Solution-diffusion transport

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

We may conclude that our findings support independent water and salt permeation processes, and suggest that the salt permeation is governed by a solution-diffusion transport mechanism. 

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...

Figure 2.5 Pressure driven permeation of a one-component solution through a membrane according to the solution-diffusion transport model...

Salt and water permeate reverse osmosis membranes according to the solution-diffusion transport mechanism are described in Chapter 2. The water flux,. /, is linked to the pressure and concentration gradients across the membrane by the equation... 

H. 1965 - Solution-Diffusion transport model described by Lonsdale, et. al (See Chapter 4.1.1)... 

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. 

Nanofiltration (NF) and RO are closely related in that both share the same composite membrane structure and are generally used to remove ions from solution. However, NF membranes use both size and charge of the ion to remove it from solution whereas RO membranes rely only on "solution-diffusion" transport to affect a separation (see Chapters 16.2 and 4.1, respectively). Nanofiltration membranes have pore sizes ranging from about 0.001 to 0.01 microns, and therefore,... 

The model describes the total flux of the gas target species to be facihtate transported, i, (see Table 7.2) with respect to gas species,J, as the sum of the ordinary solution-diffusion transport through the noncomplexing solvent phase (i) and facihtated transport mediated by the carrier (2). Assuming a partial pressure of the target species, / , to equal zero on the permeate side, one can write the fluxes for each of the transport modes as ... 

Solution-diffusion transport mechanism When the feed contacts the membrane, the solutes (denoted i in Fig. 3.6-10) adsorb on and subsequently absorb in the membrane surface by solute-polymer interactions (Fig. 3.6-lOA). Preferential solute-polymer interactions imply that the solvating power of the polymer is higher for the solutes than for the bulk solvent. 

Then Uemiya et al. [2] reported another Pd membrane reactor for WGS reaction using Fe-Cr oxide catalysts. The model of flow in the palladium membrane reactor is illustrated in Figure 6.3. They proposed that hydrogen is permeated through palladium membrane via a solution diffusion transport mechanism, and the rate of hydrogen permeation, /, per unit area of membrane, is written in terms of Fick s first law as follows ... 

Freeman [40] demonstrates that solution-diffusion transport theory predicts the existence of an upper bound if diffusion is an activated process, the activation energy depends linearly on the square of the molecular diameter, and solubility depends exponentially on the Lennard-Jones temperature. Although one adjustable parameter is introduced to specify the dependence of activation energy on molecular size, a single value gives excellent predictions of the location of the upper bound for all gas pairs examined. 

The membranes used in GS can be distinguished in two main categories, polymeric and inorganic. Polymeric membranes, specifically used for GS, are generally asymmetric or composite and based on a solution-diffusion transport mechanism. These membranes, made as flat sheet or hollow fibres, have a thin, dense skin layer on a micro-porous support that provides mechanical strength [7]. Typically, polymeric membranes show high, but finite, selectivities with respect to porous inorganic materials due to their low free-volume... 

Penetrant sorption has three impacts on small-molecule permeability. A direct impact is the proportionality between permeability P and solubility in solution-diffusion transport [1,154]... 

In the case of non-facilitated transport, solutes are transported from the feed to the strip phase by the following steps (i) diffusion in the boundary layer on the feed side from the bulk of the feed solution to the feed-LM interface (ii) solubilization (capture) in the organic phase at the feed-LM interface (in) diffusion across the LM under the action of the concentration gradient (iv) solubilization (release) in the receiving strip phase at the LM-strip interface and (v) diffusion in the boundary layer on the strip side from the LM-strip interface to the bulk of the receiving phase. Based on this, non-facilitated transport can be indicated simply as solution-diffusion transport. The efficiencies of solubilization steps are determined by the partition coefficient while the diffusion is by the diffusivities of the solutes in the organic phase. A not very selective separation... 

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