Surface area, effect transport

Reactor Sub Set 1 (Volume/Surface area) - effectiveness factor - influence of intra-particle transport on selectivity - thermal stability - gas-liquid reaction regime (slow, fast pseudo first order or instantaneous)... 

Gas Transport Effects. While small pores are essential to give high surface areas, larger transport pores are necessary to minimize difhisional inhibition although, as the porosity increases, both the support crush strength and attrition resistance decrease. 

In this exercise we shall estimate the influence of transport limitations when testing an ammonia catalyst such as that described in Exercise 5.1 by estimating the effectiveness factor e. We are aware that the radius of the catalyst particles is essential so the fused and reduced catalyst is crushed into small particles. A fraction with a narrow distribution of = 0.2 mm is used for the experiment. We shall assume that the particles are ideally spherical. The effective diffusion constant is not easily accessible but we assume that it is approximately a factor of 100 lower than the free diffusion, which is in the proximity of 0.4 cm s . A test is then made with a stoichiometric mixture of N2/H2 at 4 bar under the assumption that the process is far from equilibrium and first order in nitrogen. The reaction is planned to run at 600 K, and from fundamental studies on a single crystal the TOP is roughly 0.05 per iron atom in the surface. From Exercise 5.1 we utilize that 1 g of reduced catalyst has a volume of 0.2 cm g , that the pore volume constitutes 0.1 cm g and that the total surface area, which we will assume is the pore area, is 29 m g , and that of this is the 18 m g- is the pure iron Fe(lOO) surface. Note that there is some dispute as to which are the active sites on iron (a dispute that we disregard here). 

The above brief analysis underlines that the porous structure of the carbon substrate and the presence of an ionomer impose limitations on the application of porous and thin-layer RDEs to studies of the size effect. Unless measurements are carried out at very low currents, corrections for mass transport and ohmic limitations within the CL [Gloaguen et ah, 1998 Antoine et ah, 1998] must be performed, otherwise evaluation of kinetic parameters may be erroneous. This is relevant for the ORR, and even more so for the much faster HOR, especially if the measurements are performed at high overpotentials and with relatively thick CLs. Impurities, which are often present in technical carbons, must also be considered, given the high purity requirements in electrocatalytic measurements in aqueous electrolytes at room temperature and for samples with small surface area. 

Assume that current is passed either through the total nucleus surface area or through part thereof, such as the edge of a two-dimensional nucleus of monoatomic thickness. The transition of the ion Mz+ to the metallic state obeys the equation for an irreversible electrode reaction, i.e. Eqs (5.2.12), (5.2.23) and (5.2.37). The effect of transport processes is neglected. The current density at time t thus depends on the number of nuclei and their active surface area. If there is a large number of nuclei, then the dependence of their number on time can be considered to be a continuous function. For the overall current density at time t we have... 

Experimental methods which yield precise and accurate data are essential in studying diffusion-based systems of pharmaceutical interest. Typically the investigator identifies a mechanism and associated mass transport model to be studied and then constructs an experiment which is consistent with the hypothesis being tested. When mass transport models are explicitly involved, experimental conditions must be physically consistent with the initial and boundary conditions specified for the model. Model testing also involves recognition of the assumptions and constraints and their effect on experimental conditions. Experimental conditions in turn affect the maintenance of sink conditions, constant surface area for mass transport, and constant and known hydrodynamic conditions. 

At a more molecular level, the influences of the composition of the membrane domains, which are characteristic of a polarized cell, on diffusion are not specifically defined. These compositional effects include the differential distribution of molecular charges in the membrane domains and between the leaflets of the membrane lipid bilayer (Fig. 3). The membrane domains often have physical differences in surface area, especially in the surface area that is accessible for participation in transport. For example, the surface area in some cells is increased by the presence of membrane folds such as microvilli (see Figs. 2 and 6). The membrane domains also have differences in metabolic selectivity and capacity as well as in active transport due to the asymmetrical distribution of receptors and transporters. 

