Dispersion relative importance

The relative importance of these mechanisms, and the value of the overall kt, depends on the molecular weight and dispersity of the propagating species, the medium and the degree of conversion. The value of k, is not a constant ... 

We might properly refer to this value as the apparent Peclet number, because by many formal definitions the Peclet number accounts for the relative importance of advection and molecular diffusion, without mention of hydrodynamic dispersion. 

Assess the relative importance of dispersion versus advection in the GWS for 2,4-dinitrophenol infiltrating from the river and detected in one of the wells. Discuss all three regimes. 

Once the Curie contribution to R2M is estimated and subtracted, the contribution of contact and dipolar interactions can be estimated by examining the correlation time dependence of the paramagnetic relaxation depicted in Figs. 3.9 and 3.11. It appears that the maximum for R m occurs at dipolar term and at contact term. Taking for simplicity xf Ip = r °", this means that in the intermediate situation where ft>s T p > 1 > relative importance of the contact term is even smaller than that estimated in the fast motion limit. The equation for R2M has non-dispersive terms in both the dipolar and contact contributions (accounting for one-fifth and one-half of the total effect measured in the fast motion limit respectively), and therefore the conclusions drawn in the fast motion limit are still qualitatively correct. 

To understand the relative importance of different rate processes such as reaction, mixing, diffusion, or dispersion, knowledge of the relevant timescales of these processes is invaluable. The ratios of such timescales form a set of dimensionless quantities. While we cannot possibly give an exhaustive account here (the reader is referred to reactor design texts), we mention the most important dimensionless quantities. 

The seasonal distribution of particle-associated PAHs is controlled by a combination of emission factors (EFs), dispersion conditions and chemical mechanisms (Caricchia et al., 1999 Menichini et al., 1999). This balance depends on the relative importance of degradation processes and emission sources (Guo et al., 2003b). The highest PAH concentrations of a sampling site were usually obtained from winter samples, and the differences were far higher in northern cities than southern ones, suggesting that coal combustion for space heating contributes the most PAHs in winter in Northern China. 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

The present evidence is thus that kinetic effects may account for half or more of permittivity decreases of ionic solutions and this may be an important factor in determing the amplitude of the Y dispersion in conducting biopolymer solutions and lead to revisions in estimated nature and amount of bound water. The effect may also have some bearing on dielectric properties of cell interiors and membranes if these have appreciable conductances. It would seem premature to attempt definitive answers to such questions until the relative importance of static and kinetic effects in presumably simpler ionic solutions has been better established experimentally in comparison with theory which treats them self-consistently. 

In addition to the form of in first-layer absorption, its magnitude is also of significance as regards validity or relative importance of Model 2. Here it is assumed that Model 2 may be based on dispersion forces with polarizations to produce larger than normal first-layer adsorbate-adsorbent potentials (the a term in Equation 6b) and longer than normal range adsorbate-adsorbate repulsions. One may evaluate a and b by curve fitting as follows ... 

Effects of Capillary Number, Capillary Pressure, and the Porous Medium. Since the mechanisms of leave-behind, snap-off, lamella division and coalescence have been observed in several types of porous media, it may be supposed that they all play roles in the various combinations of oil-bearing rocks and types of dispersion-based mobility control (35,37,39-41). However, the relative importance of these mechanisms depends on the porous medium and other physico-chemical conditions. Hence, it is important to understand quantitatively how the various mechanisms depend on capillary number, capillary pressure, interfacial properties, and other parameters. 

Theoretical formulations of reorganization in the course of electron-transfer processes have undergone a number of advances in recent years. The relative importance of various solvent contributions (including translational as well as orientational response, and inductive and dispersion as well as elecrostatic interactions) can depend strongly on the polarity (i.e., dipolar, higher multipolar, or nonpolar) as well as other molecular features of the solvent [21, 47-49]. Molecular-level perspectives on solvent response are of great utility in helping to parameterize effective cavity models (e.g., in conjunction with conventional [50] or spatially nonlocal [47] dielectric models). Additivity relationships traditionally assumed to pertain to sol-... 

The relative importance of advection relative to hydrodynamic dispersion is often assessed using the dimensionless Peclet number = v L/Djjjy i, in which L is the length scale of interest. Hydro-dynamic dispersion tends to dominate for small L, whereas advection dominates for large L, say on the scale of a mountain belt. The dissipative effects of hydrodynamic dispersion probably operate over length scales of < 100 m (Bickle and McKenzie, 1987 Bickle, 1992). 

Cini et al. [25] reviewed those aspects of activated carbon which are often forgotten when applied to potable water systems. Among the adsorbate/adsor-bent interactions they mentioned dispersion forces, polarization forces and electrostatic forces but did not provide examples of their relative importance. 

As abundantly documented in Section IV.B.I, some adsorption systems involving aromatic adsorbates are very much influenced by electrostatic interactions. Clearly, a model that takes into account both electrostatic and dispersion interactions is needed. Such a model has been presented by Muller and coworkers [523-525]. Radovic and coworkers [674] used this model to illustrate the possibly dramatic effects of modifications of carbon surface chemistry on equilibrium uptakes of / -nitrophenol they have also extended it to evaluate the relative importance of electrostatic and dispersive interactions [738]. This approach is summarized next. 

The dispersion of Hg in the secondary environment can be considered to result from both solution and vapour transport. However, the relative importance of these two mechanisms for different geological, geomorphological and climatic environments cannot be estimated based on our theoretical knowledge of the behaviour of Hg, but must be deduced from observations of the distribution of Hg, relative to other metals, around weathering sulphide bodies. 

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