Effective diffusion coefficient material

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. 

Gas diffusion in the nano-porous hydrophobic material under partial pressure gradient and at constant total pressure is theoretically and experimentally investigated. The dusty-gas model is used in which the porous media is presented as a system of hard spherical particles, uniformly distributed in the space. These particles are accepted as gas molecules with infinitely big mass. In the case of gas transport of two-component gas mixture (i = 1,2) the effective diffusion coefficient (Dj)eff of each of the... 

The term in the square bracket is an effective diffusion coefficient DAB. In principle, this may be used together with a material balance to predict changes in concentration within a pellet. Algebraic solutions are more easily obtained when the effective diffusivity is constant. The conservation of counter-ions diffusing into a sphere may be expressed in terms of resin phase concentration Csr, which is a function of radius and time. 

An example of a material (Li3Sb) with a very large Wagner factor is shown in Fig. 8.3. The effective chemical diffusion coefficient is compared with the diffusivity as a function of non-stoichiometry. These data were determined by electrochemical techniques (see Section 8.5). An increase of the diffusion coefficient is observed at about the ideal stoichiometry which corresponds to a change in the mechanism from a predominantly vacancy to interstitial mechanism. The Wagner factor W is as large as 70 000 at the ideal stoichiometry. This gives an effective diffusion coefficient which is more typical of liquids than solids. It is a common... 

To calculate the release through diffusion of an entrapped residue, Barraclough et al. (2005) considered the size of organic matter particles (effective radius 10" to 10 cm) and the effective diffusion coefficient of small organic molecules in a sorbing medium (D 10 cm s )- The time for 50% of the material in a sphere to diffuse out is given by... 

One should take into account the specific features of gas diffusion in porous solids when measuring effective diffusion coefficients in the pores of catalysts. The measurements are usually carried out with a flat membrane of the porous material. The membrane is washed on one side by one gas and on the other side by another gas, the pressure on both sides being kept... 

An important problem in catalysis is to predict diffusion and reaction rates in porous catalysts when the reaction rate can depend on concentration in a non-linear way.6 The heterogeneous system is modeled as a solid material with pores through which the reactants and products diffuse. We assume for diffusion that all the microscopic details of the porous medium are lumped together into the effective diffusion coefficient De for reactant. 

Figure 12.20 A schematic representation of the effective diffusion coefficients as a function of the diffusion time in the case of hindered diffusion. For short diffusion times Deff equals the diffusion coefficient of the particle in the material in the absence of diffusion barriers. For longer diffusion times the diffusion is slowed down by the barriers. In the long time limit the diffusion coefficients approaches Ttortuosity...

For both samples a small decrease of the effective diffusion coefficient for short A is found. This could indicate some diffusion restriction. However, the samples consisted of small pieces of material pressed together in the NMR tube. Unfortunately, at the moment the possibility that the initial decrease of Deff is caused by a motion (approximately 1 pm would be sufficient ) of some of the particles caused by the pulsed field gradients cannot be excluded. For short diffusion times such a motion has a large effect, for longer A such motions can be neglected. 

For pore sizes ranging from 50 to 200 A, which are comparable to the sizes of the diffusing solute molecules and are called microporous, the diffusion of solutes may be substantially restricted by polymer materials. A diffusing molecule may be hindered from entering the pores and be chafed against the pores walls. Equation (6.30) incorporates these factors into the effective diffusion coefficient as ... 

This test, which lasts 64 days and is described in Dutch standard NEN 7345, is intended to determine leaching from products or stabilized waste materials as a function of time. The product is immersed in acidified demineralized water. This eluate is refreshed at seven specified times. Analysis of the eluates enables the leaching per square meter of product surface area and the effective diffusion coefficient to be calculated. 

The effective diffusion coefficient becomes negative for some range of composition when x is sufficiently large. The separation of phases requires an up-hill diffusion (characterized by negative Deff) in which the material moves against concentration gradients. The kinetics of the separation and the morphology of separated phases depend on the details of such diffusion. 

In the present work, a simulation strategy is formulated to study the performance of cathode materials in lithium ion batteries. Here micro scale properties, for example, diffusion of spherical electrode particle within the periodic boundaiy condition, 0electrode particles move in each step to its nearest neighbor distance, employing the condition ir j) > e -dLi lds ), where ir represents the random number, dLil is the nearest neighbor distance for the Li ion in the absence of solvent and ds being the thickness of the sohd phase. The MC codes involve macro scale properties, namely, solvation effects, diffusion coefficients and the concentration gradient... 

It is further assumed that B is not present in the feed oil, i.c. Cno =0 and that the reactions are taking place in spherical particles of porous material and are controlled by effective diffusion coefficients Da = Da = D. (The actual catalyst particles used in the experiments were short cylinders). 

Just as we were able to estimate an effective diffusion coefficient for the porous pellet, so we can obtain an effective thermal conductivity, such that the heat flux across a unit area within the pellet is times the gradient of temperature normal to that area. Wc shall not go into the relation between kt and the other physical properties of the porous material—this is well covered by Petersen in his fifth chapter—but it is worth pointing out that whereas the diffusion of matter is largely through the pores, that of heat is rather through the solid material. Values of kt for porous materials are of the order of cal/sec cm°C. 

FIGURE 5.16 Examples of hindered diffusion, (a) The effective diffusion coefficient (D ) of water in various materials as a function of their mass fraction of water (o>w). (Adapted from Bruin and Luyben see Bibliography.) (b) The effective diffusion coefficient (D ) of some molecules and a virus in polymer gels of various concentrations (%). (Very approximate results, obtained from Muhr and Blanshard see Bibliography.)... 

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