Temperature mass transport effect

Fig. 5.6 shows a plot of Eqn 5.5 which represents a reaction run with varying quantities of catalyst at a fixed pressure, temperature and agitation rate. When mass transport is an insignificant factor in the reaction, km approaches zero and the rate, r, equals kfX, which is the asymptote of the curve at low catalyst quantities. With larger amounts of catalyst, the curve approaches the second asymptote, r = km, for a reaction controlled by mass transport effects. There is... 

The most interesting parameter here is the exchange current density jo, which describes a hypothetical limit of how much current could be produced by the catalyst in the absence of aU mass transport effects (i.e., very close to the open cell voltage). The value ofjo depends on the oxygen concentration at the catalyst surface and the temperature. The concentration dependence can be expressed as follows [62-64] ... 

As a rule of thumb, axial dispersion of heat and mass (factors 2 and 3) only influence the reactor behavior for strong variations in temperature and concentration over a length of a few particles. Thus, axial dispersion is negligible if the bed depth exceeds about ten particle diameters. Such a situation is unlikely to be encountered in industrial fixed bed reactors and mostly also in laboratory-scale systems. Radial mass transport effects (factor 1) are also usually negligible as the reactor behavior is rather insensitive to the value of the radial dispersion coefficient. Conversely, radial heat transport (factor 4) is really important for wall-cooled or heated reactors, as such reactors are sensitive to the radial heat transfer parameters. 

One of the most important parameters is the temperature, the starting temperature, and the initial reaction rate. One can determine experimentally the initial reaction rate after elimination of diffusion and mass transport effects and then determine the Arrhenius constants, which depend on the temperature. The collision factor (ko) and activation energy (E) parameters influence significantly the activity pattern and selectivity. Figure 3.1 illustrates the influence of the temperature on these parameters for different reactions and metallic catalysts. This effect is known as compensation effect, although empirically there are attempts on theoretical interpretations for different heterogeneous systems [1, 2]. 

Fig. 1. General dialysis is a process by which dissolved solutes move through a membrane in response to a difference in concentration and in the absence of differences in pressure, temperature, and electrical potential. The rate of mass transport or solute flux, ( ), is directly proportional to the difference in concentration at the membrane surfaces (eq. 1). Boundary layer effects, the difference between local and wall concentrations, are important in most...

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Dissolved oxygen reduction process Corrosion processes governed by this cathode reaction might be expected to be wholly controlled by concentration polarisation because of the low solubility of oxygen, especially in concentrated salt solution. The effect of temperature increase is complex in that the diffusivity of oxygen molecules increases, but solubility decreases. Data are scarce for these effects but the net mass transport of oxygen should increase with temperature until a maximum is reached (estimated at about 80°C) when the concentration falls as the boiling point is approached. Thus the corrosion rate should attain a maximum at 80°C and then decrease with further increase in temperature. 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

A plot of the adatom density versus T is shown in Fig. 4. An anomalous increase in the density is observed at high temperatures. The dashed line represents the adatom population that would be predicted if there were no lateral interactions. However, the LJ potential between adatoms tends to stabilize them at the higher coverages, and it is this effect that causes the deviation from Arrhenius behavior at high temperatures. A similar temperature dependence is observed in the rate of mass transport on some metal surfaces (8,9), and it is possible that it is caused by the enhanced population of the superlayer at high temperatures. 

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. 

The effect of temperature on the rate of a typical heterogeneous reaction is shown in Figure 3.25. At low temperatures the reaction is chemically controlled and at high temperatures it is diffusion or mass transport controlled. 

Mass transfer may be influenced by gradients in variables other than concentration and pressure. In the pharmaceutical sciences, gradients in electrical potential and in temperature are two important examples of these other driving forces. Section IV.B.l describes the effect of electrical potential gradients on the transport of ions, and Section IV.B.2 discusses mass transport in the presence of temperature gradients, known as combined heat and mass transfer. 

Rigorous calibration is a requirement for the use of the side-by-side membrane diffusion cell for its intended purpose. The diffusion layer thickness, h, is dependent on hydrodynamic conditions, the system geometry, the spatial configuration of the stirrer apparatus relative to the plane of diffusion, the viscosity of the medium, and temperature. Failure to understand the effects of these factors on the mass transport rate confounds the interpretation of the data resulting from the mass transport experiments. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

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. 

The Hl value is reduced by an increase in the viscosity of the solvent or by a decrease in the temperature. Longitudinal diffusion can thus be reduced by decreasing the diffusion coefficient and increasing the flow rate however, these two actions are counter-effective in liquid chromatography because of the mass transport term. 

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