Graduation Year


Document Type




Degree Granting Department

Civil Engineering

Major Professor

Campbell, Scott W.


spiegler-kedem model, diffusion, nanofiltration, ro membranes, kimura-sourirajan model, ion hydration


This dissertation investigates the importance of diffusional and convective fluxes for salts in reverse osmosis (RO) and nanofiltration (NF) membranes. Moreover, the physical and thermodynamic factors controlling the salt permeability are analyzed. The study utilizes direct osmosis (DO) experiments and RO experiments, the later using both flat sheet and spiral wound membrane configurations. The salts considered are chlorides and acetates of alkali metals and alkaline earth metals. The equation governing the salt transport in DO experiments is derived and a phenomenon inverse to concentration polarization in RO is observed. The salt permeability in DO is equal to the salt permeability calculated for the valid cases of the used RO models. DO is suggested as an alternative method in characterizing the salt transport in membranes. The method can be more advantageous than RO due to the lower costs and simplicity of the apparatus.

The models used to calculate the salt transport parameters in RO experiments are Spiegler-Kedem model, which considers both diffusion and convection of salt, and Kimura-Sourirajan model, which considers only diffusion of salt. It is found that diffusion is the dominant mechanism of transport in both RO and NF membranes. The percentage of the salt diffusional flux of the total flux is highest for seawater membranes and it is approximately equal for brackish water and nanofiltration membranes. The salt diffusive flux contribute more to the total flux for the 1:2 salts than for 1:1 salts. The two RO models are found equivalent in determining the salt permeability for only the seawater membranes. The Kimura-Sourirajan model overestimates the salt permeability coefficient for salts with rejection coefficient lower than 86%.

The permeation rates for studied salts follow the lyotropic series regardless the membrane type (RO or NF), the membrane configuration (flat sheet or spiral wound), the process (DO or RO), or the models used for the calculations. This order of salt permeability is explained by the hydration of the cations, which is quantified by the enthalpy and entropy of hydration. The relative free energy theory can also be used to predict the salt permeability in a membrane based on preliminary data.