Solution-diffusion transport nonporous

The solution-diffusion transport model was originally described by Lonsdale et al. This model assumes that the membrane is nonporous (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. 

Solution—Diffusion Model. In the solution—diffusion model, it is assumed that (/) the RO membrane has a homogeneous, nonporous surface layer (2) both the solute and solvent dissolve in this layer and then each diffuses across it (J) solute and solvent diffusion is uncoupled and each is the result of the particular material s chemical potential gradient across the membrane and (4) the gradients are the result of concentration and pressure differences across the membrane (26,30). The driving force for water transport is primarily a result of the net transmembrane pressure difference and can be represented by equation 5 ... 

Most theoretical studies of osmosis and reverse osmosis have been carried out using macroscopic continuum hydrodynamics [5,8-13]. The models used include those that treat the wall as either nonporous or porous. In the nonporous models the membrane surface is assumed homogeneous and nonporous. Transport occurs by the molecules dissolving in the membrane phase and then diffusing through the membrane. Mass transfer across the membrane in these models is usually described using the solution-diffusion... 

In order to illustrate the effects of media structure on diffusive transport, several simple cases will be given here. These cases are also of interest for comparison to the more complex theories developed more recently and will help in illustrating the effects of media on electrophoresis. Consider the media shown in Figure 18, where a two-phase system contains uniform pores imbedded in a matrix of nonporous material. Solution of the one-dimensional point species continuity equation for transport in the pore, i.e., a phase, for the case where the external boundaries are at fixed concentration, Ci and Cn, gives an expression for total average flux... 

As seen, diffusion in nonporous gel membranes differs from that in macro-porous or microporous membranes. Various theories based on solute diffusion through the macromolecula r free volume in the membrane have been proposed. It is clear from these theories that structural parameters of the polymer network such as degree of swelling, molecular weight between crosslinks, and crystallinity in addition to factors such as solute size and solvent free volume play important roles in this type of transport. 

The most important characteristic of nonporous membranes is that they are hydrophobic and contain no pores in the polymeric structure. This means that these membranes not only selectively act as a barrier to particles and polar species, but they also provide unique selectivity and specificity for the permeation and transport of a specific group of compounds that can readily solubilize and diffuse in the membrane material. The analyte extraction rate (permeability) in a nonporous membrane separation process is governed by the solution-diffusion mechanism, as commented on earlier. 

The separation performance of membranes with nonporous barriers is - because of the transport via solution-diffusion (cf. Section 2.2) - predominantly influenced by the polymer material itself. Therefore, the material selection is directly related to the intrinsic (bulk) properties of the polymer, but - as for porous membranes - filmforming properties, mechanical and thermal stability form the basis of applicability (cf. Section 2.3.2.1). The following characteristics should be considered ... 

Transport models fall into three basic classifications models based on solution/diffusion of solvents (nonporous transport models), models based on irreversible thermodynamics, and models based on porous membranes. Highlights of some of these models are discussed below. 

In the latter case (nonporous membrane), the space in which the transport occurs is not fixed in size and location. The free volume is the volume that is not occupied by the polymer molecules in the solid phase, and its size and location fluctuate with time at a given temperature. Accordingly, the transport through such a membrane is completely different from the transport through fixed pores, and can be expressed by the solution-diffusion mechanism. The permeant is first dissolved in the membrane phase, and the dissolved permeant diffuses through the membrane following the chemical potential gradient. 

Reverse osmosis membranes are characterized by an MWCO of -100 Da, and the process involves transmembrane pressures (TMP) of 10-50 bar (1000-5000 kPa), which are 5-10 times higher than those used in UF [11,36]. Unlike UF, the separation by RO is achieved not by the size of the solute but due to a pressure-driven solution-diffusion process [36]. Like UF membranes, RO membranes are uniquely stmctured films from synthetic organic polymers and consist of an ultrathin skin layer superimposed on a coarsely porous matrix [3]. The skin layer of the RO membrane is nonporous, which may be treated as a water-swollen gel, and water is transported across membrane by dissolving in this gel and diffusing to the low-pressure side... 

Transport through nonporous membranes follows the solution-diffusion mechanism, and separation is achieved either by differences in solubility or diffusivity. Therefore,... 

POLYMER MEMBRANES. The transport of gases through dense (nonporous) polymer membranes occurs by a solution-diffusion mechanism. The gas dissolves in the polymer at the high-pressure side of the membranes, diffuses through the polymer phase, and desorbs or evaporates at the low-pressure side. The rate of mass transfer depends on the concentration gradient in the membrane, which is proportional to the pressure gradient across the membrane if the solubility is proportional to the pressure. Typical gradients for a binary mixture are shown in Fig. 26.2. Henry s law is assumed to apply for each gas, and equilibrium is assumed... 

