Partition equilibrium transfer

When the equilibrium partitioning or transfer rate of a given element between two reservoirs depends on atomic mass, isotopic fractionation may arise. For elements... 

In the above discussion it is assumed that during storage a partition equilibrium is established between the packaging and food. However, this is not always the case. Given the time ti/2, which is the time required for half of solvent contained in the packaging material to be transferred to the food, then one gets ... 

The treatment of partition equilibrium was further generalized to the cases in the presence of ion-pair formation [19] and ion-ionophore complex formation [21]. An important corollary of this theory of partition equilibrium based on standard ion transfer potentials of single ions is to give a new interpretation to liquid extraction processes. Kakutani et al. analyzed the extraction of anions with tris(l,10-phenan-throline) iron(II) cation from the aqueous phase to nitrobenzene [22], which demonstrated the effectiveness of the theory and gave a theoretical backbone for ion-pair extraction from an electrochemical point of view. 

P-T conditions are ordinarily calculated based on the T-dependence of a cation partitioning equilibrium (e.g., Fe-Mg exchange between garnet and biotite), and the F-dependence of a net-transfer equilibrium (e.g., anorthite = grossular + aluminosilicate -h quartz). Most barometers have moderate slopes, so the calculated P depends moderately on T. The basic problem... 

Craig machine A separation device based on liquid-liquid extraction, whose principle is analogous to chromatography. A large munber of interconnected tubes each contain the same amount of a "stationary" liquid. After the sample is introduced in the first tube, the operation involves two successive operations repeated a large number of times. The tubes are shaken to quicken mass transfer and achieve partition equilibrium between the two liquids. Then the "mobile" liquid in the last tube is collected, the mobile liquid in each other tube is moved from one tube to the next, and fresh mobile liquid is added to the first tube. Eventually, the sample components are all extracted and separated. 

The models of adsorption from semi-infinite bulk phases predict in general a monotonic decrease of the interfacial tension even when a transfer of matter across the interface exists. In particular, if the initial bulk concentrations are in partition equilibrium the adsorption reaches asymptotically the equilibrium state, while otherwise the system achieves a stationary state. 

For some application, however, the assumption of semi-infinite bulk phases is not realistic, for example for drops of surfactant solution in a liquid. The effect of the transfer across the interface on adsorption dynamics is particularly remarkable when such system of limited volume are considered which are initially far from the partitioning equilibrium. A first theoretical approach to this problem has been given by Rubin and Radke [136], where stirred bulks are considered. 

An important aspect with regard to the atmospheric fate of SVOCs is their partitioning between the gas and particle phases. Once released into the atmosphere, generally SVOCs would be partitioned in these two phases and reach a partitioning equilibrium according to temperature dependences and the vapor pressure of the chemicals (Pankow and Bidleman 1992 Cotham and Bidleman 1995). The particulate-bound SVOCs could be transferred from the atmosphere to... 

Conventional approaches based on electrochemical techniques, surface tension, and extraction methods have allowed the estabhshment of thermodynamic and kinetic information concerning partition equilibrium, rate of charge transfer, and adsorption of surfactant and ionic species at the hquid/Uquid interface [4—6]. In particular, electrochemical methods are tremendously sensitive to charge transfer processes at this interface. For instance, conventional instm-mentation allowed the monitoring of ion transfer across a hquid/hquid interface supported on a single micron-sized hole [7, 8]. On the other hand, the concentration profile of species reacting at the interface can be accurately monitored by scanning electrochemical microscopy [9, 10]. However, a detailed picture of the chemical environment at the junction between the two immiscible liquids caimot be directly accessed by purely electrochemical means. The implementation of in-situ spectroscopic techniques has allowed access to key information such as ... 

Considering a chromatographic process controlled by a partition equilibrium and neglecting extracolumn effects (i.e., band broadening caused by factors outside the column, e.g., tubings, detector etc.), several factors can contribute to the overall solute band broadening eddy diffusion, longitudinal diffusion, and resistance to mass transfer in mobile and stationary phase. 

Mass transfer resistance. (Fig. 2c) The migration of the solute molecules from the mobile phase to the stationary phase and vice versa is not instantaneous, and it prevents the existence of true partition equilibrium. The corresponding contribution to the height equivalent to a theoretical plate, for the mass transfer resistance in mobile phase, and for the mass transfer resistance in stationary phase, depends... 

Finally a more comprehensive model for simulating the Ru /Fe system was solved using finite-element methods. This model takes into account mass transport due to diffusion and migration, electron transfer due to electron hopping, homogeneous chemical reaction in the membrane, heterogeneous reactions, double-layer charging, and Donnan partition equilibrium between the membrane and diffusion layer. 

Partition equilibrium between the fluid phases and external mass transfer... 

Clearly the partitioning equilibrium is defined by both the resolvation effect (A/n or A ,), defining short-range interactions with local surroundings, and ZiF(4 ° y - the electrostatic free energy of transfer ( o/y is the electric equilibrium potential drop across the polymer/electrolyte interface. 

The drop shape method is possibly the most useful one for the investigation of the adsorptive transfer, i.e. the adsorption kinetics at the interface between two liquid phases containing the surfactant from the partition equilibrium. This phenomenon is particularly significant when situations far from the partition equilibrium are considered, in systems characterised by a high solubility of the surfactant in the recipient phase or by a large solubility of the surfactant in both phases. The latter case represents a typical situation for many types of ionic surfactants in water-oil and water-alkane systems, as demonstrated by the partition coefficients measured for various solvents [52, 53, 54, 55, 56]. 

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