Solute transfer rate

Controlled contact between two immiscible liquids has also been achieved by flowing one liquid along a solid support submerged in the second phase [28,29]. Several different arrangements have been used, although all are based on similar principles. For example, a wetted wall column which offered liquid-liquid contact times of 0.5-10 s was used to measure solute transfer rates [29]. 

Under changing flow conditions it can be important to include some consideration of the hydrodynamic changes within the column (Fig. 3.48), as manifested by changes in the fractional dispersed phase holdup hn and the phase flow rates Ln and Gn which, under dynamic conditions, can vary from stage to stage. Such variations can have a considerable effect on the overall dynamic characteristics of an extraction column, since variations in hn also affect the solute transfer rate terms Qn by virtue of the corresponding variation in the specific interfacial area an. 

Equilibrium constant Solute transfer rate Volume... 

Accordingly, evaluation of k from line-width measurements gives a bimolecular rate constant of 0.5 X 1081 sec-1 M-1. This is one of the fastest electron exchange reactions studied in aqueous solution. Transfer rate here may not describe direct electron transfer between Cu1 and Cu11 Stranks has suggested (129) that the rate may refer to transfer within a bridged activated complex, e.g.,... 

Jaynes, D.B., Logsdon, S.D., and Horton, R. (1995) Field method for measuring the mobile/immobile water and solute transfer rate coefficient. Soil Science Society of America Journal 59 352-356. 

The overall solute transfer rate, must be related to the solute flux Into the globules present as ... 

Essentially the same procedure used to solve for the concentrations in gas permeators will be used. That is, after assuming that is not zero and is independent of the solvent transfer rate, and that )iv is independent of the solute transfer rate, we will solve Eqs. tl7-16cl and Q7-181 for V, set the two equations equal to each other, and solve for the desired concentratiom Setting the equations equal, we obtain... 

In the past few years, the AEC has required solution excursion analyses for new construction as well as plants already in operation. These hypothetical excursions should be chosen to be representative of the most severe excursion that could be reasonably expected in the particular systems involved since the results of the analysis will, in turn, determine the size and types of the hot exhaust filtering system and shielding thickness, etc. An example of the "most severe excursion may be helpful. Consider a tank 3 ft in diameter by 4 ft high which is shown by a safety review to have solution. For the excursion parameter of maximum total fissions, the most severe condition is a tank that is critical when nearly full hence, the full tank volume is used for the total fission estimate. The specifications of the process systems are usually such that the excursions chosen are limited by practic design considerations to tanks of 2- to 5-ft diam with a height of 1 to 2 diam and a solution transfer rate of 7i gpm or less. 

Figure 8.1.46(d) illustrates a few curves from a more detailed plot by Michaels (1966) with A as a parameter. As Qii is decreased for a given blood flow rate Qf, th decreases, since Cid increases, leading to a reduced solute transfer rate. At any given Qf/Qd, Vi increases as A increases, since the solute transfer rate is increased. There is an additional interpretation of the parameter A. From an analysis of the packed countercurrent column design equation (8.1.54a), we know... 

At low currents, the rate of change of die electrode potential with current is associated with the limiting rate of electron transfer across the phase boundary between the electronically conducting electrode and the ionically conducting solution, and is temied the electron transfer overpotential. The electron transfer rate at a given overpotential has been found to depend on the nature of the species participating in the reaction, and the properties of the electrolyte and the electrode itself (such as, for example, the chemical nature of the metal). 

At higher current densities, the primary electron transfer rate is usually no longer limiting instead, limitations arise tluough the slow transport of reactants from the solution to the electrode surface or, conversely, the slow transport of the product away from the electrode (diffusion overpotential) or tluough the inability of chemical reactions coupled to the electron transfer step to keep pace (reaction overpotential). 

Ladanyi B M and Hynes J T 1986 Transition state solvent effects on atom transfer rates in solution J. Am. Ohem. Soc. 108 585-93... 

Design Procedure. The packed height of the tower required to reduce the concentration of the solute in the gas stream from to acceptable residual level ofjy 2 may be calculated by combining point values of the mass transfer rate and a differential material balance for the absorbed component. Referring to a sHce dh of the absorber (Fig. 5),... 

The equations of combiaed diffusion and reaction, and their solutions, are analogous to those for gas absorption (qv) (47). It has been shown how the concentration profiles and rate-controlling steps change as the rate constant iacreases (48). When the reaction is very slow and the B-rich phase is essentially saturated with C, the mass-transfer rate is governed by the kinetics within the bulk of the B-rich phase. This is defined as regime 1. 

To obtain an indication of the rate of solute transfer from the particle surface to the bulk of the Hquid, the concept of a thin film providing the resistance to transfer can be used (2) and the equation for mass transfer written as ... 

The monomer can also be copolymerized with acrylamide. Because of the high chain-transfer rate of aUyflc radicals, the molecular weights tend to be lower than for acryflc polymers. These polymers are sold either as a viscous solution or a dry powder made by suspension polymeriza tion (see Allyl monomers AND POLYPffiRS). 

Equipment for food freezing is designed to maximize the rate at which foods are cooled to —18° C to ensure as brief a time as possible in the temperature zone of maximum ice crystal formation (12,13). This rapid cooling favors the formation of small ice crystals which minimize the dismption of ceUs and may reduce the effects of solute concentration damage. Rapid freezing requires equipment that can deHver large temperature differences and/or high heat-transfer rates. 

The physical mass-transfer rate of o2one into water is affected by the gaseous o2one concentration, temperature, pressure, gas dispersion, turbulence, mixing, and composition of the solution, ie, pH, ionic strength, and the presence of reactive substances. Mass transfer of gaseous o2one into... 

Removing an analyte from a matrix using supercritical fluid extraction (SEE) requires knowledge about the solubiUty of the solute, the rate of transfer of the solute from the soHd to the solvent phase, and interaction of the solvent phase with the matrix (36). These factors collectively control the effectiveness of the SEE process, if not of the extraction process in general. The range of samples for which SEE has been appHed continues to broaden. Apphcations have been in the environment, food, and polymers (37). 

Wa Interpbase mass-transfer rate of solute A per interfacial area with respect to fixed coordinates kmoP(s-m ) (lbmol)/(h-fF)... 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

Use of Mass-Transfer-Rate Expression Figure 14-3 shows a section of a packed absorption tower together with the nomenclature that will be used in developing the equations which follow. In a differential section dh, we can equate the rate at which solute is lost from the gas phase to the rate at which it is transferred through the gas phase to the interface as follows ... 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

The main objective for calculating the number of theoretical stages (or mass-transfer units) in the design of a hquid-liquid extraction process is to evaluate the compromise between the size of the equipment, or number of contactors required, and the ratio of extraction solvent to feed flow rates required to achieve the desired transfer of mass from one phase to the other. In any mass-transfer process there can be an infinite number of combinations of flow rates, number of stages, and degrees of solute transfer. The optimum is governed by economic considerations. 

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