Mass transport mechanisms

At any instant, pressure is uniform throughout a bubble, while in the surrounding emulsion pressure increases with depth below the surfaee. Thus, there is a pressure gradient external to the bubble which causes gas to flow from the emulsion into the bottom of the bubble, and from the top of the bubble back into the emulsion. This flow is about three times the minimum fluidization velocity across the maximum horizontal cross section of the bubble. It provides a major mass transport mechanism between bubble and emulsion and henee contributes greatly to any reactions which take place in a fluid bed. The flow out through the top of the bubble is also sufficient to maintain a stable arch and prevent solids from dumping into the bubble from above. It is thus responsible for the fact that bubbles can exist in fluid beds, even though there is no surface tension as there is in gas-liquid systems. 

As shown above, a thermodynamic analysis indicates what to expect from the reactants as they reach the deposition surface at a given temperature. The question now is, how do these reactants reach that deposition surface In other words, what is the mass-transport mechanism The answer to this question is important since the phenomena involved determines the reaction rate and the design and optimization of the CVD reactor. 

Thus, the side-by-side device, when properly calibrated, is a versatile and useful method to determine diffusion coefficients, to evaluate mass transport mechanisms, and to evaluate up-to-date drug delivery systems. 

This method provides for one-dimensional diffusion and should be useful for studying mass transport to or from a variety of multiphase systems. The method provides for studying stirring rate dependence and the mass transport mechanisms related to the system under study. 

The most serious causes of error are (i) wave and peak distortion caused by excessively fast scan rates, which are themselves caused by diffusion being an inefficient mass transport mechanism, (ii) current maxima caused by convective effects as the mercury drop forms and then grows, and (iii) IR drop, i.e. the resistance of the solution being non-zero. Other causes of error can be minimized by careful experimental design. 

The determination of the capillary pressure of a diffusion layer is critical, not only to have a better understanding of the mass transport mechanisms inside DLs but also to improve their design. In addition, the accuracy of mafhemafical models can be increased with the use of experimental data obtained through reliable techniques. Both Gostick et al. [196] and Kumbur et al. [199] described and used the MSP method in detail to determine the capillary pressures of differenf carbon fiber paper and carbon cloth DLs as a function of the nonwetting phase saturation. Please refer to the previous subsection and these publications for more information regarding how the capillary pressures were determined. 

Figure 40 The heat and mass transport mechanisms in a fuel bed. [49]...

When a solute is transferred from a solid into a high-pressure gas, it is then taken downstream in the bulk fluid by convective transport. Depending on turbulence, the solute may travel further by other mass-transport mechanisms such as dispersion. Dispersion spreads the solute axially and radially in a cylindrical stet. Eaton and Akgerman [30] considered both axial and radial effects in a model for the desorption of heavy organics, from carbon, by a dense gas. 

Torgersen, T., Clarke, W. B. (1992) Geochemical constraints on formation fluid ages, hydrothermal heat flux, and crustal mass transport mechanisms at Cajon Pass. J. Geophys. 

Fisher, H.B. (1972) Mass transport mechanisms in partially stratified estuaries. J. Fluid Mech. 53, 671-687. 

Another difficulty is related to the mass transfer by convection, as, by definition, the films are stagnant and hence, there should be no mass transport mechanism, except for molecular diffusion in the direction normal to the interface (Kenig, 2000). Nevertheless, convection in films is directly accounted for in correlations. Moreover, in case of reactive systems, the film thickness should depend on the reaction rate, which is beyond the two-film theory consideration. 

Microporous and, particularly, ultramicropous membranes are more difficult to characterize. Different procedures based on the low-pressure part of the N2 adsorption isotherm have been proposed [36], but they often require knowledge of the shape of the pores and of gas-surface interaction parameters which are not always available. Small angle X-ray scattering (SAXS) is another technique which is well suited to micro-porous powders, but difficult to execute in the case of composite layers, as in microporous membranes. Xenon-129 NMR has recently been proposed [37] for the characterization of amorphous silica used in the preparation of microporous membranes, but the method requires further improvement. Methods based on permeability measurements appear to be limited by the lack of understanding of the mass transport mechanisms in (ultra)microporous systems. 

An in-depth description of the electrochemical treatment of organic-polluted wastewater in which the concentration profiles of every compound in the electrochemical cell are calculated is particularly difficult, as it would lead to a very complex mathematical system. This complex situation arises since the concentration of every compound depends on the time and on the distance to the electrode surface, and that the particular concentration of every species for a given case depends on three different mass-transport mechanisms diffusion, convection, and migration. 

