Kinetics of mass transfer

All these processes are, in common, liquid-gas mass-transfer operations and thus require similar treatment from the aspects of phase equilibrium and kinetics of mass transfer. The fluid-dynamic analysis ofthe eqmpment utihzed for the transfer also is similar for many types of liquid-gas process systems. 

The efficiency of extraction is mainly dependent on temperature as it influences physical properties of the sample and its interaction with the liquid phase. The extraction is influenced by the surface tension of the solvent and its penetration into the sample (i.e. its viscosity) and by the diffusion rate and solubility of the analytes all parameters that are normally improved by a temperature increase. High temperature increases the rate of extraction. Lou et al. [122] studied the kinetics of mass transfer in PFE of polymeric samples considering that the extraction process in PFE consists of three steps ... 

Steps (i) and (ii) are controlled by molecular diffusion. Higher operating temperatures can improve the kinetics of mass transfer in all three steps. Vandenburg et al. [37] described the kinetics of PFE extraction using the hot-ball model [286] derived for SFE extractions. 

Wick, L. Y., Colangelo-Failla, T. and Harms, H. (2001). Kinetics of mass transfer-limited microbial growth on solid PAHs, Environ. Sci. Technol, 35, 354-361. 

George, C J. Y. Saison, J. L. Ponche, and P. Mirabel, Kinetics of Mass Transfer of Carbonyl Fluoride, Trifluoroacetyl Fluoride, and Trifluoroacetyl Chloride at the Air/Water Interface, J. Phys. Chem., 98, 10857-10862 (1994b). 

Plate theory disregards the kinetics of mass transfer. Thus, it reveals little about the factors influencing HETP values. Plate theory tells us that HETP becomes smaller with decreasing flow-rate however, experimental evidence shows that a plot of HETP versus flowrate always goes through a minimum. 

Boyarchuk and Planovskil (B13), 1962 Study of the kinetics of mass transfer in film-type distillation equipment. 

The use of additives such as small amounts of acids of bases in the mobile phase is often used to achieve separations on these in conjunction with these stationary phases. The net result is an improved kinetics of mass transfer and improved peak shape [116]. 

Helgeson, H. C. Kinetics of mass transfer among silicates and aqueous solutions, Geochim. Cosmochim. Acta 35,... 

W Diffusion control We consider the kinetics of mass transfer when convection may be neglected and where the actual adsorption process is fast when compared to diffusion. In other words, once a molecule has diffused towards the surface it is Instantcmeously adsorbed. 

Temperature is the single most important parameter influencing the kinetics of mass transfer in PHSE or, in other words, the most important factor contributing to increasing... 

Real chromatograms (Fig. 2.6-3) take into account the thermodynamic influences as well as the kinetics of mass transfer and fluid distribution. A rectangular concentration profile of the solute at the entrance of the column soon changes into a bell-shape Gaussian distribution, if the isotherm is linear. Figure 2.7a shows this distribution and some characteristic values, which will be referred to in subsequent chapters. With mass transfer resistance or nonlinear isotherms the peaks become asym-... 

In ideal chromatography, we assume that the column efficiency is infinite, or in other words, that the axial dispersion is negligibly small and the rate of the mass transfer kinetics is infinite. In ideal chromatography, the surface inside the particles is constantly at equilibrium with the solution that percolates through the particle bed. Under such conditions, the band profiles are controlled only by the thermodynamics of phase equilibria. In linear, ideal chromatography, all the elution band profiles are identical to the injection profiles, with a time or volume delay that depends only on the retention factor, or slope of the linear isotherm, and on the mobile phase velocity. This situation is unrealistic, and is usually of little importance or practical interest (except in SMB, see Chapter 17). By contrast, nonlinear, ideal chromatography is an important model, because the profiles of high-concentration bands is essentially controlled by equilibrium thermodynamics and this model permits the detailed study of the influence of thermodynamics on these profiles, independently of the influence of the kinetics of mass transfer... 

When the kinetics of mass transfer is slow e.g., in some applications of liqmd-solid chromatography, ion-exchange chromatography or affinity chromatography to the separation of large peptides, proteins, or polynucleotides), a relationship of the following form is written to take this into accoxmt. 

Depending on the specific problem studied, one or several steps can be considered as much faster than the other ones and the corresponding contribution to the overall kinetics of mass transfer neglected. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

Accurate determination of the isotherm parameters requires a rather large number of data points, corresponding to a wide range of absolute and relative concentrations. The acquisition of pure component data as well as equilibrium data for 1 3, 1 1, and 3 1 mixtures seems to be a bare minimtun [14]. Compared to other methods of isotherm determination, the frontal analysis method has the advantage of being nearly independent of the kinetics of mass transfer and axial dispersion, i.e., of the column efficiency. On the other hand, the results achieved can be very reproducible if proper experimental care is taken. Figure 4.24 [9] illustrates, for cis- and fraus-androsterone, the reproducibility of two runs before and... 

The transport approach has been used very early, and most extensively, to calculate the chromatographic response to a given input function (injection condition). This approach is based on the use of an equation of motion. In this method, we search for the mathematical solution of the set of partial differential equations describing the chromatographic process, or rather the differential mass balance of the solute in a slice of column and its kinetics of mass transfer in the column. Various mathematical models have been developed to describe the chromatographic process. The most important of these models are the equilibrium-dispersive (ED) model, the lumped kinetic model, and the general rate model (GRM) of chromatography. We discuss these three models successively. 

For single-component systems, the theoretical solutions obtained are easy to compare to experimental profiles. They differ only by the smoothing effect due to axial dispersion and to the finite kinetics of mass transfers in actual columns. In many cases, because of the qualities of the stationary phases currently available, these effects appear to be secondary compared to the major role of thermodynamics in controlling the band proffles in overloaded elution. Admittedly, the influence of the finite coliunn efficiency on the band profiles prevents a successful quantitative comparison between theoretical and experimental band profiles. However, these profiles are similar enough at high concentrations and the solutions of the ideal model indicate which are the trends to be expected. 

As discussed already in Chapter 2 (Section 2.2.6), Giddings [10] has developed a nonequilibrium theory of chromatography and showed that the influence of the kinetics of mass transfers can be treated as a contribution to axial dispersion. As illustrated in Chapter 6, this approximation is excellent in linear chromatography, as long as the column efficiency exceeds 20 to 30 theoretical plates. 

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