The classic Merten and Lonsdale transport model for reverse osmosis membranes was reformulated to explicitly demonstrate the effects of concentration polarization and solution phase thermodynamic non-idealities on salt transport. A framework presented here accounts for the concentration dependence of ion activity coefficients in salt solutions, which was not explicitly included in the classic model. This approach was applied to four salt solutions, NaCl, MgCl2, CaCl2, and Na2SO4, tested in cross-flow conditions for a commercial RO membrane, Dow Filmtec™ BW30XFR. Salt transport coefficients corrected for concentration polarization and non-ideal thermodynamic effects, Ba, were calculated as a function of permeate flux and compared with apparent salt transport coefficients, B. These corrections were significant, resulting in Ba values greater than B values by a factor of 1.3–2.1 for 2:1 and 1:2 salts (i.e., MgCl2, CaCl2, and Na2SO4). Ba values for NaCl (a 1:1 salt), however, were similar to or somewhat smaller than B values.
- Reverse osmosis (RO)
- Salt transport
- The Merten and Lonsdale model