Multicomponent Drop

A droplet 5 mm in diameter containing a mixture of acetone(l)-benzene(2)-methanol(3) is 

SOLUTION For the purposes of this calculation we shall assume the drop to be noncirculating. Thus, the matrix of multicomponent mass transfer coefficients [A] may be computed from Eqs. 9.4.18 and 9.4.19 with the help of Sylvester s expansion formula or the modal transformation. At both the long and short contact time limits, however, we may calculate the ratios of mass transfer coefficients ky2/kii and A 21/A 22 without evaluating the series expansions needed in Eq. 9.4.19. 

For short contact times, [A] is proportional to which may be computed using 

Sylvester s expansion formula, or by the modal transformation method. Both methods require the eigenvalues of [D], which are 

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The creatmenc of the boundary conditions given here ts a generali2a-tion to multicomponent mixtures of a result originally obtained for a binary mixture by Kramers and Kistecnaker (25].These authors also obtained results equivalent to the binary special case of our equations (4.21) and (4.25), and integrated their equations to calculate the p.ressure drop which accompanies equimolar counterdiffusion in a capillary. Their results, and the important accompanying experimental measurements, will be discussed in Chapter 6 ... 

In real-life appHcations, many other failure mechanisms are present and this type of curve is not necessarily obtained. For example, in a multicomponents system the quaUty related failures do not necessarily all drop out early but might be phased out over a longer period of time. 

The shape of the coohng and warming curves in coiled-tube heat exchangers is affected by the pressure drop in both the tube and shell-sides of the heat exchanger. This is particularly important for two-phase flows of multicomponent systems. For example, an increase in pressure drop on the shellside causes boiling to occur at a higher temperature, while an increase in pressure drop on the tubeside will cause condensation to occur at a lower temperature. The net result is both a decrease in the effective temperature difference between the two streams and a requirement for additional heat transfer area to compensate for these losses. 

The mercury film electrode has a higher surface-to-volume ratio than the hanging mercury drop electrode and consequently offers a more efficient preconcentration and higher sensitivity (equations 3-22 through 3-25). hi addition, the total exhaustion of thin mercury films results in sharper peaks and hence unproved peak resolution in multicomponent analysis (Figure 3-14). 

The most widely studied deformable systems are emulsions. These can come in many forms, with oil in water (O/W) and water in oil (W/O) the most commonly encountered. However, there are multiple emulsions where oil or water droplets become trapped inside another drop such that they are W/O/W or O/W/O. Silicone oils can become incompatible at certain molecular weights and with different chemical substitutions and this can lead to oil in oil emulsions O/O. At high concentrations, typical of some pharmaceutical creams, cosmetics and foodstuffs the droplets are in contact and deform. Volume fractions in excess of 0.90 can be achieved. The drops are separated by thin surfactant films. Selfbodied systems are multicomponent systems in which the dispersion is a mixture of droplets and precipitated organic species such as a long chain alcohol. The solids can form part of the stabilising layer - these are called Pickering emulsions. 

Certain SEC applications solicit specific experimental conditions. The most common reason is the limited sample solubility. In this case, special solvents or increased temperature are inavoid-able. A possibility to improve sample solubility and quality of eluent offer multicomponent solvents (Sections 16.2.2 and 16.8.2). The selectivity of polymer separation by SEC drops with the deteriorating eluent quality due to decreasing differences in the hydrodynamic volume of macromolecules with different molar masses. The system peaks appear on the chromatograms obtained with mixed eluents due to preferential solvation of sample molecules (Sections 16.3.2 and 16.3.3). The multicomponent eluents may create system peaks also as a result of the (preferential) sorption of their components within column packing [144,145]. The extent of preferential sorption is often sensitive toward pressure variations [69,70,146-149]. Even if the specific detectors are used, which do not see the eluent composition changes, it is necessary to discriminate the bulk sample solvent from the SEC separated macromolecules otherwise the determined molecular characteristics can be affected. This is especially important if the analyzed polymer contains a tail of fractions possessing lower molar masses (Sections 16.4.4 and 16.4.5). 