According to Cuperus and Nijhuis [5], the mechanisms in which NF membrane works are not completely clear. Possibly both size exclusion and solution-diffusion mechanisms play a role. This is in agreement with the work of Subramanian et al. [29]. These authors observed that solution-diffusion is the predontinant mechanism of the transport of vegetable oil constituents through nonporous (dense) membranes. The effect of viscosity (temperature) on permeation suggests that transport by convective flow exists in these membranes but the extent observed is not significant. 

Solution-diffusion model is the generally accepted mechanism of mass transport through nonporous membranes (Figure 9.3). According to this mechanism, PV consists of three consecutive steps ... 

Gas transport in nonporous polymer membranes typically proceeds by a solution-diffusion mechanism in which the permeability (P) is given by. xD, where S and D denote the solubility and diffusivity of the permeating species, respectively. The solubility provides a measure of interaction between the polymer matrix and penetrant molecules, whereas the diffusivity describes molecule mobility, which is normally governed by the size of the penetrant molecule as it winds its way through the permanent and transient voids afforded by the free volume of the membrane [42], Therefore gas transport has to be strongly dependent on the amount of free volume in the polymer matrix. 

Nonporous membranes are used to perform separations on a molecular level. However, rather than molecular weight or molecular size, the chemical nature and morphology of the polymeric membrane and the extent of interaction between the polymer and the permeants are the important factors to consider. Transport through nonporous membranes occurs by a solution-diffusion mechanism and separation is achieved ei er by differences in solubility and/or diffusivity. Hence such membranes cannot be characterised by the methods described in the previous section, where the techniques involved mainly characterised the pore size and pore size distribution in the membranes. The determination of the physical properties related to the chemical structure is now more important and in this respect the following methods will be described ... 

Basically, the transport of a gas, vapour or liquid through a dense, nonporous membrane can be described in terms of a solution-diffusion mechanism, i.e. 

The last part of.Ais chapter will be devoted to a comparison of meiribr c processes v where transport occurs through nonporous membranes. A solution-diffusion model will be used where each component dissolves into the membrane and diffuses through the membrane independently [41]. A similar approach was recently followed by Wijmans[43]. As a result, simple equations will be obtained for the component fluxes involved in the various processes which allows to compare the processes in terms of transport parameters. 

Small molecule transport through nonporous polymers proceeds by the solution-diffusion mechanism. This a three-step mechanism where penetrant molecules... 

Since the scope of this article is limited to transport in dense, nonporous pol5nners, the rest of this discussion is hmited to transport where a solution-diffusion mechanism is assumed to occur. In this regime, the flux of A is given by (175)... 

The possibility of gas transport through nonporous polymeric membranes is one of the basic phenomena of polymer materials [1]. It is based on solution-diffusion concept. It means that the presence of mieroseopie open pores or capillaries is not necessary for mass transfer through polymerie films. On the other hand, closed porosity or the presence of free-volume elements within a polymer matrix is required for gas permeation in the polymers considered for use as materials for gas separation membranes. 

The mechanism of separation by non-porous membranes is different from that by porous membranes. The transport through nonporous polymeric membranes is usually described by a solution-diffusion mechanism (Figure 9.12a). The most current commercial polymeric membranes operate according to the solution-diffusion mechanism. The solution-diffusion mechanism has three steps (1) the absorption or adsorption at the... 

Equation 2 is an analytical statement of the solution-diffusion mqdel of penetrant transport in polymers, which is the most widely accepted explanation of the mechanism of gas permeation in nonporous polymers (75). According to this model, penetrants first dissolve into the upstream (i.e, high pressure) face of Ae film, diffuse through the film, and desorb at the downstream (Le. low pressure) face of the film. Diffusion, the second step, is the rate limiting process in penetrant permeation. As a result, much of the fundamental research related to the development of polymers with improved gas separation properties focuses on manipulation of penetrant diffusion coefficients via systematic modification of polymer chemical structure or superstructure and either chemical or thermal post-treatment of polymer membranes. Many of the fundamental studies recorded in this book describe the results of research projects to explore the linkage between polymer structure, processing history, and small molecule transport properties. 

Gas transport through nonporous inorganic membranes falls into two categories. It is known that the conventional solution-diffusion permeation mechanism is valid for nonporous membranes of silica, zeolite and inorganic salts. It is no longer so when the membrane is metallic in nature (Hwang and Kammermeyer, 1975). Diatomic gases such as O2, H2 and N2 dissolve atomically in the metallic membrane (see (3.3.67)). While a conventional flux expression is valid for atomic species i dissolved in the membrane, Le. 

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