One must understand the physical mechanisms by which mass transfer takes place in catalyst pores to comprehend the development of mathematical models that can be used in engineering design calculations to estimate what fraction of the catalyst surface is effective in promoting reaction. There are several factors that complicate efforts to analyze mass transfer within such systems. They include the facts that (1) the pore geometry is extremely complex, and not subject to realistic modeling in terms of a small number of parameters, and that (2) different molecular phenomena are responsible for the mass transfer. Consequently, it is often useful to characterize the mass transfer process in terms of an effective diffusivity, i.e., a transport coefficient that pertains to a porous material in which the calculations are based on total area (void plus solid) normal to the direction of transport. For example, in a spherical catalyst pellet, the appropriate area to use in characterizing diffusion in the radial direction is 47ir2. 

Another limitation is that there is no quantitative relationship between active drug transport in the cell culture models and in vivo e.g. [92, 93]. The reason may be that the expression level of the transporter in Caco-2 cells is not comparable to that in vivo or that there is a difference in effective surface area (see Section 4.3.2.2 below). One solution to this problem is to determine the apparent transport constants, Km and Vmax, for each transporter and subsequently, to determine a scaling factor. However, this is not readily done. In addition these studies are further complicated by the lack of specific substrates. For example, there are almost no specific substrates for the drug efflux transporters [18]. Therefore, other epithelial... 

Enhanced chemical reactivity of solid surfaces are associated with these processes. The cavitational erosion generates unpassivated, highly reactive surfaces it causes short-lived high temperatures and pressures at the surface it produces surface defects and deformations it forms fines and increases the surface area of friable solid supports and it ejects material in unknown form into solution. Finally, the local turbulent flow associated with acoustic streaming improves mass transport between the liquid phase and the surface, thus increasing observed reaction rates. In general, all of these effects are likely to be occurring simultaneously. 

Reduction of particle size increases the total specific surface area exposed to the solvent, allowing a greater number of particles to dissolve more rapidly. Furthermore, smaller particles have a small diffusion boundary layer, allowing faster transport of dissolved material from the particle surface [58]. These effects become extremely important when dealing with poorly water-soluble drugs, where dissolution is the rate-limiting step in absorption. There are numerous examples where reduction of particle size in such drugs leads to a faster dissolution rate [59-61], In some cases, these in vitro results have been shown to correlate with improved absorption in vivo [62-64]. 

Imamura, Kaito, and coworkers—metal-support effects observed after calcination. Imamura et al 9X reported a strong metal-support interaction between Rh and Ce02, whereby high surface area ceria calcined at low temperature (550 °C) was able to transport Rh particles to the bulk, as measured by XPS. They suggested that despite the low degree of exposure of the Rh particle at the surface, the exposed Rh was highly active for the methanol decomposition reaction. 

Pahlow et al. [67] have also carefully examined the role of cell shape on nutrient uptake by diatoms in the presence of advection, under the assumption that nonspherical cells will rotate intermittently. In that case, the relative increase in transport capacity is small for solitary, nonspherical cells with respect to spheres [67], These authors found that advection could significantly increase transport for cell chains, even though it did not compensate for the loss in diffusive flux when calculations were made on a cell surface area basis. Therefore, although advection has a much greater effect on the supply of solute to chains than it does to solitary cells, solitary cells will always maintain an advantage over chains. 

Wilson, F.A. and Dietschy, J.M. (1974). The intestinal unstirred layer—its surface area and effect on active transport kinetics. Biochem. Biophys. Acta. 363 112-126. 

Substrate transport through the film may be formally assimilated to membrane diffusion with a diffusion coefficient defined as12 Ds = Dch( 1 — 9)/pjort. In this equation, the effect of film structure on the transport process in taken into account in two ways. The factor 1—0 stands for the fact that in a plane parallel to the electrode surface and to the coating-solution interface, a fraction 9 of the surface area in made unavailable for linear diffusion (diffusion coefficient Dcj,) by the presence of the film. The tortuosity factor,, defined as the ratio between the average length of the channel and the film thickness, accounts for the fact that the substrate... 

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