The tray temperatures in our preflash tower, shown in Fig. 4.4, drop as the gas flows up the tower. Most of the reduced sensible-heat content of the flowing gas is converted to latent heat of evaporation of the downflowing reflux. This means that the liquid flow, or internal reflux rate, decreases as the liquid flows down the column. The greater the temperature drop per tray, the greater the evaporation of internal reflux. It is not unusual for 80 to 90 percent of the reflux to evaporate between the top and bottom trays in the absorption section of many towers. We say that the lower trays, in the absorption section of such a tower, are drying out. The separation efficiency of trays operating with extremely low liquid flows over their weirs will be very low. This problem is commonly encountered for towers with low reflux ratios, and a multicomponent overhead product composition. 

Experimental studies were carried out to derive correlations for mass transfer coefficients, reaction kinetics, liquid holdup, and pressure drop for the packing MULTIPAK (35). Suitable correlations for ROMBOPAK 6M are taken from Refs. 90 and 196. The nonideal thermodynamic behavior of the investigated multicomponent system was described by the NRTL model for activity coefficients concerning nonidealities caused by the dimerisation (see Ref. 72). 

The second subject is the effect of the surface on the chemical potential of a component contained in a small drop. We consider a multicomponent system in which one phase is a bulk phase and the second phase is kept constant with the conditions that the interface between the two phases is contained wholly within the bulk phase and does not affect the external pressure. The differential of the Gibbs energy of a two-phase system may be written as... 

Reactive absorption processes present essentially a combination of transport phenomena and reactions taking place in a two-phase system with an interface. Because of their multicomponent nature, reactive absorption processes are affected by a complex thermodynamic and diffusional coupling which, in turn, is accompanied by simultaneous chemical reactions [14—16], Generally, the reaction has to be considered both in the bulk and in the film region. Modeling of hydrodynamics in gas-liquid contactors includes an appropriate description of axial dispersion, liquid hold-up and pressure drop. 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

Many industrial columns use temperatures for composition control because direct composition analyzers can be expensive and unreliable. Although temperature is uniquely related to composition only in a binary system (at known pressure), it is still often possible to use the temperatures on various trays up and down the column to maintain approximate composition control, even in multicomponent systems. Probably 75 percent of all distillation columns use temperature control of some tray to hold the composition profile in the column. This prevents the light-key (LK) impurities from dropping out the bottom and the heavy-key (HK) impurities from going overhead. 

Sulfacetamide, A benzoyl sulfanilamide and sulfathiazole have been determined in pharmaceutical preparations by measuring absorbance of the mixture in 0.1 N hydrochloric acid at 220,235 and 280 nm respectively (42). Madsen et al. (43,44) have performed computer analysis of the multicomponent UV spectra of sulfonamides. The errors in concentration determined from the spectra between 240 and 272 nm are lower when the spectra are analysed by a linear-squares method considering the data over the whole wavelength range compared with the determination using the data at a single wave length. The method has been applied to the assay of sulfacetamide sodium eye-drops. 

The equations (3.109), (3.117) or (3.118) and (3.120) for the velocity, thermal and concentration boundary layers show some noticeable similarities. On the left hand side they contain convective terms , which describe the momentum, heat or mass exchange by convection, whilst on the right hand side a diffusive term for the momentum, heat and mass exchange exists. In addition to this the energy equation for multicomponent mixtures (3.118) and the component continuity equation (3.25) also contain terms for the influence of chemical reactions. The remaining expressions for pressure drop in the momentum equation and mass transport in the energy equation for multicomponent mixtures cannot be compared with each other because they describe two completely different physical phenomena. 

A particularly simple and frequently used method comes from Lockhart and Martinelli [4.84], It is based on measurements of air-water and air-oil mixtures in horizontal tubes at low pressure. However the procedure has also proved itself in upward, vertical flow of two-phase single and multicomponent mixtures. The basic idea of the Lockhart-Martinelli method is that the frictional pressure drop in a two-phase flow can be determined, with use of a correction factor, from the frictional pressure drop in the individual phases. This means that the two-phase multipliers and are defined according to (4.127) and (4.128). 

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