Effective gas diffusivity

The magnitude of the ratio of effective gas diffusivities in the macro- and micropore regions is in the range 10 - 100 for most industrially important catalysts [6]. This ratio depends upon the pore size distributions of the pellets. Hashimoto and Smith [7] have... 

To a very high Pe number, one can consider a fixed-bed reactor as a pseudo-homogeneous one, therefore, a reactor with ideal behavior. In these conditions, its superficial velocity is high and/or the effective gas diffusion in the pores (D ) is low. It means that if (1/Pe) 0, the gas residence time in the reactor tends to the average... 

V. P. Schulz, P. P. Mukheijee, J. Becker, A. Wiegmann, and C. Y. Wang, Numerical Evaluation of Effective Gas Diffusivity - Saturation Dependence of Uncompressed and Compressed Gas Diffusion Media in PEFCs , ECS Trans., 3,1069 (2006). 

Effective gas diffusion coefficients of H2 and CO in Eqs.(3-4) arel.467xl0" ° 3.828x10 " x/ respectively. Reduction fraction in a controlled volume... 

The existence of a close analogy in the kinetics and mechanism of electrocatalytic processes controlled by activation of hydrogen substantially simplifies selection of the best catalyst. It becomes possible to model slow reactions taking place in complicated apparatus more rapidly and simply. In the development of effective gas-diffusion... 

Since the blocked gas inside of the capillary is dissolving in the liquid and then diffusing towards the exit of the channel, the meniscus of the liquid crosses the position l and goes deeper. This second stage of capillary filling with liquid is called diffusive imbibition and plays an important role in PT processes. The effect of diffusive imbibition upon PT sensitivity has been studied in [7]. 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

In addition to oxidation itself, gas diffusion into the base metal can be more damaging than the actual loss of metal from the surface. Thus the loss in mechanical properties owing to diffusion of oxygen into niobium makes it more difficult to protect niobium against oxidation damage than molybdenum, even though molybdenum has less resistance to normal oxidation effects than niobium. 

Foams are thermodynamically unstable. To understand how defoamers operate, the various mechanisms that enable foams to persist must first be examined. There are four main explanations for foam stabiUty (/) surface elasticity (2) viscous drainage retardation effects (J) reduced gas diffusion between bubbles and (4) other thin-film stabilization effects from the iateraction of the opposite surfaces of the films. 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

The overall set of partial differential equations that can be considered as a mathematical characterization of the processing system of gas-liquid dispersions should include such environmental parameters as composition, temperature, and velocity, in addition to the equations of bubble-size and residence-time distributions that describe the dependence of bubble nucleation and growth on the bubble environmental factors. A simultaneous solution of this set of differential equations with the appropriate initial and boundary conditions is needed to evaluate the behavior of the system. Subject to the Curie principle, this set of equations should include the possibilities of coupling effects among the various fluxes involved. In dispersions, the possibilities of couplings between fluxes that differ from each other by an odd tensorial rank exist. (An example is the coupling effect between diffusion of surfactants and the hydrodynamics of bubble velocity as treated in Section III.) As yet no analytical solution of the complete set of equations has been found because of the mathematical difficulties involved. To simplify matters, the pertinent transfer equation is usually solved independently, with some simplifying assumptions. 

In a discussion of these results, Bertrand et al. [596,1258] point out that S—T behaviour is not a specific feature of any restricted group of hydrates and is not determined by the nature of the residual phase, since it occurs in dehydrations which yield products that are amorphous or crystalline and anhydrous or lower hydrates. Reactions may be controlled by interface or diffusion processes. The magnitudes of S—T effects observed in different systems are not markedly different, which indicates that the controlling factor is relatively insensitive to the chemical properties of the reactant. From these observations, it is concluded that S—T behaviour is determined by heat and gas diffusion at the microdomain level, the highly localized departures from equilibrium are not, however, readily investigated experimentally. 

Solids-liquid-gas mixing 275 Solids-liquid mixing 275 Solids—solids mixing 275 Sonic velocity 150, 156,158, 189 Sorel effect, thermal diffusion 589 Spalding, D. B, 393,562 Sparrow, E. M. 465, 564 Specific energy, open channel flow 98... 

Table 1.6 Characteristic quantities to be considered for micro-reactor dimensioning and layout. Steps 1, 2, and 3 correspond to the dimensioning of the channel diameter, channel length and channel walls, respectively. Symbols appearing in these expressions not previously defined are the effective axial diffusion coefficient D, the density thermal conductivity specific heat Cp and total cross-sectional area S, of the wall material, the total process gas mass flow m, and the reactant concentration Cg [114].

If the gas diffusion between bubbles is reduced, the collapse of the bubbles is delayed by retarding the bubble size changes and the resulting mechanical stresses. Therefore single films can persist longer than the corresponding foams. However, this effect is of minor importance in practical situations. Electric effects, such as double layers, form opposite surfaces of importance only for extremely thin films (less than 10 nm). In particular, they occur with ionic surfactants. 

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