Mass transport processes diffusive

Mass transport processes - diffusion, migration, and - convection are the three possible mass transport processes accompanying an - electrode reaction. Diffusion should always be considered because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the electrode and the bulk solution arise, which will induce diffusion processes. Reactant species move in the direction of the electrode surface and product molecules leave the interfacial region (- interface, -> interphase) [i-v]. The - Nernst-Planck equation provides a general description of the mass transport processes. Mass transport is frequently called mass transfer however, it is better to reserve that term for the case that mass is transferred from one phase to another phase. 

Diffusion, migration and convection are the three possible mass transport processes. Diffusion should always be considered because, as the reagent is con-... 

Table 1 Summary of Experimental Methods for Evaluating Diffusion Coefficients and Investigating Mass Transport Processes of Pharmaceutical Interest... 

Whether Knudsen or bulk diffusion dominates the mass transport process depends on the relative magnitudes of the two terms in the denominator of equation 12.2.6. The ratio of the two diffusivity parameters is obviously important in establishing these magnitudes. In this regard, it is worth noting that DK is proportional to the pore diameter and independent of pressure whereas DAB is independent of pore size and inversely proportional to the pressure. Consequently, the higher the pressure and the larger the pore, the more likely it is that ordinary bulk diffusion will dominate. 

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

There are three types of mass transport processes within a microfluidic system convection, diffusion, and immigration. Much more common are mixtures of three types of mass transport. It is essential to design a well-controlled transport scheme for the microsystem. Convection can be generated by different forces, such as capillary effect, thermal difference, gravity, a pressurized air bladder, the centripetal forces in a spinning disk, mechanical and electroosmotic pumps, in the microsystem. The mechanical and electroosmotic pumps are often used for transport in a microfluidic system due to their convenience, and will be further discussed in section 11.5.2. The migration is a direct transport of molecules in response to an electric field. In most cases, the moving... 

In analysis of a mass transport process, the Peclet number, Pe, the ratio of the direct flow to the diffusion, is used and given as... 

If only linear diffusion is the operating mass transport process, it has been shown that the current (i) in a planar electrode is related to the concentration (c) gradient at the surface of the electrode (x = 0) by [332]... 

Mass transfer (continued) in monolith, 27 89 in porous catalyst, 27 60-63, 68 in tubular reactor, 27 79, 82, 87 Mass transport processes, 30 312-318 convective, 30 312-313 diffusive, 30 313-315 selectivity, 30 316... 

Diffusion. Often, the most important mode of mass transport is diffusion. The rate of diffusion can be defined in terms of Pick s laws. These two laws are framed in terms of flux, that is, the amount of material impinging on the electrode s surface per unit time. Pick s first law states that the flux of electroactive material is in direct proportion to the change in concentration c of species i as a function of the distance x away from the electrode surface. Pick s first law therefore equates the flux of electroanalyte with the steepness of the concentration gradient of electroanalyte around the electrode. Such a concentration gradient will always form in any electrochemical process having a non-zero current it forms because some of the electroactive species is consumed and product is formed at the same time as current flow. 

The two major causes of uneven current distribution are diffusion and ohmic resistance. Nonuniformity due to diffusion originates from variations in the effective thickness of the diffusion layer 8 over the electrode surface as shown in Figure 10.13. It is seen that 8 is larger at recesses than at peaks. Thus, if the mass-transport process controls the rate of deposition, the current density at peaks ip is larger than that at recesses since the rate of mass transport by convective diffusion is given by... 

Optimal values for adsorption properties may be deduced by considering effects on the two transport processes, diffusion and mass flow. To estimate detailed figures, it is necessary to solve transport equations for the particular boundary conditions of the system under study, but in general terms... 

The discussion of this section has neglected all effects resulting from mass transport and diffusion in the atmosphere, and to this extent is inadequate. A number of other chemical processes may also modify the picture presented here. In particular, there is the possibility that 02(lS +) could be formed from 02(1A I) by the energy-pooling process (11), although... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

There are three kinds of mass transport process relevant to electrode reactions migration, convection and diffusion. The Nernst—Planck equation... 

Mass transport processes are involved in the overall reaction. In these processes the substances consumed or formed during the electrode reaction are transported from the bulk solution to the interphase (electrode surface) and from the interphase to the bulk solution. This mass transport takes place by diffusion. Pure diffusion overpotential t]A occurs if the mass transport is the slowest process among the partial processes involved in the overall electrode reaction. In this case diffusion is the rate-determining step. 

The eight reaction steps in the sensor model include a variety of chemical and physical processes, all of which are influenced by the system components shown in Fig. 1. The sensor is usually designed so that the kinetics of the physical processes (i.e., mass transport by diffusion) are limiting, but it is possible to construct sensors that exhibit performance characteristics limited by the kinetics of the chemical/electrochemical processes. 

The modeling of membrane bioreactors is in the initial stage. There are not available more or less sophisticated mathematical tools to describe the complex biochemical processes. It is not known how the mass-transport parameters, diffusion coefficients, convective velocity, biological kinetic parameters might vary in function of the operating conditions, of the biolayer (enzyme/micro-organism membrane layer)... 

We note first that immediately following the injection of a sample at the head of the channel, the flow of carrier is stopped briefly to allow time for the sample particles to accumulate near the appropriate wall. As the particles concentrate near the wall, the growing concentration gradient leads to a diffusive flux which counteracts the influx of particles. Because channel thickness is small (approximately 0.25 mm), these two mass transport processes quickly balance one another, leading to an equilibrium distribution near the accumulation wall. This distribution assumes the exponential form... 

In this book we are concerned only with mass transport, or diffusion, in solids. Self-diffusion refers to atoms diffusing among others of the same type (e.g., in pure metals). Interdiffusion is the diffusion of two dissimilar substances (a diffusion couple) into one another. Impurity diffusion refers to the transport of dilute solute atoms in a host solvent. In solids, diffusion is several orders of magnitude slower than in liquids or gases. Nonetheless, diffusional processes are important to study because they are basic to our understanding of how solid-liquid, solid-vapor, and solid-solid reactions proceed, as well as [solid-solid] phase transformations in single-phase materials. 

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