Differential permeation, with permeate

Table A6.1 Excel Spreadsheet Designators and Formulas for Differential Permeation with Permeate Flow Calculations ...

Table A6.2 Differential Permeation with Permeate Flow... 

The most usual problem encountered is that of determining the degree of separation for a single-stage embodiment, which can certainly be complicated. The extension to multistage and differential permeation operations will only be alluded to, with referral made to Hoffman (2003). 

The use of differential permeation in countercurrent flow with recycle is developed in Chapter 7 and Appendix 7 of Hoffman (2003). 

As can be expected, the derivations and calculations become increasingly complicated for multistage and differential permeation. The subject is detailed in the later pages of Hoffman (2003), with examples provided, including systematic spreadsheet calculations. 

Size-exclusion chromatography (SEC) is a method in which molecules are separated by size due to differential permeation into a porous support. It requires complete solubility of the analytes in the mobile phase and elimination of all interactions with the bonded phase. In these respects, SEC is not as useful for the separation of peptides as it is for proteins because peptides vary drastically in solubility, charge, and hydrophobicity. Peak capacity in SEC is fairly low compared to other HPLC methods because all separations must occur in the internal volume (Vi) of the support, which is generally less than half the volume of mobile phase in the column. Despite these deficiencies, SEC can be very effective for separating peptides from dimers, aggregates, small molecules, proteins, and other molecules which differ by size. 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

Gel permeation chromatography. A method of separating molecules by size, usually carried out on columns that are tightly packed with gel and completely filled with solvent. Differential permeation into the gel pores... 

Molar flow rates f are the variable rates inside the separator, with subscripts P andf designating, respectively, the permeate side and residue side of the membrane. A material balance around the differential volume is written for component i. The component differential permeate rate equals the differential change in the component residue rate ... 

Of special consideration is the investigation of the cell as a continuum, first with point withdrawal of the permeate, then in both concurrent and countercurrent flow for the permeate and the reject phases. For this treatment, differential permeation is the mode of attack. The differential... 

Differential Permeation with Point Permeate Withdrawal... 

In differential permeation, the point compositions of the phases are considered to vary linearly with position along the surface(s) of the membrane. A steady state is assumed, so that the compositions are independent of time. 

Figure 5.1 Differential permeation with point permeate withdrawal.

By analogy with Section 5.6 of Chapter 5, for differential permeation with point permeate withdrawal, the equation to be integrated is... 

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