Descriptions of separation

M. Williams, "Measurement and Mathematical Description of Separation Characteristics of Ha2ardous Organic Compounds with Reverse Osmosis Membranes," dissertation. University of Kentucky, Lexiagton, Ky., 1993. 

Irreversible processes are mainly appHed for the separation of heavy stable isotopes, where the separation factors of the more reversible methods, eg, distillation, absorption, or chemical exchange, are so low that the diffusion separation methods become economically more attractive. Although appHcation of these processes is presented in terms of isotope separation, the results are equally vaUd for the description of separation processes for any ideal mixture of very similar constituents such as close-cut petroleum fractions, members of a homologous series of organic compounds, isomeric chemical compounds, or biological materials. 

A number of ACE assays dealing with the characterization of interactions between cyclodextrines as auxiliary substances and drugs have been presented. Other authors put more emphasis on the description of separation phenomenona by determination of binding constants. Model substances such as phenols are often used to examine the influence of ligand size and substitution as well as to evaluate the mathematical approaches for the calculation of binding constants. 

The coverage of separation techniques in many important textbooks in chemical analysis is largely limited to chromatography (e.g., refs. 9, 12, 13). While chromatography is of central importance in analysis, the omission of modern electrophoretic (both gel and capillary) and field-flow fractionation techniques leaves a large void in the description of separative capabilities, particularly in the biochemical and macromolecular realm. 

An open system is one which can undergo all the changes allowed for a closed system and in addition it can lose and gain matter across its boundaries. An open system might be one phase in an extraction system, or it might be a small-volume element in an electrophoretic channel. Such systems, which allow for the transport of matter both in and out, are key elements in the description of separation processes. 

The molecular bulkiness de.scriptors may be related to the ability of an analyte to take pan in nonspecific intermolecular interactions (dispersive interactions or London interactions) with the components of a chromatographic system. These descriptors are the most often found to be significant in QSRR analysis. The bulkiness parameters are decisive in the description of separations of closely congeneric analytes. For example, carbon number normally suffices to differentiate the members of homologous series. On... 

In some cases it is not necessary to use a columm for isolation purposes hence affinity chromatography is also carried out with membranes or disks.Classical columns with a hydrostatic eluent feed offer a further possibility. This chapter, however, is conhned to a description of separations with high-performance stationary phases (10 pm and below) with which rapid chromatography can be achieved. Very small columns may be used. 

Figure 7.1 Migration across a stationary phase packing. Left, illustrative description of separation in SEC by a porous packing according to the size of the pores. The non porous part of the bead, called the backbone, is inaccessible to the sample molecules. Right, a chromatogram displaying the separation of three species (1, 2, 3) of different sizes. The large molecules (excluded) 1 are the first to arrive followed hy medium sised molecules (partial access) 2, and finally by the smallest (full access) 3. The elution volumes are located between Vj for ATsec = 0 and Vm for K ec = ...

Included also in this chapter is a qualitative description of separations based on intraphase mass transfer (dialysis, permeation, electrodialysis, etc.) and discussions of the physical property criteria on which the choice of separation operations rests, the economic factors pertinent to equipment design, and an introduction to the synthesis of process flowsheets. 

FLUENT provides the volume of fluid model (VOF) for the description of separated multiphase flows. The VOF model is based on the resolution of the phase interface in a fixed Eulerian mesh. The conservation equations here are not solved separately for the individual phases but rather for the entire calculation domain with material properties averaged across the phases. For this purpose, an additional conservation equation is introduced for the volume fraction f in the continuous phase. A cell contains either the dispersed phase only f = 0), the continuous phase only f = 1), or the phase interface (0 < / < 1). In order to avoid blurring... 

A classification of some separation processes in terms of the physical or chemical properties of the components to be separated is given in table 1.1. This table is far from complete and a more detailed description of separation processes can be found in a number of excellent textbooks (see e.g.[3]). 

Chapter 2 presents the description of quantities needed to quantify separation in open systems with flow(s) in and out of single-entry and double-entry separators for binary, multi-component and continuous cheimcal mixtmes, as well as a size-distributed particle populatioiL Separation indices useful for describing separation in open systems with or without recycle or reflux are illustrated for steady state operation (Sections 2.2 and 2.3) those for a particle population are provided in Section 2.4. At the end (Section 2.5), indices for description of separation in time-dependent systems, e.g. chromatography, have been introduced. 

Separation is a major activity of chemical engineers and chemists. To separate a mixture of two or more substances, various operations called separation processes are utilized. Before we understand how a mhmire can he separated using a given separation process, we should he able to describe the amount of separation obtained in any given operation. This chapter and Chapter 2 therefore deal with qualitative and quantitative descriptions of separation. Chapter 2 covers open systems this chapter describes separations in a closed system. 

In Section 1.1, we briefly Illustrate the meaning of separation between two regions for a system of two components in a closed vessel. Section 1.2 extends this to a multicomponent system. In Section 1.3, various definitions of compositions and concentrations are given for a two-component system. In Section 1.4, we are concerned with describing the various indices of separation and their interrelationships for a two-region, two-component separation system. A number of such indices are compared with regard to their capacity to describe separation in Section 1.5 for a binary system. Next, Section 1.6 briefly considers the definitions of compositions and indices of separation for the description of separation in a multicomponent system between two regions in a closed vessel. Finally, Section 1.7 briefly describes some terms that are frequently encountered. 

Description of separation Condition 1 Condition 2 Condition 3 Condition 4 ... 

In Section 1.2, we introduced a brief description of separation for multicomponent systems. Although we learnt there that perfect separation in such a system requires as many regions as there are components, we will restrict ourselves here to separation systems with only two regions in a closed vessel. Thus perfect separation is, in general, ruled out from our considerations. 

For a qualitative description of separation of a single multicomponent feed mixture of n species into k product regions or fractions, Lee etal. (1977a) have defined a relative molar fraction of species i in product regionj by ny = Xij/Xif, where each of the mole fractions refer to its averaged value in a given region. Further, rj is defined as... 

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