Transport coefficients diffusion

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

Generalized charts are appHcable to a wide range of industrially important chemicals. Properties for which charts are available include all thermodynamic properties, eg, enthalpy, entropy, Gibbs energy and PVT data, compressibiUty factors, Hquid densities, fugacity coefficients, surface tensions, diffusivities, transport properties, and rate constants for chemical reactions. Charts and tables of compressibiHty factors vs reduced pressure and reduced temperature have been produced. Data is available in both tabular and graphical form (61—72). 

The Peclet number Pe = v /Dc, where Dc is the diffusion coefficient of a solute particle in the fluid, measures the ratio of convective transport to diffusive transport. The diffusion time Tp = 2/D< is the time it takes a particle with characteristic length to diffuse a distance comparable to its size. We may then write the Peclet number as Pe = xD/xs, where xv is again the Stokes time. For Pe > 1 the particle will move convectively over distances greater than its size. The Peclet number can also be written Pe = Re(v/Dc), so in MPC simulations the extent to which this number can be tuned depends on the Reynolds number and the ratio of the kinematic viscosity and the particle diffusion coefficient. 

The results presented by Bagley et al. [45] imply that the oxide diffusion coefficient is much smaller in the steady-state regime than in the diffusion-controlled regime where physical bombardment is absent. It may be possible to account for this effect in terms of the diffusive transport model presented earlier by using a smaller oxide diffusion coefficient in the steady-state regime. To explore this possibility, one may set dX/dt= 0 in Eq. 7 to obtain... 

The Mc term can be used to approximate initial sorption or desorption on the glass surface, and the kt1 2 term the longer-term diffusion transport into or out of the surface (3). As shown in Figure 2, the sorption term decreases and the diffusion term increases with temperature for the obsidian experiments. Tabulated values for Equation 1 are presented in Table 1 along with the regression coefficient, r2, for glass data. 

This method is commonly used to obtain the diffusion coefficient through porous membranes. The schematic diagram illustrating the best technique for application of the time-lag method for determination of diffusion transport is shown in Fig. 4. As in the test setup shown in Fig. 4 a, the soil is contained between the source and collection reservoirs. Using this technique for diffusion coefficient determination of pollutants requires that the following conditions are satisfied ... 

In dense membranes, no pore space is available for diffusion. Transport in these membranes is achieved by the solution diffusion mechanism. Gases are to a certain extent soluble in the membrane matrix and dissolve. Due to a concentration gradient the dissolved species diffuses through the matrix. Due to differences in solubility and diffusivity of gases in the membrane, separation occurs. The selectivities of these separations can be very high, but the permeability is typically quite low, in comparison to that in porous membranes, primarily due to the low values of diffusion coefficients in the solid membrane phase. 

The following compilation is restricted to the transport coefficients of protonic charge carriers, water, and methanol. These may be represented by a 3 X 3 matrix with six independent elements if it is assumed that there is just one mechanism for the transport of each species and their couplings. However, as discussed in Sections 3.1.2.1 and 3.2.1, different types of transport occur, i.e., diffusive transport as usually observed in the solid state and additional hydrodynamic transport (viscous flow), especially at high degrees of solvation. Assuming that the total fluxes are simply the sum of diffusive and hydrodynamic components, the transport matrix may... 

Dilute solution theory considers only the interactions between each dissolved species and the solvent. The motion of each charged species is described by its transport properties, namely, the mobility and the diffusion coefficient. These transport properties can... 

The species diffusivity, varies in different subregions of a PEFC depending on the specific physical phase of component k. In flow channels and porous electrodes, species k exists in the gaseous phase and thus the diffusion coefficient corresponds with that in gas, whereas species k is dissolved in the membrane phase within the catalyst layers and the membrane and thus assumes the value corresponding to dissolved species, usually a few orders of magnitude lower than that in gas. The diffusive transport in gas can be described by molecular diffusion and Knudsen diffusion. The latter mechanism occurs when the pore size becomes comparable to the mean free path of gas, so that molecule-to-wall collision takes place instead of molecule-to-molecule collision in ordinary diffusion. The Knudsen diffusion coefficient can be computed according to the kinetic theory of gases as follows... 

