Diffiisivity experimental value

H-bond lifetimes tiq from ref. 46. (2) Probability pg calculated ftdlowing the procedure in Section V.A. (3) Relaxation times calculated from Eq. (6.1) with the same conditions (6.2) for H2O and D2O. (4) Experimental values of dielectric relaxation times from ref. 75 ( ) at 10°C (t) extrapolated. (5) Self-diffiision coefficients calculated from Eq. (7.5) assuming for D2O the same Dj-(ij/) used for H2O. (6) Self-diffusion experimental data from ref. 63. 

Estimate the diffiisivity of allyl chloride (C3H5C1) in air at 298 K and 1 bar using the Wilke-Lee equation (1-49). The experimental value reported by Lugg (1968) is 0.098... 

It is important to note that the rates of reactions in solid polymers will be controlled not only by the rate of diffiision but also by the solubility of the permeant in the polymer. For example, the diffiision constant for oxygen is quite large in many polymers, but usually the solubility is very low, and as a result, rates of oxidation tend to be quite small. Experimental values of the permeability P and diffiision constant D for various organic permeants and oxygen in low-density polyethylene (8) illustrate this point (see Table 2). 

This section provides some Qqiical experimental values of interdiffiision coefficients in gases, in solutions of nonelectrolytes, electrolytes, and macromolecules, in solids, and for gases in porous solids. Theoretical and empirical correlations for predicting diffiisivities will also be discussed for use in those cases where estimates must be made because eiqierimental data are unavailable. A critical discussion of predicting diffiisivities in a fluid phase can be found in the book by Reid et al. 

At ambient temperature and pressure, gas-phase diffiision coefficients are of the order of 10 -10 fP/s (lO -lO" mVs). Table 2.3-1 presents some rqiresentative values for binary gas mixtures at 1 atm. Marrero and Muon" have provided an extensive review of experimental values of gas phase binaiy diffiisivities. 

The permeability coefficient k for viscous flow through fibrous media is observed to vary in proportion to the bulk porosity and density of nanofiber mat and in inverse proportion to the pore size of the mat Tomadakis et al. (Robert and Lochner, 1990) conducted a comparative survey of various established permeability models for non woven mats, and the conduction-based model was found to yield results closest to experimental values. This model was modified to take into account bulk diffiision tortuosity, and the mathematical formula for evaluating permeability constant k for randomly overlapping fiber structure was derived as given by Eqn (8.8). 

The treatment can be modified to include effects of the temperature development and tilting of the susceptor by using the temperature dependence of the diffiision coefficient and adjusting d and (191). In this manner, the experimental data can be correlated, but the model has limited capability for predicting behavior beyond the particular set of experiments used to fit the model. In fact, because of the low values of the Reynolds number (<50) in typical horizontal CVD reactors, film theory and simple... 

Experimental and theoretical studies on H diffusion in silicon at lower temperatures, where trapping of hydrogen at defects and impurities and H2-molecule formation are significant, discovered much lower effective diffiisivities. Values for the H-diffiision coefficient in silicon expected from an extrapolation of the diffusion coefficient of (11.1) to lower temperatures are several orders of magnitude higher than experimentally obtained diffiisivities. This is illustrated in Fig. 11.2, which shows (11.1) and (11.2) extrapolated to low temperatures with experimentally determined values from Johnson et al. (1986). 

I gwe / Desorption curves of benzaUehyde from amberUte partkles into methanol. Experimental (XAD-4). Experimental (XAD-7). Transient upttAe solution of Eq. 3.5.e-5a for the indented values of the apparent diffiisivity. Jn is the total armnait of betaaldehyde desorbed at infinite time (from Komiyanu and Smith [70]). 

Let s compare of this value D with the diffiision coefficients of the macro-radicals in polymeric matrixes TGM-3, TGM-3-GMA and GMA which estimated experimentally [24] based on the kinetics of macroradicals decay, which under the given temperature consist of 10 + 10 mVs. 

There is a very important difference, however. Notice, particularly, that the width of the three bands in any of the three figures is independent of the D values. You see, in using the binomial expansion to represent the results of a multistage separation process, only the role played by equilibrium considerations was considered. To obtain results that match experimental reality, however, this must be amended to include the effects of diffiision and other related nonequilibrium processes. This will be dealt with in the next section, which concerns chromatography. 

A single experimental measurement of the average diflbsivity over the whole composition range gave a value of 7.4 X 10 " m /s. These solutions do form neatly ideal liquid mixtures so the diffiisivity of a 50/50 mixture could be estimated from Vignes correlation ... 

And, thus, the macroscopic diffusivity can be obtained from a consideration of the random atomic motions. The importance of this and the previous derivation is that uq and t are both parameters that can be easily extracted from a KMC simulation and thus diffiisivities can be obtained that can be used to compare with experimentally determined values or that can be used to calibrate less easily measured parameters, such as atom-electrolyte interactions or interspecies bonding, that are used to determine the energy barriers in the local bond-breaking model for diffusion and dissolution. 

The ternary diffusion coefficient strongly depends on the solution concentration. In order to calculate accurate mass transfer coefficients, experimental data of diffusion coefficients at the interest concentrations and temperatures are necessary. However, data are not available at concentrations and temperature used at the present study, it was assumed that the ternary diffusion coefficients were equal to the binary diffusion coefficients. The binary diffusion coefficients of the KDP-water pairs and the urea-water pairs were taken from literature (Mullin and Amatavivadhana, 1967 Cussler, 1997). The values were transformed into the Maxwell-Stefan diffiisivities using the thermodynamic correction factor. 

Fig.3. Diffiision coefficients D as derived from a fit of the experimental data in Fig.2 with the solution of the diffusion equation for cylindrical sample (open circles) in addition, values corrected for the amount of gas to be transported (D d>pseudo, fuU circles) are depicted. For comparison the theoretical diffusion coefficients for gas phase diffusion in cylindrical pores are also included (dashed lines) hereby the value of the macroporosity (50%) and a tortuosity factor of 3 are taken into account. The macroporosity was calculate fix)m the bulk density of the sample and the micropore volume (macroporDsity=total porosity—microporosity= 86 % - 36%).

Hie %ur ce diffiision is therefore related to transport alrmg the micropores rather than the external sur ce of the particles that form the skeleton of dm angels. In addition, gas phase tran rt takes place that can be described by a superposition of molecular diffusion and viscous flow in capillaries with an avnage diameter of about the pore size in dm respective sample and a tintimsity of about 3. The value of 3 was chosen to matdi the experimental data it is slighdy U er dam the value of about 1.8 deteded for odmr carbon aerogels ([10] 1.8 =1.35. ... 

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