Solution-diffusion imperfection

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... 

Solution - Diffusion Imperfection Model (porous model)... 

Experiments have shown that the solution - diffusion imperfection model fits data better than the solution - diffusion model alone and better than all other porous flow models.6 However, the solution-diffusion model is most often cited due to its simplicity and the fact that it accurately models the performance of the perfect RO membrane. 

Finely Porous Model. In this model, solute and solvent permeate the membrane via pores which connect the high pressure and low pressure faces of the membrane. The finely porous model, which combines a viscous flow model eind a friction model (7, ), has been developed in detail and applied to RO data by Jonsson (9-12). The most recent work of Jonsson (12) treated several organic solutes including phenol and octanol, both of which exhibit solute preferential sorption. In his paper, Jonsson compared several models including that developed by Spiegler eind Kedem (13) (which is essentially an irreversible thermodynamics treatment), the finely porous model, the solution-diffusion Imperfection model (14), and a model developed by Pusch (15). Jonsson illustrated that the finely porous model is similar in form to the Spiegler-Kedem relationship. Both models fit the data equally well, although not with total accuracy. The Pusch model has a similar form and proves to be less accurate, while the solution-diffusion imperfection model is even less accurate. 

Both 7 and 7 are diffusive fluxes through the membrane. If there are large pores in the membrane, there will be convection through such pores or defects. The total flux of any species will no longer be completely diffusive and therefore should be expressed in terms of Ni (Soltanieh and GiU, 1981). A simple model for the fluxes through a reverse osmosis membrane having large pores (or defects or imperfections) has been provided by Sherwood et al. (1967) it is called the solution-diffusion-imperfection model ... 

There are a number of other models of transport of solvent and solute through a reverse osmosis membrane the Kedem-Katchalsky model, the Spiegler-Kedem model, the frictional model, the finely porous model, the preferential sorption-capUlary flow model, etc. Most of these models have heen reviewed and compared in great detail hy Soltanieh and GiU (1981). We will restrict ourselves in this hook to the solution-diffusion and solution-diffusion-imperfection flux expressions for a number of reasons. First, the form of the solution-diffusion equation is most commonly used and is also functionally equivalent to the preferential sorption-capiUary flow model. Secondly, the solution-diffusion-imperfection model is functionally representative of a number of more exact three-transport-coefficient models, even though the transport coefficients in this model are concentration-dependent... 

The solution-diffusion-imperfection model based on three parameters and proposed by Sherwood et al. (1967) (illustrated in flux expressions (3.4.60a,b)) appears to be able to describe better the observed solute rejections vs. solvent flux behavior in RO membranes (Applegate and Antonson, 1972). Rewrite the flux expressions (3.4.60a,b) for a dilute solution as... 

Equation 7 shows that as AP — oo, P — 1. The principal advantage of the solution—diffusion (SD) model is that only two parameters are needed to characterize the membrane system. As a result, this model has been widely appHed to both inorganic salt and organic solute systems. However, it has been indicated (26) that the SD model is limited to membranes having low water content. Also, for many RO membranes and solutes, particularly organics, the SD model does not adequately describe water or solute flux (27). Possible causes for these deviations include imperfections in the membrane barrier layer, pore flow (convection effects), and solute—solvent—membrane interactions. 

The solution-diffusion transport model was originally described by Lonsdale et. al.3 This model assumes that the membrane is nonpo-rous (without imperfections). The theory is that transport through the membrane occurs as the molecule of interest dissolves in the membrane and then diffuses through the membrane. This holds true for both the solvent and solute in solution. 

Water flux through the membrane is represented by Equation 4.3. This flux is based on the solutions - diffusion model with the added term to reflect transport due to the imperfections. 

Again, the solute flux is equivalent to that for the solution - diffusion model (Equations 4.1 and 4.2) with the added term to represent the flow through the imperfections. 

The Solution Diffusion Model assumes that solute and solvent dissolve in the membrane, which is imagined as a dense, non-porous layer. The membrane also has a layer of bound water at the surface, due to its low dielectric constant. The solute and solvent have different solubility and diffusion coeffieients in the membrane, and rejection of solute depends on its ability to diffuse through structured water inside the membrane (Staude (1992)). All solutes diffuse independendy, driven by their chemical potential across the membrane. It is the same as the irreversible thermodynamics model for the case where no coupling occurs. This model has lost credibility in the past due to neglected membrane imperfections, membrane-solute interactions, and solute-molecule interactions (no convection, no external forces, no coupling of flow) (Braghetta (1995)). 

The solution-diffusion theory models the performance of the perfect membrane. In reality, industrial membranes are plagued with imperfections that some argue must be considered when developing a complete theory that models performance. The basis of the Diffusion Imperfection Model is the assumption that slight imperfections in the membrane occur... 

Interstitial diffusion is rarely possible when two metals interdiffuse, since their atomic radii are usually of the same order. Several mechanisms have been proposed, but it is now generally accepted that interdiffusion is due to the motion of vacant sites within the lattice, solvent and solute atoms moving as the vacant sites migrate. The diffusion process is thus dependent upon the state of imperfection of the solvent metal and the alloy being formed. 

Fluid motion acts to decrease the diffusion boundary layer thickness. Strategies of the microorganism to increase solute flux by decreasing its size or surface concentrations of the solute, c°, will be examined in Section 6. In this section, the solute concentration at the surface of the organism, c°, is assumed to be zero, i.e. the cell is a perfect absorber (sink), since this will provide an upper limit for the importance of fluid motion. It is clear that if fluid motion has no effect for a perfect absorber, it will have no effect for an imperfect one. 

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