Diffusivity corrected diffusion coefficient

As with the diffusion coefficient, sedimentation coefficients are frequently corrected for concentration dependence and reduced to standard conditions ... 

Multicomponent Diffusion. In multicomponent systems, the binary diffusion coefficient has to be replaced by an effective or mean diffusivity Although its rigorous computation from the binary coefficients is difficult, it may be estimated by one of several methods (27—29). Any degree of counterdiffusion, including the two special cases "equimolar counterdiffusion" and "no counterdiffusion" treated above, may arise in multicomponent gas absorption. The influence of bulk flow of material through the films is corrected for by the film factor concept (28). It is based on a slightly different form of equation 13 ... 

X 10 m /s. Diffusion coefficients may be corrected for other conditions by assuming them proportional to Schmidt numbers depend only weaMy on temperature (113). 

The Displacement Distance theory suggests that since the stmcture of the flame is only quantitatively correct, the flame height can be obtained through the use of the displacement length or "displacement distance" (35,36) (eq. 12), where h = flame height, m V = volumetric flow rate, m /s and D = diffusion coefficient. 

Many more correlations are available for diffusion coefficients in the liquid phase than for the gas phase. Most, however, are restiicied to binary diffusion at infinite dilution D°s of lo self-diffusivity D -. This reflects the much greater complexity of liquids on a molecular level. For example, gas-phase diffusion exhibits neghgible composition effects and deviations from thermodynamic ideahty. Conversely, liquid-phase diffusion almost always involves volumetiic and thermodynamic effects due to composition variations. For concentrations greater than a few mole percent of A and B, corrections are needed to obtain the true diffusivity. Furthermore, there are many conditions that do not fit any of the correlations presented here. Thus, careful consideration is needed to produce a reasonable estimate. Again, if diffusivity data are available at the conditions of interest, then they are strongly preferred over the predictions of any correlations. 

The Stokes-Einstein equation has already been presented. It was noted that its vahdity was restricted to large solutes, such as spherical macromolecules and particles in a continuum solvent. The equation has also been found to predict accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids is given by Tanford. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. 

Do diffusion coefficient corrected for thermodynamic driving force, mvs... 

With the Laplace operator V. The diffusion coefficient defined in Eq. (62) has the dimension [cm /s]. (For correct derivation of the Fokker-Planck equation see [89].) If atoms are initially placed at one side of the box, they spread as ( x ) t, which follows from (62) or from (63). 

The correct and critical estimate of the diffusion coefficients may be used to get informations on the morphological modifications occurring in presence of the sorbed moisture. 

X 10 cm by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dfnic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of... 

Dt and the mutual diffusion coefficient, D, are interconvertible by correcting for the penetrant activity in the polymer [12], For highly concentrated systems where the penetrant volume fraction, < >, is low,/can be approximated by... 

Another group of surveys has focused on the direct modeling of some effective transport phenomena which are essential for predicting parameters that have an important role in underground gas sequestration process such as diffusivity and convection. Azin et al., in 2013, have conducted study regarding correct measurement of diffusivity coefficient [114]. 

Fig. 7. Dependence of uncorrected (A) diffusion coefficient (D) and (B) number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The data shown here are not corrected for the effect of viscosity and refractive indices of the urea solutions. Experimental condition is the same as in Figure 6. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Compound 6 contains seven iron-based units [ 12], of which the six peripheral ones are chemically and topologically equivalent, whereas that constituting the core (Fe(Cp)(C6Me6)+) has a different chemical nature. Accordingly, two redox processes are observed, i.e., oxidation of the peripheral ferrocene moieties and reduction of the core, whose cyclic voltammetric waves have current intensities in the 6 1 ratio. Clearly, the one-electron process of the core is a convenient internal standard to calibrate the number of electron exchanged in the multi-electron process. In the absence of an internal standard, the number of exchanged electrons has to be obtained by coulometry measurements, or by comparison with the intensity of the wave of an external standard after correction for the different diffusion coefficients [15]. 

The mobility of eh was determined by measuring the equivalent conductance following pulse irradiation (Schmidt and Buck, 1966 Schmidt and Anbar, 1969). After correcting for the contribution of H30 and OH ions, they found the equivalent conductance of eh = 190 10 mho cm2. From this, these authors obtained the mobility p(eh) = 1.98 x 10"3 cm2/v.s. and the diffusion coefficient D(eh) = 4.9 x 10-5 cm2/s using the Nernst-Einstein relation, with about 5% uncertainty. The equivalent conductance of eh is the same as that for the OH - ion within experimental uncertainty. It is greater than that of the halide ion and smaller than that of eam... 

The diffusion coefficients for eh, H30+, OHa, H, OH, and H202, in units of 10-5 cm2s-1, are taken respectively as 4.5, 9.0, 5.0, 7.0, 2.8, and 2.2. Of these, the first three are for charged species taken from experiment. D0h is taken the same as for self-diffusion of water. Dh2o2 is derived from self-diffusion of water using Stokes law to correct for the size effect. DQh is obtained from the diffusion of He. 

Several important assumptions have been implicitly incorporated in Eqs. (15) and (16). First, these equations describe the release of a drug from a carrier of a thin planar geometry, equivalent equations for release from thick slabs, cylinders, and spheres have been derived (Crank and Park, 1968). It should also be emphasized that in the above written form of Fick s law, the diffusion coefficient is assumed to be independent of concentration. This assumption, while not conceptually correct, has been... 

Fig. 7. Predicted diffusion coefficients for hydrogen (H) and deuterium (D) in niobium, as calculated by Schober and Stoneham (1988) from a model taking account of tunneling between various states of vibrational excitation and comparison with experimental measurements (solid lines). Theoretical curves are shown both for a model using harmonic vibrational wave functions (dashed lines) and for a model with anharmonic corrections (dashed-dotted lines).

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