Transfer Units for Multicomponent Systems

The composition of the vapor along the length may be determined by integrating (numerically) Eq. 12.3.47. Each step of the integration requires the estimation of the matrix of overall number of transfer units. 

If we use the simplified models discussed in Section 8.8 for the matrices of mass transfer coeflicients we may relate the inverse matrices of numbers of transfer units to the matrices of inverse binary mass transfer coefficients as (cf. Eqs. 12.2.20 and 12.2.21) 

For multicomponent systems it is possible to define matrices of HTU values. Thus, for the vapor phase 

To evaluate the matrices of heights or numbers of transfer units we may use the empirical methods of Section 12.3.3 to estimate the binary (Maxwell-Stefan) mass transfer coefficients as functions of the Maxwell-Stefan diffusion coefficients. The elements of the [A] matrices may then be computed with the aid of Eqs. 12.2.17 and 12.2.18 as illustrated in Example 12.3.3. 

Experimental studies carried out with a view to testing these models have been reported by Dribicka and Sandall (1979), by Gorak and co-workers (1983, 1985, 1987, 1988, 1990, 1991), by Krishna et al. (1981), and by Arwickar (1981). All of these groups assumed equimolar overflow in the analysis of their data. There are additional differences between the equations integrated by these groups that the interested reader can discern for themselves. 

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The numbers of transfer units for each binary pair may be obtained as described in Section 12.1.5 or from experimental data and these binary numbers of transfer units used directly in the estimation of the matrices of numbers of transfer units for multicomponent systems as Example 12.2.3 demonstrates. 

Correlations of numbers of transfer units developed for binary systems may be used to compute numbers of transfer units for multicomponent systems as described in Section 12.1.5. An alternative method that follows the ideas put forward by Toor in his development of the linearized theory of mass transfer is to generalize binary correlations by replacing the binary diffusivity with the matrix of Fick diffusion coefficients (in much the same way that we generalized correlations of binary mass transfer coefficients in Section 8.8.2). Let the number of transfer units in a binary system be expressed as... 

V" kg Gas-phase mass transfer coefficient for multicomponent systems, same units as Icg... 

In order to determine the packed height it is necessary to obtain a value of the overall number of transfer units methods for doing this are available for binary systems in any standard text covering distillation (73) and, in a more complex way, for multicomponent systems (81). However, it is simpler to calculate the number of required theoretical stages and make the conversion ... 

The transfer unit approach permits consideration of varying vapor and liquid flows, varying properties, and differences in packing geometry. However, computation of transfer units, especially for multicomponent systems, is not straightforward. Instead, a hybrid approach can be used ... 

For a bineiy distillation system of components A and B, NV n = Nv,b and N0 iA = For multicomponent systems, it is possible for each component to have a different value of die transfer unit. For a discussion of die majticomponent problem, see Krishnamuithy and Taylor. The usual practice is to deni with the multicomponent mixture as if a staged columa were to be used and then convert from theoretical stages to transfer units by die relationships... 

For multicomponent systems, q may be defined on the basis of a unit mass of any of the streams. To wit, if Q is total heat transfer, the thermal absorption per unit mass of A and B becomes... 

A variety of other porphyrin-quinone-based multicomponent systems bearing four or more donor and acceptor moieties have been reported. For example, P-P-P-Q tetrad 53 and related compounds have been reported by Sessler and coworkers [64, 65, 73, 220, 232-236]. Fluorescence and time-resolved absorption experiments with 53 were interpreted in terms of rapid ( 10-ps) singlet-singlet energy transfer between the porphyrin units in the linear array and extremely fast (<350-fs) photo-induced electron transfer to the quinone from the proximal porphyrin excited singlet state to give a charge-separated species. 

Fig. 10.5 The basis of an OFF/ON redox switch of fluorescence. Either an energy transfer (FT) or an electron transfer (cT) mechanism can be responsible for the quenching of the light emitting fragment fluorophore (FI ) in a multicomponent redox unit-spacer-fluorophore system. Switch efficiency requires that the control unit C in its oxidized form, quenches the proximate photo-excited fluorophore FI and the reduced form does not (OFF/ON switch). The other favorable on/off situation can be obtained when quenches FI and does not (Reprinted with permission from Bergonzi et al. 1998, Copyright 1998 Elsevier)...

Engineering systems mainly involve a single-phase multicomponent fluid mixture with fluid friction, heat transfer, mass transfer, and a number of chemical reactions. A local thermodynamic state of the fluid is specified by two intensive parameters, for example, velocity of the fluid and the chemical composition in terms of component mass fractions. For a unique description of the system, balance equations must be derived for the mass, momentum, energy, and entropy. The balance equations, considered on a per unit volume basis. 

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