Diffusion-Viscous Flow

In polyclusters, at a sufficiently high temperature, when the atomic diffusion at the boundaries becomes appreciable, there occurs a diffusion-viscous flow, similar to that of polycrystals. In this case, in a macroscopically homogeneous solid, the rate of the plastic deformation, eik, and the tensor aik = aik — Sp r(k/3 are related as 

The diffusion-viscous flow changes to an inhomogeneous slip at a rather high strain rate or with temperature decrease. The boundary between homogeneous and inhomogeneous plastic deformations of a polycluster on the (a, T) plane is given by [6.29] 

In deriving this expression, we assumed that Ds o2vcexp( — E,/J). For s = 2eV [6.73], vc 1012 sec-1, rci 102a, the above expression is in fair agreement with the experimentally established boundary of the homogeneous-inhomogeneous flow transition for the amorphous Pd-Si alloy [6.63]. 

If a a, then a mixed flow may occur, at which the diffusion-viscous plastic-deformation is accompanied by a thermally activated formation of new glide layers. 

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For a given pressure gradient across a porous medium, the mass balance equation can be described as follows, provided that Knudsen diffusion, viscous flow and surface diffusion are additive to the total flux. 

The Knudsen diffusion, viscous flow and surface diffiision for strongly adsorbing vapors are well described at low range of pressures in this paper. The collision-reflection flictor for Knudsen diffusion is found to be not constant but exhibit a modest increase with an increase in pressure. The dependence of the Knudsen diflusion for n-hexane on pressure is stronger than that of the other vapors. Moreover the activation energy for the surflice diffiision of ra-hexane exhibits a faster decreasing behavior in comparison with the others. Conclusively, the reason for the minimum appearance in the total permeability of ra-hexane can be attributed by the interplay between the Knudsen diflusion and surface diffusion. 

The mathematical models of such processes in SOFC as charge, heat and mass transfer, diffusion, viscous flow of gases in channels were elaborated. The models gave necessary information for optimizing the SOFC design. 

We have presented above the three basic equations (8.8-1 to 8.8-3) for the case where bulk diffusion-Knudsen diffusion-viscous flows are simultaneously operating. What we will do in this section is to combine them to obtain a form which is useful for analysis and subsequent computation as we shall show in Chapters 9 and 10. 

We have presented the three different formulations for the bulk diffusion-Knudsen diffusion-viscous flow in Sections 8.8.1 to 8.8.3. Now we will show how these formulations can be used to derive useful equations for limiting cases which are often encountered in adsorption systems. 

The hard-sphere model, as described in Chapter 2, only accounted in a qualitative fashion for the mass, momentum, and energy transport that underlie the phenomena of diffusion, viscous flow, and heat conduction. For systems other than monatomic gases, the model was of limited utility. Thus, its failure to predict reasonable values of the Arrhenius -factor is to be expected. 

In the absence of any concentration polarization, and Cfi are equal to Cg and respectively. The extent of concentration polarization and its effects on the solvent flux and solute transport for porous membranes and macrosolutes/proteins can be quite severe (see Section 6.3.3). This model is often termed the combined diffusion-viscous flow model (Merten, 1966), and it can be used in ultrafiltration (see Sections 6.3.3.2 and 7.2.1.3). The relations between this and other models, such as the finely porous model, are considered in Soltanieh and Gill (1981). 

From the solute flux expression (3.4.91c) in the combined diffusion-viscous flow model, one can develop an expression for S,n,e or Rn e- Consider relation (3.4.93b) ... 

Transport processes include diffusion, viscous flow, and heat conduction. There are a number of approximate theories of transport processes in liquids, most of which are based on classical statistical mechanics. 

Experimental evidence of neck growth was first demonstrated by Kuczynski, who in 1949 sintered large polycrystalline particles onto flat polycrystalline substrates. Theories, based on a two sphere model (each a single crystal), were developed to determine the rate of neck growth and the rate at which particle centres approach one another. These theories conclude that the rate of neck growth is inversely proportional to particle size raised to a power that depends on the mass transport path. Many mass transport paths were subsequently considered, bulk diffusion, surface diffusion, grain boundary diffusion, viscous flow, evaporation-condensation, liquid solution-reprecipitation, and dislocation motion (see reference 8 for a review). 

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