Distribution coefficient, effect transport

Thus, the sorption of chemicals on the surface of the solid matrix may become important even for substances with medium or even small solid-fluid equilibrium distribution coefficients. For the case of strongly sorbing chemicals only a tiny fraction of the chemical actually remains in the fluid. As diffusion on solids is so small that it usually can be neglected, only the chemical in the fluid phase is available for diffusive transport. Thus, the diffusivity of the total (fluid and sorbed) chemical, the effective diffusivity DieS, may be several orders of magnitude smaller than diffusivity of a nonsorbing chemical. We expect that the fraction which is not directly available for diffusion increases with the chemical s affinity to the sorbed phase. Therefore, the effective diffusivity must be inversely related to the solid-fluid distribution coefficient of the chemical and to the concentration of surface sites per fluid volume. 

Enhanced HOC solubility in surfactant systems generally has been quantified by a distribution coefficient that only considers HOC partitioning to surfactant micelles that exist above the critical micelle concentration (CMC). Although surfactants can form a mobile micellar pseudophase that leads to the facilitated transport of solubilized HOCs, they also can be adsorbed by the solid matrix and thereby lead to HOC partitioning to immobile sorbed surfactants and, thus, enhanced HOC retardation. Therefore, the effectiveness of a remediation scheme utilizing surfactants depends on the distribution of an HOC between immobile compartments (e.g., subsurface solids, sorbed surfactants) and mobile compartments (e.g., water, micelles). 

FIGURE 1.60. Simulated Nyquist plots exhibiting the effect of a distribution in charge transport diffusion coefficients on the impedance response recorded at a low frequency. We assume in this case a log-normal distribution in Dcr with variance where = log... 

Accessible porosity and cluster size distributions Effective transport coefficients Diffusion in restricted microgeometries Analytical solutions Lattice random walks Conclusion Glossary References... 

The random MPC solvent therefore has similar properties to the MFC solvent, except that there are no HI. The relevant parameters in both methods are the average number of particles per cell, M, the rotation angle a, and the collision time At which can be chosen to be the same. For small values of the density (Af < 5), fluctuation effects have been noticed [26] and could also be included in the random MPC solvent by a Poisson-distributed density. The velocity autocorrelation functions [15] of a random MPC solvent show a simple exponential decay, which implies some differences in the solvent diffusion coefficients. Other transport coefficients such as the viscosity depend on HI only weakly [57] and consequently are expected to be essentially identical in both solvents. 

The effective diffusivity depends on the statistical distribution of the pore transport coefficients W j. The derivation shows that the semi-empirical volume-averaging method can only be regarded as an approximation to a more complex dynamic behavior which depends non-locally on the history of the system. Under certain circumstances the long-time (t —> oo) diffusivity will not depend on t (for further details, see [191]). In such a case, the usual Pick diffusion scenario applies. The derivation presented above can, with minor revisions, be applied to the problem of flow in porous media. When considering the heat conduction problem, however, some new aspects have to be taken into accoimt, as heat is transported not only inside the pore space, but also inside the solid phase. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

Gas diffusion in the nano-porous hydrophobic material under partial pressure gradient and at constant total pressure is theoretically and experimentally investigated. The dusty-gas model is used in which the porous media is presented as a system of hard spherical particles, uniformly distributed in the space. These particles are accepted as gas molecules with infinitely big mass. In the case of gas transport of two-component gas mixture (i = 1,2) the effective diffusion coefficient (Dj)eff of each of the... 

Catalysts are porous and highly adsorptive, and their performance is affected markedly by the method of preparation. Two catalysts that are chemically identical but have pores of different size and distribution may have different activity, selectivity, temperature coefficient of reaction rate, and response to poisons. The intrinsic chemistry and catalytic action of a surface may be independent of pore size, but small pores appear to produce different effects because of the manner and time in which hydrocarbon vapors are transported into and out of the interstices. 

Selected entries from Methods in Enzymology [vol, page(s)j Boundary analysis [baseline correction, 240, 479, 485-486, 492, 501 second moment, 240, 482-483 time derivative, 240, 479, 485-486, 492, 501 transport method, 240, 483-486] computation of sedimentation coefficient distribution functions, 240, 492-497 diffusion effects, correction [differential distribution functions, 240, 500-501 integral distribution functions, 240, 501] weight average sedimentation coefficient estimation, 240, 497, 499-500. 

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