Gas boundary layer

The catalyst activity depends not only on the chemical composition but also on the diffusion properties of the catalyst material and on the size and shape of the catalyst pellets because transport limitations through the gas boundary layer around the pellets and through the porous material reduce the overall reaction rate. The influence of gas film restrictions, which depends on the pellet size and gas velocity, is usually low in sulphuric acid converters. The effective diffusivity in the catalyst depends on the porosity, the pore size distribution, and the tortuosity of the pore system. It may be improved in the design of the carrier by e.g. increasing the porosity or the pore size, but usually such improvements will also lead to a reduction of mechanical strength. The effect of transport restrictions is normally expressed as an effectiveness factor q defined as the ratio between observed reaction rate for a catalyst pellet and the intrinsic reaction rate, i.e. the hypothetical reaction rate if bulk or surface conditions (temperature, pressure, concentrations) prevailed throughout the pellet [11], For particles with the same intrinsic reaction rate and the same pore system, the surface effectiveness factor only depends on an equivalent particle diameter given by... 

Transfer from a gas phase to a microorganism occurs according to the following mechanisms (1) transport by convection in the gas bubble (2) diffusion through the gas boundary layer in the vicinity of the gas-liquid interface (3)... 

Table 4.3 Calculated Peclet numbers for several important gas separations. The boundary layer thickness is assumed to be 2000 ixm. Permeant diffusion coefficients in the gas boundary layer are taken from tables for ambient pressure diffusion coefficients in Cussler [8] and corrected for pressure. Membrane enrichments E0 are calculated using Equation (4.21)... 

In a well-fluidized gas-solid system, the bulk of the bed can be approximated to be isothermal and hence to have negligible thermal resistance. This approximation indicates that the thermal resistance limiting the rate of heat transfer between the bed and the heating surface lies within a narrow gas layer at the heating surface. The film model for the fluidized bed heat transfer assumes that the heat is transferred only by conduction through the thin gas film or gas boundary layer adjacent to the heating surface. The effect of particles is to erode the film and reduce its resistive effect, as shown by Fig. 12.3. The heat transfer coefficient in the film model can be expressed as... 

The mass transfer resistance at a liquid-vapor interface results from two resistances, the liquid boundary layer and the gas boundary layer. In conditions involving water and sparingly soluble gases, such as occurs here, the liquid-phase resistance is almost always predominant [71]. For this reason, equation (16) involves only k, the mass transfer coefficient across the liquid boundary, and a, which is the gas bubble surface area per unit volume of liquid. Often, as here, those factors cannot be estimated individually, so k is treated as a single parameter. 

At k/kGa 1, the chemical reaction is much slower than the mass transfer rate. In this case, concentration difference in the gas boundary layer does not exists. Therefore, k/kGa can be interpreted as the ratio of the reaction rate without transport limitation (cs = cG) to the reaction rate at transport limitation (cs —> 0). 

Presence of even a small amount of noncondensable gas in the condensing vapor leads to a significant reduction in heat transfer during condensation. The buildup of noncondensable gases near the film vapor interface inhibits the diffusion of vapor from the bulk mixture to the liquid film. The net effect is to reduce the effective driving force for heat and mass transfer. Figure 22.25 shows the temperature and noncondensable gas boundary layer near the film and vapor interface. 

These relations allow one to calculate (m, V ) from the experimental quantities (f osc, i grav), known parameters (y, b), sorbent mass (m ), sorptive gas density (p ), and sorbent and instrument related gas boundary layer mass (Am ). Actually, this later quantity can be determined from measurements with non-sorbing pellets (m = 0) from equation (5.64) or measurements using non-swelling sorbents (V =V ) from equation (5.65). 

Such a law can be found if the reaction at the phase boundary metal/oxide or at the phase boundary oxide/environment is rate-determining. Furthermore, such a law describes oxidation if transport of the oxidant to the metal surface from the environment determines the oxidation. In the latter case, a gas boundary layer is formed on top of the oxide scale and the reaction rate constant ki depends on the thickness of this boundary layer, i.e., on the velocity of the gas stream... 

Diffusion of the carburizing species through a gas boundary layer on the surface of the material. This step is dependent on the gas flow rate at the material surface. 

In Section 2.2.5 we have considered adsorption and desorption, the processes which occur at a gas-solid interface and determine the surface coverage wifh an adsorbate. The same phenomena dictate the gas properties in the close vicinity of the surface. With increasing distance from fhe surface fheir influence vanishes due to intermolecular collisions in the gas phase. Therefore, one can define the gas boundary layer (GBL) as a gas slab where some properties are different from those in the gas interior. The higher the gas pressure, the more frequent are intermolecular collisions. Accordingly, the thickness of fhe GBL varies inversely with the pressure. 

The solution of Eq. (7.17) depends on the boundary conditions which one imposes on cr(z) which, in turn, are determined by the processes of excitation and de-excitation of atoms near the surface. We shall consider a situation where the mean free path of the gas atoms exceeds the thickness of the gas boundary layer where the optical response is formed. Accordingly, separate boundary conditions are set for atoms moving to the surface and for those departing from it. The most simple, but often fairly realistic, assumption is that all atoms arriving at the surface are adsorbed on it and then are desorbed with completely quenched polarization, i.e.. 

External mass transport through the gas boundary layer usually provides a negligible resistance to the progress of reaction and hence has only a small effect on the overall rate. 

Case 1 describes the situation at extremely low oxygen partial pressures (oxygen partial pressures below the equilibrium partial pressure for oxide formation), where only metal halides can be formed and have to diffuse through the gas boundary layer, thus, determining the rate of metal consumption by the corrosion... 

Open system Transport rates in gas boundary layer... 

Schematic of the three situations that are used for the assessment of metal chloride evaporation, (a) Vapor pressure of the gaseous metal chloride above solid or liquid metal chloride in a closed system (value used in Equation 13.23 and for determining T ). (b) Equilibrium partial pressure of pMe Cl in a closed system containing O2 and CI2 as gas phase and Me, Me Oj, and Me,.Cly as solid or liquid phases (value used for the establishment of the "static" quasi-stability diagram), (c) Mej.Cly transport rate in the gas boundary layer (metal consumption rate) as criterion for the amount of chlorine-induced corrosion in an open system with gas flow across the surface (value used for the establishment of the "dynamic" quasi-stability diagram).

If Psio at the Si (s) surface is higher than Si02 (s) will be stable at the Si (s) surface. The Fq is obtained from the Si(s)-SiO(g)-02(g) equilibrium. However, Po. at the Si (s) is significantly different from that in a bulk gas stream due to a gas boundary layer above the Si (s) surface. Therefore, Wagner proposed a model to estimate the Fq by assuming the steady state... 

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