Pervaporation solution diffusion model

Dense membranes are used for pervaporation, as for reverse osmosis, and the process can be described by a solution-diffusion model. That is, in an ideal case there is equilibrium at the membrane interfaces and diffusional transport of components through the bulk of the membrane. The activity of a component on the feed side of the membrane is proportional to the composition of that component in the feed solution. 

Reverse osmosis, pervaporation and polymeric gas separation membranes have a dense polymer layer with no visible pores, in which the separation occurs. These membranes show different transport rates for molecules as small as 2-5 A in diameter. The fluxes of permeants through these membranes are also much lower than through the microporous membranes. Transport is best described by the solution-diffusion model. The spaces between the polymer chains in these membranes are less than 5 A in diameter and so are within the normal range of thermal motion of the polymer chains that make up the membrane matrix. Molecules permeate the membrane through free volume elements between the polymer chains that are transient on the timescale of the diffusion processes occurring. 

The solution-diffusion model applies to reverse osmosis, pervaporation and gas permeation in polymer films. At first glance these processes appear to be very... 

In this section the solution-diffusion model is used to describe transport in dialysis, reverse osmosis, gas permeation and pervaporation membranes. The resulting equations, linking the driving forces of pressure and concentration with flow, are then shown to be consistent with experimental observations. 

Figure 2.12 Chemical potential, pressure, and activity profiles through a pervaporation membrane following the solution-diffusion model...

Sorption data were used to obtain values for A" L. As pointed out by Paul and Paciotti, the data in Figure 2.17 show that reverse osmosis and pervaporation obey one unique transport equation—Fick s law. In other words, transport follows the solution-diffusion model. The slope of the curve decreases at the higher concentration differences, that is, at smaller values for c,eimi because of decreases in the diffusion coefficient, as the swelling of the membrane decreases. 

The mass transport in pervaporation is can be described by the solution diffusion model, which explains the mechanism of transport by a process consisting of ... 

The commonly used mass transfer in pervaporation is the solution-diffusion model — a transfer occurs in three steps (Figure 21.13). 

FIGURE 9.3 Schematic representation of the pervaporation transport mechanism (a) solution-diffusion model and (b) pore flow model. 

Huang, J. Li, J. Jhan, X. Chen, C., A Modified Solution Diffusion Model and Its Application in the Pervaporization Separation of Alkane/Thiophenes Mixtures with PDMS Membrane. J. Appl. Polym. Sci. 2008,110, 3140-3148. 

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 ... 

Figure 3.11 Schematic of pervaporation transport mechanism (solution-diffusion model).

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. 

There are a number of other papers in which the pervaporation phenomena was discussed by the solution-diffusion model [157]-[169]. 

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. 

Fig. 19.3 The solution-diffusion transport model in pervaporation. a Solution of compounds from the feed phase into the membrane surface, b Diffusion across the membrane barrier, c Desorption from the membrane permeate (downstream) side into the permeate phase...

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. 

Because of the phase change associated with the process and the non-ideal liquid-phase solutions (i.e., organic/water), the modeling of pervaporation cannot be accomplished using a solution-diffusion approach. Wijmans and Baker [14] express the driving force for permeation in terms of a vapor partial pressure difference. Because pressures on the both sides of the membrane are low, the gas phase follows the ideal gas law. The liquid on the feed side of the membrane is generally non-ideal. 

The most widely accepted model for describing the transport mechanism through the pervaporation membrane is a modified solution-difiusion model, where a permeating component is first dissolved or adsorbed in the membrane and then transported through it by a diffusion process. In this process, separation of the mixture is achieved by differences in the solubility and diffusibility of the individual components. 

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