Interface distribution coefficient

There have been many modifications of this idealized model to account for variables such as the freezing rate and the degree of mix-ingin the liquid phase. For example, Burton et al. [J. Chem. Phy.s., 21, 1987 (1953)] reasoned that the solid rejects solute faster than it can diffuse into the bulk liquid. They proposed that the effect of the freezing rate and stirring could be explained hy the diffusion of solute through a stagnant film next to the solid interface. Their theoiy resulted in an expression for an effective distribution coefficient k f which could be used in Eq. (22-2) instead of k. 

At the interface, the relation between Pco i and Cco>i is given by the distribution coefficient, called Henry s constant (H) for gas-liquid systems. Thus,... 

The impurity, x, builds up at the solid- liquid interface as the liquid zone moves and the solid forms. We can write for the distribution coefficient ... 

The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1-3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefficients of ions of the electrolyte present in the both phases. 

The partitioning of As in the aquifer solid-water interface can best be explained with the distribution coefficient, Kd (a ratio of solute adsorbed in sediment to that of dissolved in groundwater). Due to being simplistic in nature, Kd has long been well appreciated as well as applied by geochemical modelers. 

The properties of ITIES are in many respects analogous to those of the metal electrode/electrolyte solution interface [8]. This analogy is especially pronounced when electrolyte Ji Xi, dissolved in one phase (an organic solvent virtually immiscible with water), is strongly hydrophobic, whereas electrolyte J2X2, dissolved in the other phase (water), is strongly hydrophilic. This situation is characterized by the following inequalities for the distribution coefficients of the substances ... 

The nature of soil-phenolic acid interaction adsorption-desorption. Adsorption of a solute from solution onto a solid matrix results in a higher solute concentration at the fluid-solid interface than in the solution. Huang and coworkers (27) observed a high sorption capacity of the mineral fraction of four latosols for phenolic acids. On the basis of their results, distribution coefficients,... 

The second complicating factor is interfacial turbulence (1, 12), very similar to the surface turbulence discussed above. It is readily seen when a solution of 4% acetone dissolved in toluene is quietly placed in contact with water talc particles sprinkled on to the plane oil surface fall to the interface, where they undergo rapid, jerky movements. This effect is related to changes in interfacial tension during mass transfer, and depends quantitatively on the distribution coefficient of the solute (here acetone) between the oil and the water, on the concentration of the solute, and on the variation of the interfacial tension with this concentration. Such spontaneous interfacial turbulence can increase the mass-transfer rate by 10 times 38). 

Due to the ionic nature of cephalosporin molecules, the interfacial chemical reaction may in general be assumed to be much faster than the mass transfer rate in the carrier facilitated transport process. Furthermore, the rate controlling mass transfer steps can be assumed to be the transfer of cephalosporin anion or its complex, but not that of the carrier. The distribution of the solute anion at the F/M and M/R interfaces can provide the equilibrium relationship [36, 69]. The equilibrium may be presumably expressed by the distribution coefficients, mf and m at the F/M and M/R interfaces, respectively and these are defined as... 

Transfer velocity across gaseous boundary layer typically between 0.1 and 1 cm s"1 (up to 5 cm s 1, see Fig. 20.2). Km is the nondimensional liquid/gas distribution coefficient (for air-water interface inverse nondimensional Henry s law coefficient, i.e., Jfr w) with typical values between 10-3 and 103. DA is the molecular gaseous diffusivity, typical size 0.1 cm2s . 

Such reactions can take place predominantly in either the continuous or disperse phase or in both phases or mainly at the interface. Mutual solubilities, distribution coefficients, and the amount of interfadal surface are factors that determine the overall rate of conversion. Stirred tanks with power inputs of 5-10 HP/1000 gal or extraction-type equipment of various kinds are used to enhance mass transfer. Horizontal TFRs usually are impractical unless sufficiently stable emulsions can be formed, but mixing baffles at intervals are helpful if there are strong reasons for using such equipment. Multistage stirred chambers in a single shell are used for example in butene-isobutane alkylation with sulfuric acid catalyst. Other liquid-liquid processes listed in Table 17.1 are numbers 8, 27, 45, 78, and 90. 

The separation performance in these processes is determined by the distribution coefficient of a component in two phases and the membrane acts only as an interface. They can be divided in gas-liquid (G-L) and liquid-liquid (L-L) membrane... 

Modeling of H F contactors is in most papers based on a simple diffusion resistance in series approach. In many systems with reactive extractants (carriers) it could be of importance to take into account the kinetics of extraction and stripping reactions that can influence the overall transport rate, as discussed in refs. [30,46], A simple shortcut method for the design and simulation of two-phase HF contactors in MBSE and MBSS with the concentration dependent overall mass-transfer and distribution coefficients taking into account also reaction kinetics in L/L interfaces has been suggested [47]. 

Dj are distribution coefficients at equilibrium at feed-membrane and membrane-strip interfaces Relation for the overall mass transfer resistance can be derived [11,25,91] ... 

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