Effective diffusion coefficient porous layer

Here, the length L in (7.38) has been replaced by porous layer thickness d and the surface area Aeff. The effective diffusion coefficient D0,eff characterizes the transport through porous medium and includes both regular diffusion and the Knudsen diffusion coefficient >o,Kn, which has a different temperature dependence from diffusion in bulk. 

The reduction of magnetite to iron with the formation of a porous metal layer can also be treated quantitatively in an analogous manner, as long as gas diffusion in the pores of the metal, and not a phase boundary reaction, is rate-determining. In this case, one needs only express the oxygen flux in eqs. (9-32) and (9-33) in terms of the appropriate effective diffusion coefficients for gas transport in porous layers. 

Porous silicon layers with a porosity of 60% on n-type (lll)Si substrates were prepared by anodic etching under white illumination. Silver/porous-silicon/Si and metal Ag/Si structures were fabricated by evaporation of thin metal films onto the porous silicon or Si surface, respectively. The diffusion annealing of structures was carried out in air at 100-250C. Examination of the Ag concentration distribution in porous silicon layers and monocrystalline Si substrates was performed by successive removal of thin layers and measurement of the energy dispersive X-ray fluorescence intensity of AgK( peaks. The effective diffusion coefficients were described by ... 

Layer-by-layer radiometric analyses, using 4 /in2+ tracers at 750 to 1050C, were carried out on essentially non-porous material with a grain size of more than 0.001 mm. The resultant effective diffusion coefficients at 900C ranged from 2.8 x 10- I to 2.0 x 10-9cm2/s, and could be described by... 

In the porous gas diffusion layer, the effective diffusion coefficient is different from the intrinsic... 

Thus, for a high value of Bi, the overall effectiveness is dominated by the influence of pore diffusion (hoveraii hpore)- The minimum value of Bi can be roughly estimated as follows The minimum mass transfer coefficient min equals the ratio of the molecular diffusivity Dmoi to the maximum thickness of the boundary layer, 5max [Eq. (3.2.67)] for a single spherical particle, 5, is about dp/2 (for Sf min = 2). Dmoi is about ten-times higher than the effective diffusion coefficient in the porous structure (Section 3.2.2.3). Thus Eq. (4.5.104) yields ... 

D = effective diffusion coefficient of hydrogen in porous anode electrode = thickness of anode electrode layer... 

Do = effective diffusion coefficient of oxygen in porous anode electrode Lj = thickness of cathode electrode layer p... 

A brief review of the limited number of in situ measurements is then presented. This is followed by a review of the available correlations proposed for estimating these kinds of MTCs in Section 12.4. Section 12.5 is concerned with the subject of classical molecular diffusion in porous media at steady state. The presentation includes a brief description of the upper sediment layers, measurement techniques, laboratory measurement data of effective diffusion coefficients, and models for prediction and extrapolation. A guide appears in Section 12.6 to steer users to suggested procedures for estimating these two types of MTCs. The chapter ends with some example problems and their solutions in Section 12.7. 

In Eq. (14-1) is the external mass-transfer coefficient discussed in Chap. 10 [Eq. (10-10)]. The rate through the product layer, Eq. (14-2), is evaluated at r = r Z>e is the effective diffusivity of A through this porous layer. In writing Eq. (14-3) the chemical reaction at is assumed to be first order in A and irreversible. It is also taken as directly proportional to the outer surface area of unreacted core B ... 

In a porous medium the value of diffusion coefficient, beside this, is affected by porosity and dual electric layer at the separation surface of water with other media. They obstruct the diffusion in underground water and decrease the diffusion coefficient. The diffusion coefficient taking this effect into account is called intrinsic diffusion coefficient. Its value is equal to... 

Since this depth is significantly smaller than the dimensions of the piece of catalyst, and at the same time is much greater than the diameter of individual pores, the phenomenon can be represented schematically by introducing the effective coefficient of diffusion through the porous substance (which depends on the number of the pores and their diameters), and by examining a layer of the catalyst of indefinite depth with a flat surface. 

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