Bulk diffusivity

This equation relates the temporal concentration of a diffusing chemical to its location in space. In real soil and aquifer materials, the diffusion coefficient can be affected by the temperature and properties of the solid matrix, such as mineral composition (which affects sorption, a process that can be difficult to separate from diffusion), bulk density, and critically, water content. 

The MD simulations show that second shell water molecules exist and are distinct from freely diffusing bulk water. Freed s analytical force-free model can only be applied to water molecules without interacting force relative to the Gd-complex, it should therefore be restricted to water molecules without hydrogen bonds formed. Freed s general model [91,92] allows the calculation of NMRD profiles if the radial distribution function g(r) is known and if the fluctuation of the water-proton - Gd vector can be described by a translational motion. The potential of mean force in Eq. 24 is obtained from U(r) = -kBT In [g(r)] and the spectral density functions have to be calculated numerically [91,97]. 

It has been found that a higher deposition temperature causes a wider deposition zone. The above deposition process has been analyzed through a theoretical model that reveals the importance of the vapor and gas diffusivities, bulk phase reactant concentrations and the pore size of the support [Lin and Burggraaf, 1992]. Practically speaking, in order for the pores of the support to be plugged, their pore diameters should not be too large, preferably significantly smaller than 1 pm. 

In addition to diffusion, bulk flow can occur within a reacting pellet (Beveridge and Goldie, 1968 Gower, 1971 Sohn and Sohn, 1980). This effect is considerably magnified for reactions with volume change such as... 

Mass transport in an adsorbent particle can be viewed as a combination of several mechanisms, as shown in Figure 14.8. Macropore and micropore diffnsion are shown and conld be considered as examples of intraparticle diffusion. Bulk flow or conveyance through the particle (e.g., via connected pores) is shown in that figure but, to be significant, requires high porosity or a large... 

In technological applications as well as in scientific experiments specific boundary conditions are often given, such as definite changes of the interfacial area. A schematic representation is given in Fig. 4.2. which shows various bulk and interfacial transport processes of surface active molecules diffusion in the bulk, interfacial diffusion, bulk flow of different origin, interfacial compression and dilation. 

SiC content Thermal diffusivity Bulk den.sity Flcat capacity Cp (.Eg -K l Thermal... 

Sintering can be brought about by a variety of reactions. Of these, material transport by viscous flow is important in glasses but less so in metals or ceramics. Evaporation and condensation is important in rather volatile compounds such halides and some oxides. Diffusion - bulk, grain boundary and surface diffusion - is important for refractory materials and, for these materials, the presence of traces... 

The rate of flow of material into the neck region between two spheres will depend on the mechanism of atomic transport. Four different mechanisms were investigated by Kuczynski, some 50 years ago. These were viscous flow, surface diffusion, bulk diffusion and vapour transport by evaporation and condensation. The rate of neck growth was found to be quite different from one mechanism to another. They are usually expressed in terms of the ratio of the neck radius x to the sphere radius r (defined in Figure 8.22) ... 

Further development of this model incorporating diffusion, bulk flow, transmembrane flux, and matrix shrinkage [42-44] showed that the cell membrane is the main barrier to mass transfer only for single cells or thin slices of tissue. When the thickness of the sample increases, the extracellular space may become the limiting factor [45]. 

In Fig. 8.4-14 the strrface potential y/ is shown as a function of the distance D. The highly ordered Helmholtz layer exists close to the surface for Z) 0 and can be distinguished from the diffuse bulk layer. The gieek letter cr in (8.4-63) denotes the strrface charge density. 

Bulk Diffusion Bulk or ordinary diffusion, with the diffusion coefficient Dab or DA.mix> occurs in the void space of the pores as a result of collisions between gas molecules and is likely to dominate when (i) the pores are macropores larger than 100 A in radius, (ii) the gas is relatively dense, that is, at high pressures, and (iii) the pores are filled with a liquid. 

Burghardt and Aerts [12] proposed a method for evaluation of the pressure change in an isothermal porous pellet within which a single chemical reaction takes place, accompanied by mass transfer by Knudsen diffusion, bulk diffusion and viscous convective flow of the reacting mixture. The pressure change did also depend on the reaction and on the mixture composition on the pellet surface. It was concluded that the pressure changes in a catalyst pellet under conditions normally encountered in industry are most likely so small that they can be neglected in process simulations. 

Maxwellian diffusion (bulk molecular diffusion) in moderately large pores (macropores) or Knudsen diffusion in pores (micropores) which have a diameter smaller than the mean free path of the adsorbate molecules ... 

Bulk (Molecular) Diffusion Bulk or molecular diffusion is the predominant mode of diffusion in large pores. For a gas, molecular diffusion occurs when r km- For liquids, molecular diffusion occurs when r is much greater than the radius of the diffusing molecule. In the molecular diffusion regime, collisions between molecules are much more frequent than collisions between molecules and the walls of the pore. Diffusion takes place through molecule-molecule interactions. 

In a porous electrode, reaction takes place most easily at the gas—electrodeelectrolyte boundaries (triple-phase boundary, TPB). Oxygen adsorbed on the electrode must be transported to the electrolyte through the surface or bulk diffusion. Bulk diffusivity has been studied for various perovskites and related oxides. 

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