Selectivity solution-diffusion model

Good quality RO membranes can reject >95-99% of the NaCl from aqueous feed streams (Baker, Cussler, Eykamp et al., 1991 Scott, 1981). The morphologies of these membranes are typically asymmetric with a thin highly selective polymer layer on top of an open support structure. Two rather different approaches have been used to describe the transport processes in such membranes the solution-diffusion (Merten, 1966) and surface force capillary flow model (Matsuura and Sourirajan, 1981). In the solution-diffusion model, the solute moves within the essentially homogeneously solvent swollen polymer matrix. The solute has a mobility that is dependent upon the free volume of the solvent, solute, and polymer. In the capillary pore diffusion model, it is assumed that separation occurs due to surface and fluid transport phenomena within an actual nanopore. The pore surface is seen as promoting preferential sorption of the solvent and repulsion of the solutes. The model envisions a more or less pure solvent layer on the pore walls that is forced through the membrane capillary pores under pressure. 

Neglecting convection effects, the solution-diffusion model gives the following expressions for water (1) and salt (2) molar fluxes through a membrane with a selective layer thickness of L and a transmembrane pressure drop Ap (Merten, 1966) ... 

Kimura and Sourirajan have offered a theory of preferential adsorption of materials at interfaces to describe liquid phase, selective transport processes in portms membranes. Lonsdale et al. have ofiered a simpler explanation of the transport behavior of asymmetric membranes which lack significant porosity in the dense surface layer. Their solution-diffusion model seems to adequately describe the cases for liquid transport considered to date. Similarly gas transport should be de-scribable in terms of a solution-diffusion model in cases where the thin dense membrane skin acts as the transport moderating element. 

Since the solubility of various gases in ILs varies widely, they may be uniquely suited for use as solvents for gas separations [97]. Since they are non-volatile, they cannot evaporate to cause contamination of the gas stream. This is important when selective solvents are used in conventional absorbers, or when they are used in supported liquid membranes. For conventional absorbers, the ability to separate one gas from another depends entirely on the relative solubilities (ratio of Henry s law constants) of the gases. In addition, ILs are particularly promising for supported liquid membranes because they have the potential to be incredibly stable. Supported liquid membranes that incorporate conventional liquids eventually deteriorate because the liquid slowly evaporates. Moreover, this finite evaporation rate limits how thin one can make the membrane. This means that the net flux through the membrane is decreased. These problems could be eliminated with a non-volatile liquid. In the absence of facilitated transport (e.g., complexation of CO2 with amines to form carbamates), the permeability of gases through supported liquid membranes depends on both their solubility and diffusivity. The flux of one gas relative to the other can be estimated using a simplified solution-diffusion model ... 

This simple equation gives the maximum possible enrichment of one gas of a two-component mixture when separated by a membrane with a selectivity of a. The equation becomes more complex when the permeate pressure cannot be neglected [320]. Following the simple solution-diffusion model the gas fluxes for gas 1 and 2 through the membrane are... 

Usually the mathematical description of the process is expressed by a solution-diffusion model, which could take into account some non-linear phenomena for both the sorption and the diffusion steps. Anomalous behaviours are frequently observed and are typical for polymers, which very often constitute the material of the selective layer of the membrane. Swelling, which accompanies the sorption of chemicals into polymers, is just one of the most important non-linear phenomena. Due to the presence of the per-meants in the membrane, swelling is not uniform and produces non-linear gradients of permeant concentration inside the membrane. 

Solution-diffusion model In the solution-diffusion model, permeates dissolve in the membrane material and then diffuse through the membrane down a concentration gradient. Separation is achieved between different permeates because of differences in the amount of material that dissolves in the membrane and the rate at which the material diffuses through the membrane. The solution-diffusion model is the most widely accepted transport mechanism for many membrane processes [209,210]. Selectivity and permeability of a pervaporation membrane mainly depend on the first two steps, that is, the solubility and diffusivity of the components in the membrane. According to this model, mass transport can be divided into the three steps the mechanism is shown in Fig. 3.11 ... 

Pervaporation is used to separate the liquid mixture. A phase transition occurs at the phase boundary on the permeate side, allowing desorption by vaporization. According to the solution-diffusion model, selectivity is primarily achieved because not all components in the mixture of substances can be dissolved equally well in the membrane material. Pervaporation involves a second selectivity step as a result of the required vaporization of the permeating components. For this, the partial pressure on the permeate side of the components must be lower than the saturated steam pressure. If only some of the components dissolved by the membrane boil at the operating point, the remainder of the components are not desorbed. 

Pervaporation (PV) is a membrane-based process used to separate the components of a liquid mixture. It requires dense membranes. The liquid feed is heated up and placed in contact with the active layer, whereas a vacuum or a sweep gas is applied downstream. The driving force is a chemical potential gradient through the membrane cross section. The separation phenomenon is explained according to the solution-diffusion model. The selective separation depends on the different dissolution of feed molecules into the membrane matrix and their diffusivity. 

Figure 1. Comparison of conditions imposed for the sensing of trace metal by (a) an ion-selective electrode, (h) a mercury film asv electrode, and (c) the model cell. In each case the system is divided into four zones bulk solution, diffusion layer of thickness (B), cell/electrode surface, and cell/electrode interior.

In the case of selective neutrality—this means that all variants have the same selective values—evolution can be modeled successfully by diffusion models. This approach is based on the analysis of partial differential equations that describe free diffusion in a continuous model of the sequence space. The results obtained thereby and their consequences for molecular evolution were recently reviewed by Kimura [2]. Differences in selective values were found to be prohibitive, at least until now, for an exact solution of the diffusion approach. Needless to say, no exact results are available for value landscapes as complicated as those discussed in Section IV.3. Approximations are available for special cases only. In particular, the assumption of rare mutations has to be made almost in every case, and this contradicts the strategy basic to the quasi-species model. 

Selective separation of hquids by pervaporation is a result of selective sorption and diffusion of a component through the membrane. PV process differs from other membrane processes in the fact that there is a phase change of the permeating molecules on the downstream face of the membrane. PV mechanism can be described by the solution-diffusion mechanism proposed by Binning et al. [3]. According to this model, selective sorption of the component of a hquid mixture takes place at the upstream face of the membrane followed by diffusion through the membrane and desorption on the permeate side. 

After asserting the nanostructured nature of ionic liquids, the structural analysis of these fluids continued in two different directions. The first was to check how the built-in flexibility of the isolated ions of the model affect (or are affected by) the nanostructured nature of the ionic liquid, and how that can influence properties like viscosity, electrical conductivity, or diffusion coefficients. It must be stressed that the charges in the CLAP model are fixed to the atomic positions, which means that the most obvious way to probe the relation between the structure of the ionic liquid as a whole in terms of the structure of its individual ions is to investigate the flexibility (conformational landscape) of the latter. The second alternative direction was to probe the structure of ionic liquids not by regarding into the structure of the component ions but by instead using an external probe (for example, a neutral molecular species), solubility experiments with selected solute molecules being the most obvious experimental approach. 

The results obtained with the solid film linear driving force model, the pore diffusion model, and the micropore diffusion model were compared by Ruthven [14]. In contrast to linear chromatography, numerical solutions obtained with different models are different, especially in the initial time region. For moderate loadings i.e., for Req > 0-5), the differences remain small. As the loading increases, however, and Req becomes lower than 0.5, the differences between the numerical solutions derived from the various models studied increase. Accordingly, differences observed between experimental results and the profiles predicted by a kinetic model are most often due to the selection of a somewhat inappropriate model. 

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