Reverse osmosis theory

In reverse osmosis membranes, the pores are so smaH, in the range 0.5— 2 nm in diameter, that they ate within the range of the thermal motion of the polymer chains. The most widely accepted theory of reverse osmosis transport considers the membrane to have no permanent pores at aH. Reverse osmosis membranes are used to separate dissolved microsolutes, such as salt, from water. The principal appHcation of reverse osmosis is the production of drinking water from brackish groundwater or seawater. Figure 25 shows the range of appHcabHity of reverse osmosis, ultrafiltration, microfiltration, and conventional filtration. 

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

Kabadi, V. N., Doshi, M. R., and Gill, W. G. (1979). Radial flow hollow fiber reverse osmosis Experiments and theory. Chem. Eng. Common. 3, 339-365. 

A. E. Yaroshchuk, S. S. Durkhin. Phenomenological theory of reverse osmosis in macroscopically homogeneous membranes and its specification for the capillary charged model. J Memb Sci 79 133, 1993. 

S. Murad, J. G. Powles, B. Holtz. Osmosis and reverse osmosis in solutions Monte-Carlo simulations and van der Waals one-fluid theory. Mol Phys 55 1473, 1995. 

In the literature, there are many transport theories describing both salt and water movement across a reverse osmosis membrane. Many theories require specific models but only a few deal with phenomenological equations. Here a brief summary of various theories will be presented showing the relationships between the salt rejection and the volume flux. 

As summarized above, there are many transport models and flow mechanisms describing reverse osmosis. Each requires some specific assumptions regarding membrane structure. In general, membranes could be continuous or discontinuous and porous or non-porous and homogeneous or non-homogeneous. One must be reasonably sure about the membrane structure before he analyzes a particular set of experimental data based on one of the above theories. Since this is difficult, in many cases, it would be desirable to develop a model-independent phenomenological theory which can interpret the experimental data. 

An exact mathematical relationship is obtained between the salt rejection and total volume flux in reverse osmosis based on a purely phenomenological theory assuming constant salt permeability. This approach does not require a specific membrane model ... 

This volume is the result of a symposium honoring Drs. Sidney Loeb and S. Sourirajan on the 20th anniversary of their discovery of the first functionally useful reverse osmosis membrane. Both of these esteemed gentlemen participated as plenary speakers and described not only how their membrane originated but also reviewed membrane theory and put the membrane field into present and future perspective. 

Reverse Osmosis and Synthetic Membranes. Theory-Technology-Engineering Edited by Sourirajan, S., National Research Council, Canada (1977)... 

Singh R. and Tembrock J., Effectively controlled reverse osmosis systems. Chemical Engineering Progress 95 1999 57-66. Koltuniewicz A. and Nowor)fta A., Dynamic properties of ultrafiltration systems in light of the surface renewal theory. Industrial Engineering and Chemical Research 33 1994 1771-1779. 

Rozelle, L.T. Cadotte, J.E. Cobian, K.E. Kopp, C.V., Jr. Nonpolysaccharide membranes for reverse osmosis NS-lOO membranes. In Reverse Osmosis and Synthetic Membranes, Theory—Technology— Engineering , Sourirajan, S., Ed. National Research Council of Canada Ottawa, 1977 249-261. 

Perhaps because much attention has centered on reverse osmosis membranes, the fine pores present in their skins were observed prior to the discovery of the functionally larger pores of ultrafiltration (UF) membranes. Recently, pores of v30 A have been observed by Zeman (35) in the skins of UF membranes. Their density, uniformity and diameters leave no doubt that these are actually the pores which function during UF. Our ability to actually "see" the intermicellar defect pores (the population of larger size pores) in the skins of RO membranes extends to the 10 X range. Therefore, it is reasonable to expect that at some point we shall be able to extend this ability to the population of smaller sized pores, whose existence is predicted by Sourlrajan s pore theory (36). 

Blatt et al.(29) developed what has become known as the "gel polarization" theory for ultrafiltration, in which the amount of macromolecular material in the fouling layer is controlled by its back-diffusion rate into the feed stream. The gradual decline in flux observed in some practical systems was explained in terms of an irreversible consolidation of the gel layer with time, leading to a reduction in the layer s permeability. Kimura and Nakao (,1) used Blatt s approach to model the fouling of reverse osmosis... 

A concentration boundary layer theory clearly is needed to relate C to C, so that membrane properties such as L, a, and P can be correlated with R, at various operating conditions. Slso, since ir in Equations 1 and 5 is an independently determined function of C, a boundary ayer theory could correlate the observed filtrate velocity, J (averaged along the fiber length), with average applied pressure AP. For sufficiently high axial flow velocities, C == C, and a major theoretical barrier to data analysis is removeS. Some early work in reverse osmosis ( ) was done with flat-sheet membranes and large feed stream velocities. 

