Diffusion-convection layer distribution within

We assume that the concentration distribution within the diffusion—convection layer can be treated in the similar way to that described in Chapter 2, and then the concentration distribution of the oxidant near the electrode surface can be schematically expressed in Figure 5.2. Thus, the diffusion—convection current density (ioc.o) can be expressed in a similar form to those Eqns (2.57) and (2.58) ... 

In order to get the current—potential relationship on the RDE, particularly the expression of limiting current density as the function of the electrode rotating rate and the reactant concentration, Pick s second law has to be used to give the equations of reactant concentration change with time at the steady-state situation of diffusion—convection. When the surface concentration of oxidant reaches zero during the reaction at the steady-state situation, the concentration distribution within the diffusion—convection layer is not changing with time anymore, meaning that the diffusion rate is... 

Although the assumption of a quasistationary distribution of the concentration of component A within the diffusion boundary layer seems to be very rough, nevertheless under conditions of sufficiently intensive convection the dissolution kinetics of solids in liquids is well described by equations (5.1) and (5.8)-(5.10) (see Refs 301, 303, 304, 306-308). Clearly, these equations are generally applicable at a low solubility of the solid in the liquid phase (about 10-100 kg m or up to 5 mass %). Note that they may also describe fairly well the dissolution process in systems of much higher solubility. An example is the Al-Ni binary system in which the solubility of nickel in aluminium amounts to 10 mass % even at a relatively low temperature of 700°C (in comparison with the melting point of aluminium, 660°C).308... 

For large rate constants kv of the volume chemical reaction, a thin diffusion boundary layer is produced near the drop surface its thickness is of the order of ky1//2 at low and moderate Peclet numbers, and the solute in this layer has time to react completely. As the Peclet number is increased further, because of the intensive liquid circulation within the drop, there is not enough time to complete the reaction in the boundary layer. The nonreacted solute begins to get out of the boundary layer and penetrate into the depth of the drop along the streamlines near the flow axis. If the circulation within the drop is well developed, a complete diffusion wake is produced with essentially nonuniform concentration distribution that pierces the entire drop and joins the endpoint and the origin of the diffusion boundary layer. In case of a first-order volume chemical reaction, an appropriate analysis of convective mass transfer within the drop for Pe > 1 and kv > 1 was carried out in [150,151]. It should be said that in this case, in view of the estimate (5.4.8), which is uniform with respect to the Peclet number, the mass transfer intensity within the drop is bounded by the rate of volume chemical reaction. 

Because the kinetic and mass-transport phenomena occur in a thin region adjacent to the electrode surface, this area is treated separately from the bulk solution region. Since kinetic effects are manifested within 100 A of the electrode surface, the resulting overpotential is invariably incorporated in the boundary conditions of the problem. Mass transport in the boundary layer is often treated by a separate solution of the convective diffusion equation in this region. Continuity of the current can then be imposed as a matching condition between the boundary layer solution and the solution in the bulk electrolyte. Frequently, Laplace s equation can be used to describe the potential distribution in the bulk electrolyte and provide the basis for determining the current distribution in the bulk electrolyte. 

Individual adsorbent particles within a packed bed are surrounded by a boundary layer, which is looked upon as a stagnant liquid film of the fiuid phase. The thickness of the film depends on the fluid distribution in the bulk phase of the packed bed. Molecular transport toward the boundary layer of the particle by convection or diffusion is the first step (1) of the separation process. 

Unfortunately, the case presented in Figure 2.10 is ideal, not necessary to reflect the real situation. For a practical electrode, both diffusion and convection processes coexist. Even inside the diffusion layer, there is some degree of convection—that is, the solution within the diffusion layer is not static. Therefore, the diffusion layer thickness should be determined by both the diffusion and convection processes. Fortunately, using mathematical modeling, the reactant concentration distribution profile near the electrode surface has been found to be similar to tbat shown in Figure 2.9, from which the effective (or equivalent) diffusion-layer thickness can also be defined in tbe same way as Eqn (2.51). Eor a detailed expression about tbis diffusion layer thickness induced by both diffusion and convection process, we will give more discussion in Chapter 5. 

Instantaneous diffusion oo-approach) model assumes that the catalyst is virtually distributed at the gas/washcoat interface so that there is infinitely fast mass transport within the washcoat. This model eliminates the washcoat parameters, such as its thickness and porosity, and the diameters of the inner pores. Therefore, oo-approach does not account for internal mass transport limitations that are due to a porous layer. It means that mass fractions of gas-phase species on the surface are obtained by the balance of production or depletion rate with diffusive and convective processes (Deutschmann, 2008 Kee et al., 2001 Wamatz, 1992). Thus, the net production rate of each chemical species due to surface reactions can be balanced with the diffusive flux of that species at the gas-surface boundary, assuming that no deposition or ablation of chemical species occurs on/from the catalyst surface ... 

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