Concentration dependence modeling of reverse osmosis

Osmosis is the natural flow of a solvent through a semi-permeable membrane from a less concentrated solution to a more concentrated one. This is driven by the osmotic pressure difference. If opposing external pressure is used that exceeds the osmotic pressure, the solvent will flow from the more concentrated solution towards the less concentrated one. Besides the external pressure, the flux of the solvent (water) describing the reverse osmosis is the function of the osmotic pressure, which, in the case of an ideal solution, according to the van’t Hoff principle, is proportional to the salt concentration. The current study examines the concentration dependence of the permeate flux, complementing the traditional model with the osmotic pressure difference caused by the concentration polarization stemming from the crossflow. In the calculations for the real solution, the osmotic coefficient was used instead of the empirical forms of osmotic pressure, making the model more correct theoretically as well. The validity of the model was certified and the parameters determined with independently measured results based on literature regarding the reverse osmotic desalination of seawater.