Diffusion-Dispersion

As the particles in a coUoidal dispersion diffuse, they coUide with one another. In the simplest case, every coUision between two particles results in the formation of one agglomerated particle,ie, there is no energy barrier to agglomeration. Applying Smoluchowski s theory to this system, the half-life, ie, the time for the number of particles to become halved, is expressed as foUows, where Tj is the viscosity of the medium, k Boltzmann s constant T temperature and A/q is the initial number of particles. 

Liquid-phase mass transfer coefficient Gas-liquid interfacial area per unit volume of dispersion Gas volume fraction in dispersion Diffusivity of cyanogen in solution Henry law coefficient... 

Initially the free C02 is distributed in radially decreasing concentrations in zones around the injection site (Fig. 2a van der Meer 1996). Nearest the injection site lies a zone of near completely saturated pores, containing isolated beads of trapped brine, some of which evaporate into the C02 (Pruess etal. 2003). The middle zone contains mixed brine and C02 (Saripalli McGrail 2002 Pruess et al. 2003). In the outer zone C02 is present only as aqueous species. Following injection, C02 saturations around the injection site are predicted to decrease over tens of years as the free C02 rises buoyantly, spreads laterally, and dissolves into the brine (Weir et al. 1995). Over time-scales of hundreds of years, dispersion, diffusion, and dissolution can reduce the concentration of both free and aqueous C02 to near zero (McPherson Cole 2000). 

In porous media the flow of water and the transport of solutes is complex and three-dimensional on all scales (Fig. 25.1). A one-dimensional description needs an empirical correction that takes account of the three-dimensional structure of the flow. Due to the different length and irregular shape of the individual pore channels, the flow time between two (macroscopically separated) locations varies from one channel to another. As discussed for rivers (Section 24.2), this causes dispersion, the so-called interpore dispersion. In addition, the nonuniform velocity distribution within individual channels is responsible for intrapore dispersion. Finally, molecular diffusion along the direction of the main flow also contributes to the longitudinal dispersion/ diffusion process. For simplicity, transversal diffusion (as discussed for rivers) is not considered here. The discussion is limited to the one-dimensional linear case for which simple calculations without sophisticated computer programs are possible. 

In this discussion equation (8) is used to model the transport of TCE during the test. The parameters needed for the model include the effective dispersion/diffusion coefficients, retardation factor, and the pore fluid velocity. 

The profiles of TCE concentration of the control and test columns were used to determine the effective dispersion/diffusion coefficients. As the TCE concentrations closed to the cathode were near zero during four weeks without EO (Figure 5), the variance of the four TCE concentration profiles in the control columns were used to determine the values of D/Rof TCE. The estimated Dd/R for TCE is 6.9 x 10 6 cm2/sec (equation (10)) with r-square of (0.99). Only the TCE profiles of the first week of the test column was used to determine the value of D as the peak of the TCE plume had advanced out of the boundary after two weeks of testing (Figure 6). The estimated D is 1.4 x 10 s cm2/sec. The results indicate that the effective dispersion coefficient is twice of the effective diffusion coefficient (D/R). 

Advection, Dispersion, Diffusion, to Planetary Boundary Photooxidation, Biodegradation,... 

Fig. 25 Convection, dispersion / diffusion, retardation and degradation of a species (single peak input) versus time along a flow path...

If all advection, dispersion, diffusion, and adsorption processes in three dimensions are considered, the three-dimensional MRTM governing equation can be expressed in the following form ... 

This analogy between the motion of electronic carriers and of hydrogen cannot be taken very far because the hydrogen diffusion has some added complications. Dispersive diffusion of electrons or holes occurs with a low density of carriers in a large density of traps and the trapping events are largely independent. Hydrogen diffusion takes... 

Anonymous Technical Feature Article, Non-dispersive diffusion for nitrogenation, Brauwelt International 2000, 18(2), 129-130. 

Physical. Dispersion, diffusion, and mixing with another water body will dilute the contaminant concentrations. 

A natural response to the limitations of both geochemical equilibrium models and the solute transport models (see 10.3 for a discussion) is to couple the two. Over the last two decades, a number of models that couple advective-dispersive-diffusive transport with fully speciated chemical reactions have been developed (see reviews by Engesgaard and Christensen, 1988 Grove and Stollenwerk, 1987 Mangold and Tsang, 1991). In the coupled models, the solute transport and chemical equilibrium equations are simultaneously evaluated. 

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