An early work considering osmotic pressure in the ultrafiltration of macromolecular solutions was done by Blatt, et al,. (1970), who employed a theory which had been developed for cross flow reverse osmosis systems. They essentially suggested that the film theory relationship given by Eq. (2) could be solved simultaneously with Eq. (1) to predict permeate rates, where the... 

Reverse osmosis is simply the application of pressure on a solution in excess of the osmotic pressure to create a driving force that reverses the direction of osmotic transfer of the solvent, usually water. The transport behavior can be analyzed elegantly by using general theories of irreversible thermodynamics however, a simplified solution-diffusion model accounts quite well for the actual details and mechanism in most reverse osmosis systems. Most successful membranes for this purpose sorb approximately 5 to 15% water at equilibrium. A thermodynamic analysis shows that the application of a pressure difference, Ap, to the water on the two sides of the membrane induces a differential concentration of water within the membrane at its two faces in accordance with the following (31) ... 

The mechanism of water and salt transport in reverse osmosis is not completely understood. One theory is that water and solutes diffuse separately through the polymer by a solution-diffusion mechanism. The concentration of water in the dense polymer is assumed to be proportional to the activity of water in the solution. On the low-pressure side of the dense layer, the activity is essentially unity if nearly pure water is produced at 1 atm. On the high-pressure side, the activity would be slightly less than 1.0 at atmospheric pressure (0.97 for a 5 percent NaCl solution), 1.0 at the osmotic pressure, and slightly greater than 1.0 at higher pressures. The upstream pressure is generally set at 20 to 50 atm above the osmotic... 

The study of gas transport in membranes has been actively pursued for over 100 years. This extensive research resulted in the development of good theories on single gas transport in polymers and other membranes. The practical use of membranes to separate gas mixtures is, however, much more recent. One well-known application has been the separation of uranium isotopes for nuclear weapon production. With few exceptions, no new, large scale applications were introduced until the late 1970 s when polymer membranes were developed of sufficient permeability and selectivity to enable their economical industrial use. Since this development is so recent, gas separations by membranes are still less well-known and their use less widespread than other membrane applications such as reverse osmosis, ultrafiltration and microfiltration. In excellent reviews on gas transport in polymers as recent as 1983, no mention was made of the important developments of the last few years. For this reason, this chapter will concentrate on the more recent aspects of gas separation by membranes. Naturally, many of the examples cited will be from our own experience, but the general underlying principles are applicable to many membrane based gas separating systems. 

Emphasis is on rational theory and its consequences, with the purpose of showing the underlying unity of PCH, in which diverse phenomena can be described in physically and mathematically similar ways. The magic of this unity is shown in the similar manner in which solutes concentrate in a flow containing chemically reacting surfaces, reverse osmosis membranes, and electrodialysis membranes or the similarity of particle motions in sedimentation, centrifugation, ultrafiltration, and electrophoresis. Experimental results, numerical solutions, and reference to topics not covered are noted where they serve to illustrate a concept, result, or limitation of what has been presented. Empiricism is not eschewed, but only limited use is made of it and then only when it contributes to a better understanding of an idea or phenomenon. 

Reverse osmosis and pervaporation are able to separate molecules of similar size, such as sodium chloride and water. In such cases, the affinity between the membrane and the target component is important, as the speed of permeation through the membrane. Components that have a greater affinity for the membrane material dissolve in the membrane more easily than other components, cansing the manbrane material acts as an extraction phase. Differences in diffnsion coefficients of components throngh the membrane allow the separation. According to the theory of solution diffusion, solubility and diffusivity together will control the manbrane selectivity. The mechanism by which NF membranes act is... 

D. R. Paul, Reformulation of the solution-diffusion theory of reverse osmosis, J. Memhr. Sci. 241 (2004) 371-386. 

Reverse osmosis, like freezing, is a commonly used desalination process 178, 509). The theory and applications have been described (5/0) and reviewed for pollutants 511). The efficiency of separation (which can be as high as 99.5%) increases as the concentration of solute decreases, but decreases as the concentration factor is increased (5/2). The application of reverse osmosis to the preconcentration of inorganic solutes for analytical purposes has been neglected. Some work with organic 513) or biochemical solutes 514) has been reported. Reverse osmosis has been used to concentrate radioactive waste (5/5). The addition of surfactants (2 x 10 M sodium hexadecylsulfate) to aqueous radioactive solutions has increased the separation efficiency from 30-35% to 98% for radioactive isotopes (5/6). 

The phenomeiion above describes reverse osmosis. Here, a liquid with a higher concentration of electrolyte is driven through a membrane (pore sizes are on the order of 3 nm), and the exiting solvent contains much less electrolyte. The reverse osmosis membranes usually have an of 0.995. Calculate the corresponding ipj. The present treatment is from Jacazio et al. (1972), who also compared theory to experiments. 

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