname: Nir
authors.affiliation: Faculty of Chemical Engineering, Technion - IIT, Haifa, 32000, Israel.
authors.forename: Noga Fridman
authors.initials: NF
authors.lastname: Bishop
authors.affiliation: Faculty of Civil and Environmental Engineering, Technion - IIT, Haifa, 32000, Israel.
authors.forename: Ori
authors.initials: O
authors.lastname: Lahav
authors.affiliation: Faculty of Chemical Engineering, Technion - IIT, Haifa, 32000, Israel. Electronic address: vfreger@tx.technion.ac.il.
authors.forename: Viatcheslav
authors.initials: V
authors.lastname: Freger
mesh_terms: D006863:Hydrogen-Ion Concentration; D006878:Hydroxides / Q000737:chemistry*; D008962:Models, Theoretical; D009861:Onium Compounds / Q000737:chemistry*; D009995:Osmosis; D018508:Water Purification / Q000379:methods*
chemical_list: D006878:Hydroxides; D009861:Onium Compounds; C027727:hydronium ion; C031356:hydroxide ion
keywords: Convection; Electromigration; Ion-flux; Reverse-osmosis transport; pH