Several years ago Lonsdate ct al. (t ) studied transport in composite reverse osmosis membranes;. Composite membranes consist of ~1 thin homogeneous layer bonded to a much thicker porous support. The thin homogeneous !ayer is responsibte for the desahing. tonsdate CT a!. noted that when the porous support is made out of a water-impermeable material. it partly occludes water flow through the homogeneous layer. Wittcr can leave the homogeneous layer and enter the support taqer thtoush the open pores of the fatter. On the other hand. water can enter the homogeneous lqcr through rts entire interface with the feed solution. Thus the water permeating the upper triqcr his tf nonunilorm vefocity f&d.
Lonsdatt ef al. habe citlcutated this velocity tieid for a square array of cylindrical pores penetrattng the porous support. which they assumed to blL: made of a material completety impermeable to salt and water. Using their calculated velocity fields, they were abIc to cafculate the reduction in water flow compared with that throu_ch an unocciuded humo~eneous layer for the same pressure drop. The redaction factor is a function onIS: of the pore radius knd porosity of the support layer and the thickness of the homogeneous layer. Lonsdale t'r ul. assumed that the water ilo\ through the homogeneous layer could be described by simple diffusion theory.
fn caicutating the permeation of s&t through the membrane. Lonsdate e: a/. used the so-called solution-dji~u~ion model, in which the s&t and water diffuse irr&pt~&~[~ through the membrane. In this case. the ilow lines of the water and the Ilow lines of the salt must be the same, as are the surfaces of constant pressure and the surfaces of constant salt concentration.
The reduction in salt flow through the ~~orno~ene*u~ membrane is then the same as the reduction in water flow. This mezns that the forntufa for the salt rejection derived from the so~utjon-diffusion model for an unoccfuded membrane is correct also when the membrane is partty occluded by the support matrix.
The solution-diffusion model neglects coupling between the water and salt permeating the homogeneous layer. If such coupting is taken into account, it stiil remains true. remarkably enough. that the ftow fines of salt and water are the same and that the surfaces of constant pressure are surfaces of constant concentntion. It is thus still possible to calculate the salt rejection in terms of the properties of the