Equilibrium partition coefficients

Condition (273) is the requirement that at the center of the bubble the concentrations and the temperature must be finite, and condition (274) follows from the condition that the net average flux is zero on the surface r = b which encloses each bubble. Condition (275) refers to the interfacial concentrations and the temperature on both phases, which are related through known equilibrium partition coefficients mf. Hence... 

Concentrations in Water and Particles. In order to obtain the rates of reaction, the concentrations of the two monomers and the chain transfer agent in the water and polymer phases were calculated using equilibrium partition coefficients (H). ... 

Johansson and coworkers [182-184] have analyzed polyacrylamide gel structure via several different approaches. They developed an analytical model of the gel structure using a single cylindrical unit cell coupled with a distribution of unit cells. They considered the distribution of unit cells to be of several types, including (1) Ogston distribution, (2) Gaussian distribution of chains, and (3) a fractal network of pores [182-184]. They [183] used the equilibrium partition coefficient... 

Using the formalism of statistical mechanics, Giddings et al. [135] investigated the effects of molecular shape and pore shape on the equilibrium distribution of solutes in pores. The equilibrium partition coefficient is defined as the ratio of the partition function in the pore... 

When a two- or higher-phase system is used with two or more phases permeable to the solute of interest and when interactions between the phases is possible, it would be necessary to apply the principle of local mass equilibrium [427] in order to derive a single effective diffusion coefficient that will be used in a one-equation model for the transport. Extensive justification of the principle of local thermdl equilibrium has been presented by Whitaker [425,432]. If the transport is in series rather than in parallel, assuming local equilibrium with equilibrium partition coefficients equal to unity, the effective diffusion coefficient is... 

Solute Flux Solute partitioning between the upstream polarization layer and the solvent-filled membrane pores can be modeled by considering a spherical solute and a cylindrical pore. The equilibrium partition coefficient 0 (pore/bulk concentration ratio) for steric exclusion (no long-range ionic or other interactions) can be written as... 

During equilibrium crystal growth from a melt a U-series parent and daughter will be incorporated according to their equilibrium partition coefficients, Dp and D respectively ... 

One possibility for increasing the minimum porosity needed to generate disequilibria involves control of element extraction by solid-state diffusion (diffusion control models). If solid diffusion slows the rate that an incompatible element is transported to the melt-mineral interface, then the element will behave as if it has a higher partition coefficient than its equilibrium partition coefficient. This in turn would allow higher melt porosities to achieve the same amount of disequilibria as in pure equilibrium models. Iwamori (1992, 1993) presented a model of this process applicable to all elements that suggested that diffusion control would be important for all elements having diffusivities less than... 

In Figure 10.10a, it can be seen that for porous membranes, the partial pressure and concentration profiles vary continuously from the bulk feed to the bulk permeate. This is not the case with nonporous dense membranes, as illustrated in Figure 10.10b. Partial pressure or concentration of the feed liquid just adjacent to the upstream membrane interface is higher than the partial pressure or concentration at the upstream interface. Also, the partial pressure or concentration is higher just downstream of the membrane interface than in the permeate at the interface. The concentrations at the membrane interface and just adjacent to the membrane interface can be related according to an equilibrium partition coefficient KM i. This can be defined as (see Figure 10.10b) ... 

Cheng, W.-H., Chu, F.-S., Liou, J.-J. (2003) Air-water interface equilibrium partitioning coefficients of aromatic hydrocarbons. Atmos. Environ. 37, 4807 -815. 

The soil aggregates are assumed to be spherical in form and to have constant temperature and to contain initially uniform distributions of substrate (contaminant) and biomass. The external concentrations of biomass and substrate are assumed to be zero and the external oxygen concentration is constant. Substrate is adsorbed onto the solid phase to an extent determined by an equilibrium partition coefficient. 

Now, because the water-borne radioactive element is predominantly associated with the colloids, we no longer have a need for the distribution coefficient. There will still be a partitioning because the major portion of the radioactive elements will still be adsorbed to the sediment. This is a separate equilibrium partitioning coefficient, requiring a new experiment on the clay sediments and the colloids present. The partitioning colloid-clay ratio would most likely be dependent on the surface areas of each present in the sediments. A separate size distribution analysis has resulted in a sediment-colloid surface area ratio of 99 1 for the sediment. This results in a colloid retardation coefficient oiRc = 100 rather than Ri = 4.2 x 10 or i 2 = 6 x 10. ... 

Experimentally determined air-plant equilibrium partition coefficients of SOCs as well as of other organic compounds are rather scarce. Note that, in the following,... 

Since adsorption to a surface is directly proportional to the surface area of the condensed phase, it is most useful to define the equilibrium partition coefficient, Kiasnr[, as the concentration of the compound in the gas phase (i.e., air, subscript a ) divided by the concentration per unit surface area (therefore subscript surf of the condensed phase ... 

Dissolved fraction and equilibrium partition coefficient, at sediment-water interface ... 

Since the open water column is nearly pure water (op =1, rs p = 0), for compounds with small to moderate solid-water distribution ratios (Kd < 10 m3kg ), the above equilibrium partition coefficient can be simplified to ... 

Typical transfer velocity across liquid layer 10"3 cm s 1 (range 10 5 to 10 2 cm s see Section 20.2 and Illustrative Examples 19.3, 19.4). Km is the equilibrium partition coefficient with typical values between 1 and 104 (see Table 19.1). DA is the aqueous molecular diffusivity in pore space (typical size 10"5 cmV) divided... 

Figure 19.16 Spherical structure (particle, bubble, droplet) with radius r0 surrounded by a concentric fluid boundary layer with thickness 5. r is the spherical coordinate. The concentration inside the sphere is Cs. There is a phase change at the surface of the sphere with the equilibrium partition coefficient KSlf = Csl Cp Cp is the fluid concentration in equilibrium with Cs.

The rate of H2Oz consumption and the OH production were directly related to total iron concentration. The concentrations of hydroxyl radical produced were controlled by the rate of reaction with dissolved constituents. Rate constants for adsorption (ka) and desorption (kd) of PCBs from particles were calculated by regression of data from 1.5 to 5 hr. Adsorption rate constants were estimated from Equation (6.130) assuming that the partitioning rate constants between 2 and 5 hr without OH could be used for calculation of equilibrium partition coefficients Ky)... 

Equilibrium partition coefficient between aqueous and adsorbed... 

Equilibrium partitioning coefficient, Kd (cm3/g) Mass transfer rate, a (1/d)... 

---