Diffusion with chemical reaction

Figure 4.5. Steady-state diffusion with chemical reaction.

Schumann, U. 1989. Large eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmospheric Environment 23(8) 1713-26. 

The constants A and B can be determined from the solutions available for the simple cases in which either = 0 or uw = 0. The first limiting case corresponds to the dissolution of a planar wall in a semiinfinite liquid in steady flow (Blasius flow), while the second limit corresponds to steady-state diffusion with chemical reaction in a stagnant fluid. For Blasius flow at large Schmidt numbers [2],... 

Bischoff, K.B., Chem. Eng. Sci. 22 (1967), 525-530 An extension of the general criterion for importance of pore diffusion with chemical reactions... 

This last condition is the most doubtful, especially in the case of small particles. A thorough treatment of diffusion rates, based on Eq. (13), has recently been presented (Hansen and Ugelstad, 1978). In this derivation the concentration profile inside the particles, as illustrated in Fig. 2, is also taken into account. The derivation is based on the equations for diffusion with chemical reaction (Danckwerts, 1951), expressing the steady-state rate of diffusion at the inside particle surface by... 

The basis for the solution of mass diffusion problems, which go beyond the simple case of steady-state and one-dimensional diffusion, sections 1.4.1 and 1.4.2, is the differential equation for the concentration held in a quiescent medium. It is known as the mass diffusion equation. As mass diffusion means the movement of particles, a quiescent medium may only be presumed for special cases which we will discuss first in the following sections. In a similar way to the heat conduction in section 2.1, we will discuss the derivation of the mass diffusion equation in general terms in which the concentration dependence of the material properties and chemical reactions will be considered. This will show that a large number of mass diffusion problems can be described by differential equations and boundary conditions, just like in heat conduction. Therefore, we do not need to solve many new mass diffusion problems, we can merely transfer the results from heat conduction to the analogue mass diffusion problem. This means that mass diffusion problem solutions can be illustrated in a short section. At the end of the section a more detailed discussion of steady-state and transient mass diffusion with chemical reactions is included. 

According to (2.338), for steady-state, geometric one-dimensional diffusion with chemical reaction we have... 

DeLancey, G. B. and Chiang, S. H., Analysis of Nonisothermal Multicomponent Diffusion with Chemical Reaction, Ind. Eng. Chem. Fundam., 19, 344-349 (1970b). 

Modeling Diffusion with Chemical Reaction External Resistance to Mass Transfer 771... 

The literature contains numerous studies concerning the problem of diffusion with chemical reaction, e.g. Aris, 1975a,b Carberry, 1976a,b Hite and Jackson, 1976 Jackson, 1977 Froment and Bischoff, 1979 Satterfield, 1980 Smith, 1981. 

The starting point for studying the diffusion with chemical reactions for multicomponent systems in porous catalyst pellets is to derive the mathematical models that describe the system under study. 

Example 1.18 Multicomponent, Steady-State, Gaseous Diffusion with Chemical Reaction... 

Porter,K. and D.Roberts. "Similarities between the effect of different flow pattern on diffusion with chemical reaction near an interface". Chem.Enqnq.Sci. 24 (1969) 695. 

We might also consider the problem of diffusion with a chemical reaction. In a sufficiently strong magnetic field, molecular clusters can be formed. For the case of air, the clusters N2-O2-O2 are preferable [36]. This can be regarded as a problem of diffusion with chemical reaction, which has described [31,37]... 

Diffusion with chemical reaction. A gas is absorbed by a solution with which it reacts chemically [6], The rate of diffusion in the liquid can be assumed proportional to the concentration gradient, and the diffusing gas is eliminated as it diffuses by a first-order chemical reaction. The reaction rate is proportional to the concentration of the solute gas in the liquid. Obtain an expression for the concentration in the liquid as a function of the distance from the gas-liquid interface (see Figure 3.12). 

The analytical integration of the differential equation for diffusion with chemical reaction in a catalyst particle is achievable just for first-order reactions. A generalized modulus has been proposed for extending the use of the // expression in Equations 2.61 and 2.64a to any type of rate expression [17], at least approximately. For irreversible nth order reactions, the generalized modulus for a sphere becomes dependent on the exterior surface concentration ... 

In the case of more complicated kinetic expressions like LHHW equations, the effectiveness factor rj can be determined by numerical integration of the differential equations for diffusion with chemical reaction. The complex kinetics of a number of reactions can practically be approximated by simpler power function expressions. 

Schumann U (1989) Laige-eddy simulation of the turbulent diffusion with chemical reactions in the convective boundary layer. Atmos Environ 23(8) 1713-1727 Schumann U (1992) Simulations and parameterizations of laige eddies in convective atmospheric boundary layers. In Proceedings of a workshop held at the European Centre for Medium-Range Weather Forecasts (ECMWF) on Fine Scale Modelling and the Development of Parameterization Schemes, 16-18 September 1991, ECMWF Shames IH (1962) Mechemics of fluids. McGraw-Hill, New York... 

Burghardt A, Aerts J (1988) Pressure changes during diffusion with chemical reaction in a porous peUet. Chem Eng Process 23 77-87... 

Diffusion with chemical reaction in the study of chemical catalysis or enzyme catalysis... 

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