Diffiisivity estimation

This mixing rule is used to determine the diffiisivity of any component in a / -I-1 component mixture and requires binary diffiisivities of component i with all other components. It has been estimated that errors are about 5 percent greater than the greatest error in the binary diffiisivities. Fairbanks and Wilke, using the same Eq. (2-154), made the same recommendation with essentially the... 

For concentrated binary nonpolar liquid systems (more than 5 mole percent solute), the diffiisivity can be estimated by a molar average mixing rule developed by Caldwell and Babb, " Eq. (2-156). 

The effective diffiisivities of DCB in SC C02 for these runs are optimized to De = 4 10 9 m /s. The corresponding tortuosity factors amount to Dm/Dc = 2.3 and 2.5 when estimating the molecular diffusivity by means of the correlation of [10]. These values are in reasonable agreement with respect to those found in the literature. For example in a related study of... 

Combinations of weather conditions, wind speed and wind direction along widi boiling point, vapor density, diffiisivity, and heat of vapori2ation of die chemical released vary the Irealdi impact of die released chemical on the nearby population. To model a runaway reaction, tire release of 10,000 gallons was assumed to occur over a 15-minute period. Tire concentration of the chemical released was estimated, using proc ures described in Part III (Chapter... 

Nitrogen diffusion in nitrides suchas 5-TiNi x, 5-ZrNi x and 5-HfNi-x has an activation energy of 2-3 eV. Although the metal diffiisivity in transition metal nitrides has not yet been investigated in detail, the activation energy of that process is probably much higher and can be estimated to be ca. 7-8 eV. Table 2 shows diffiisivity data of transition metal nitrides. 

In selective systems application of the Helfferich-Tunitsky criterion [2,5,16,22,23] may result in erroneous estimates of the contribution of film and intraparticle diffusion. This is because the ion diffiisivities in the resin phase that are included in this criterion can undergo very abrupt changes in magnitude with the reversal of exchange direction. This was not taken into account by Helfferich and Tunitsky in the theoretical expressions as they used them for conventional IE. Moreover the criterion neither includes the influence of the equilibrium parameters characterizing the selectivity in the resin phase nor is there any account for co-ion invasion. The effective diffusivity of the kinetic process may be quite different if these fectors are taken into consideration. 

The rate of contaminant adsorption onto activated carixm particles is controlled by two parallel diffusion mechanisms of pore and surface diffusion, which operate in different manners and extents depending upon adsorption temperature and adsorbate concentration. The present study showed that two mechanisms are separated successfully using a stepwise linearization technique incorporated with adsorption diffusion model. Surface and pore diffiisivities were obtained based on kinetic data in two types of adsorbers and isothermal data attained from batch bottle technique. Furthermore, intraparticle diffiisivities onto activated carbon particles were estimated by traditional breakthrough curve method and final results were compared with those obtained by more rigorous stepwise linearization technique. 

In this paper, we will present a procedure to separate pore diffusion and surface diffusion in GAC adsorption by use of a stepwise linearization. Furdiermore, a simplified method to estimate concentration dependency of apparent diffiisivities from breakthrough curves will be proposed. 

At least in the sterns studied, errors of less than a factor of two are found between the total and partial immobilization cases. In contrast the diffusion constants obtained by the simple time lag equation [Eq. (6)] are as small as one ei th of those estimated for the Henry s law mode diffiisivity using the completly immobilized model (F = 0) in some cases. This means that actual errors of iqj to four fold in estimation of the true Henry s law mode diffiisivity, Dp, can possibly be introduced by use of the simple time lag technique for assy polymers if one faQs to acccaint for the effect of immobilization. 

For the very small particles and the very dilute two-phase system considered, the mass transfer number can be estimated by Sh=kgdp/D=2 (Ranz and Marshall, 1952). The diffiision coefficient, D, can be estimated by Fuller et al, (9) The solids hold-up equals G,/psU, (10), with G. as the solids flux in kg/(m, s), p, the particle density with u, approximating the gas velocity Ug. Values for these parameters are listed in Table 3. 

The thermal conductivity k is a transport property whose value for a variety of gases, liquids, and solids is tabulated in Sec. 2. Section 2 also provides methods Tor predicting and correlating vapor and liquid thermal conductivities. The thermi conductivity is a function of temperature, but the use of constant or averaged values is frequently sufficient. Room temperature values for air, water, concrete, and copper are 0.026, 0.61, 1.4, and 400 W/(m K). Methods for estimating contact resistances and the thermal conductivities of composites and insulation are summarized by Gebhart, Heat Conduction and Mass Diffiision, McGraw-Hill, 1993, p. 399. 

These diffiisivities are estimates obtained by in vitro experiment (stratum comeum) or by comparison with small tissues in which difTusivities have been measured (aU others). They do not account for regional variations across the body surface, so on both counts must be considered highly qjproximate. 

A sesgle experimental measurement of the average diffiisivity over the whole composition range gave a vnlne of 7.4 X 0 M m2/s. These solutions do form nearly ideal liquid mixtures so the diffiisivity of a 50/50 mixture could he estimated from Vjgnes correlation ... 

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... 

The pellet diffiisivity was also sqiarately measured, in the Na resin form D, = 169 X 10 cm s. More exact values for the resin form were also conqiuted from the reaction data, but as an oample of the estimation of an effectiveness frmtor, the Na value will he used here. 

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. 

Polystyrene films were prepared by doubly dipping the substrate—a silicon wafer previously cleaned by pure solvents and etched by hydrogen fluoride—into solutions of 1 gL of pure polystyrene in carbon tetrachloride (spectroscopic grade) and allowing the solvent to evaporate. Thickness of the films thus obtained was estimated to be of the order of 100 A by elastic recoil diffiision analysis (ERDA) measurements [122]. 

Using Equations (4) and (S), and the effective diffiisivity measurements from Table 16-3, the toms in Equation (3) can be calculated to provide an estimate of the conversion ratio for each of the CMS supported catalysts. There is (Mie additional complication. The McBain-Bakr balance utilized for the molecular probe studies was limited to measurments at ambient temperature. Thus, the effective diffiisivities of prqpylene and isobutylene were determined at 21X. Howevo, beonise the reactor stupes were perfcmned at 12S C, the diffiisivity ratio in Equadai (3) should also be at 12S C, for comparsicxt to the experimental d. Chihara et al. (1978) showed that the diffusion in ca n molecular sieve matoials is an activated diffusion process, and thus has an exprmential dependence on temperature,... 

In Equation 2.132, the subscript p refers to values in the primary particles. The diffiisivity in the polymer layer, Djwp, is an important parameter and is usually estimated as a function of polymer crystallinity. 

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