In this context, to describe the position dependence of the model species, it is important to take in mind that, in electrochemical wastewater-treatment processes, it can be assumed that in the treated wastewater there is always enough supporting electrolyte to minimize the migration of electroactive species. Hence the primary mass-transport mechanisms are diffusion and convection. Hence, the mass balance of a volume element assuming that reactions are restricted to the electrode surface takes the form of (4.2). 

In many structured products, water management includes several mass transport mechanisms such as hydrodynamic flow, capillary flow and molecular self-diffusion depending on the length scale. Hydrodynamic flow is active in large and open structures and it is driven by external forces such as gravity or by differences in the chemical potential, that is, differences in concentrations at different locations in the structure. Capillary flow also depends on surface tension and occurs in channels and pores on shorter length scales than in hydrodynamic flow. A capillary gel structure will hold water, and external pressures equivalent to the capillary pressure will be needed to remove the water. 

The third form of mass transport is convection driven by pressure. When forced circulation exists in electrolyte, convection may be the dominant form of mass transport. Thus, in general, a flux Jj (mol/s cm) of species j may occur due to the above three types of mass transport mechanisms. The flux can be described by the Nernst-Planck equation [5]... 

The preceding section assumed that the mass-transport mechanism in a fluid medium is dominated by molecule-molecule collisions. However, the mean free path of gases often exceeds the dimensions of small pores typical of solid catalysts. In this situation, called Knudsen diffusion, molecules collide more often with the pore walls than with other molecules. According to Equation (6.3.1), the Knudsen diffu-sivity of component A, D a, is proportional to r / , but is independent of both pressure and the presence of other species ... 

The movement of a contaminant near the surface of a part to the bulk fluid is governed by mass transport mechanisms. The molar flux of a species A from a surface may be expressed in terms of a composition driving force and a mass transfer coefficient ... 

Ideally, the zeolite membranes must be continuous with good cross-linking between crystals and free of pinholes and cracks to get high selectivities. However, most of the synthesis procedures render membranes with some intercrystaUine gaps and defects. The amount of these membranes and their sizes play an important role in the overall quahty of the membrane. Therefore, it has been considered illustrative to explain briefly the transport regimes in porous materials whatever the pore size, after which the mass transport mechanisms through microporous media will be fully described. 

For the UF of proteins, the concentration polarization model has been found to predict the filtration performance reasonably well [56]. However, this model is inherently weak in describing the two-dimensional mass transport mechanism during crossflow filtration and does not take into account the solute-solute interactions on mass transport that occur extensively in colloids, especially during MF [21,44,158,159]. The diffusion coefficient, which is inversely proportional to the particle radius, is low and underestimates the movement of particles away from the membrane [56]. This results to the well-known flux paradox problem where the predicted permeate flux is as much as two orders of magnitude lower than the observed flux during MF of colloidal suspensions [56,58,158]. This problem has then been underlined by the experimental finding of a critical flux for colloids, which demonstrates the specificity of colloidal suspension filtration wherein just a small variation in physicochemical or hydrodynamic conditions induces important changes in the way the process has to be operated [21]. 

Let us now deal with "large-pore" catalysts (e.g., a-alumina supports) in which intraparticle convection is a mass transport mechanism which cannot be ignored. 

Generally, the overall kinetics is primarily governed by the external and internal diffusion (also called the two-step mass transport mechanism Steps 2 and 3 above). The intraparticle diffusion model described below can therefore be used for calculation of ion uptake by IX resins. When the mass transfer is due only to the diffusion of adsorbate molecules through the pore liquid, a pore diffusion model is often used. On the other hand, in the case where the intraparticle mass transfer is contributed by the diffusion... 

In fixed-bed operation, in addition to the two-step mass transport mechanism, advection and dispersion play key roles in ion exchange. These factors must be considered. As influent concentration is assumed low, solution velocity can be considered constant. If pore diffusion is an important factor in the ion uptake, the following equations can be used. Similar expressions for surface diffusion can be obtained ... 

Considering the intraparticle, the convective and the diffusive mass transport mechanisms in the pores of the particles as separate mass transport mechanisms, each one characterized by its own individual and proper driving force, rather than as a convective flux augmented of a diffusive flux in the pores of the particles... 

Many macromolecular compounds exhibit very complex mass transport mechanisms. It was suggested that this phenomenon originates from the contribution... 

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