Several models for diffusive transport in and among minerals have been discussed in the literature one is the fast grain boundary (FGB) model of Eiler et al. (1992, 1993). The FGB model considers the effects of diffusion between non-adjacent grains and shows that, when mass balance terms are included, closure temperatures become a strong function of both the modal abundances of constituent minerals and the differences in diffusion coefficients among all coexisting minerals. 

I. The direction of diffusion or movement by solutes is always from a region of higher concentration to one of lower concentration. In addition, the diffusive flux, /a, of a solute A across a plane at x is equal to -D dcJ dx) where D is the diffusion coefficient and dcj dx is the concentration gradient of A at x. 2. The increase of the concentration of A with time, dcjdt, is equal to D d CA.lQx ) where d cjdx is the change in the concentration gradient. See also Diffusion Transport Processes... 

In Equation (4.31) the rate constant is either the reaction rate constant or the transport rate constant, depending on which rate controls the dissolution process. If the reaction rate controls the dissolution process, then k. t becomes the rate of the reaction while if the dissolution process is controlled by the diffusion rate, then k j becomes the diffusion coefficient (diffusivity) divided by the thickness of the diffusion layer. It is interesting to note that both dissolution processes result in the same form of expression. From this equation the dependence on the solubility can be seen. The closer the bulk concentration is to the saturation solubility the slower the dissolution rate will become. Therefore, if the compound has a low solubility in the dissolution medium, the rate of dissolution will be measurably slower than if the compound has a high solubility in the same medium. 

Chapter 4 Mass, Heat, and Momentum Transport Analogies. The transport of mass, heat, and momentum is modeled with analogous transport equations, except for the source and sink terms. Another difference between these equations is the magnitude of the diffusive transport coefficients. The similarities and differences between the transport of mass, heat, and momentum and the solution of the transport equations will be investigated in this chapter. 

If we divide equation (2.31) by the term (1 + KiPb/e), we can see that all convective and diffusive transport is retarded by equilibrium adsorption and desorption. Thus, a retardation coefficient is defined ... 

Figure 5.7 gives some relationships for eddy diffusion coefficient profiles under different conditions that will be handy in applications of turbulent diffusive transport. 

The second equality in equation (6.28) is a definition of longitudinal dispersion coefficient, Dl- Taylor (1953) assumed that some of the terms in equation (6.28) would cancel and that longitudinal convective transport would achieve a balance with transverse diffusive transport. He then solved the second equality in equation (6.28), for a fully developed tubular fiow, resulting in the relation... 

Solute Molecular weight Apparent diffusion coefficient in the presence of structured flow system Enhanced diffusion transport rate" Linear transport rate (10 8 m s 1)... 

In this equation, ,/ and mi/2 are the masses of the two isotopes making up RZ1, and the terms are condensation coefficients for the two isotopes, which are determined experimentally and are typically close to 1. Equation (7.2.1) is valid if a is independent of the evolving composition of the evaporating liquid, and the diffusive transport rate is fast enough to keep the liquid homogeneous. The last condition is violated in solids, where diffusion is very slow relative to the evaporation rate, so solids do not undergo Rayleigh distillation. 

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. 

The coefficients of transport properties considered here include the viscosity, diffusivity, and thermal conductivity of a gas. The transport coefficients vary with gas properties if the flow is laminar. When the flow is turbulent, the transport coefficients become strongly dependent on the turbulence structure. Here we only deal with the laminar transport coefficients the discussion of the turbulent transport coefficients is given in 5.2.4. 

In SLM extraction, the transport mechanism is influenced primarily by the chemical characteristics of the analytes to be extracted and the organic liquid in the membrane into which the analytes will interact and diffuse. Analyte solubility in the membrane and its partition coefficient will have the main impact on separation and enrichment. Analyte transport in SLM extraction can be substantially categorized into two major types one is diffusive transport (or simple permeation) and the other covers facilitated transport (or carrier-mediated transport).73... 

The diffusive transport phenomena in nanowires can be described by a semiclassical model based on the Boltzmann transport equation. For carriers in a one-dimensional subband, important transport coefficients, such as the electrical conductivity, a, the Seebeck coefficient, S, and the thermal conductivity, Ke, are derived as (Sun et al., 1999b Ashcroft and Mermin, 1976a)... 

---