Diffusion coefficient critical ratio

The energy distribution functions in liquid argon and liquid xenon are shown in Figure 16. These results should serve only as illustrative examples. The precision and accuracy of the calculations depend critically on the input data for Aq and A (see Gushchin et al, 1982). Aq can be taken as constant, while Aj is extracted from mobility measurements. The mobility data available in the literature show considerable scatter (see Chapter 3). A direct estimation of the electron mean energy comes from the measurement of the transversal diffusion coefficient. The ratio of diffusion coefficient and mobility is a measure of the mean energy. 

Furtliennore, since tlie bifurcation must occur from a stable homogeneous steady state we must have D ID < 1 i.e. tlie diffusion coefficient of tlie inhibitor is greater tlian tliat of tlie activator. The critical diffusion ratio at tlie bifurcation is... 

Equation 6 Calculation of optimum ratio of particle size and column length, with selectivity factor, a capacity factor of second component of critical pair under analytical chromatography conditions, fe 02 diffusion coefficient, (cm /s) (typical value for MW 1000 10 cm /s) viscosity, p (cP) specific permeability (1.2 X 10 for spherical particles), feo third term of the Knox equation, C and maximum safe operating pressure, Ap, (bar). 

Tn the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. At the critical concentration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, II, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity (15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Omstein and Zemike (25), Debye (3) made the assumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local... 

Taking into account that, for the reference homologous series of n-alkanes the relative molecular masses of the member i in the series is Mni = 2+14 i, the self-diffusion coefficient DL i can be calculated with Eqs. (6-27) and (6-28). This can be done using only two values based on experimental results, the limit value of the critical temperature, Tc, and the mean value for the ratio, VcJMni. 

It is tempting to plot the effective diffusion coefficients as a function of the ratio C/Cs (Figure 18), which varies from 5 to 100 following the a-line and from 100 to 5 following the b-line. The values of the fast diffusion coefficient obtained in the a-line and the b-line are the same, and we observe an identical evolution with C/Cs. The values of the slow mode obtained from the a-line and the b-line are little different, but their evolutions are practically identical. Only on the b-line, the amplitude of the slow mode strongly decreases and becomes undetectable after a critical value of the salt concentration. 

In the adsorbed phase, in which the particles are mobile because of surface diffusion, the chemical reaction of the metal-oxide formation takes place via dissociative chemisorption of the oxygen. This means that, since the reaction takes place in the adsorption phase and the various reaction partners can have different condensation coefficients, the ratio of the rates of incidence is a necessary but not adequate criterion. According to Ritter [293, 298], the chemisorption rate of oxygen is the critical step for the completion of the reaction ... 

Critical region behavior of the diffusion coefficient can have effects on product ratios. This is probably the explanation of the increase in yield of the photo-Fries enolization products near the critical density in the photochemical... 

Table 11.4 Initiation time of corrosion as a function of thickness of concrete cover and wjc ratio, calculated on the basis of a critical chloride content of 1 % by mass of cement, a surface content of 4% and constant diffusion coefficients for chlorides (Dapp) determined on two concretes (with 420 kg/m of Portland cement and wjc of 0.4 or 300 kg/m and w/c 0.54) submerged in the North Sea for 16 y [8]...

There is thus a critical value of the diffusion coefficient ratio, = 8 > 1, above which H k ) > 0 over a range of wavenumbers < k < /fema. Perturbations with wavenumbers within this range will grow because the associated temporal eigenvalues are positive. Perturbations with wavenumbers outside this range will decay exponentially to the homogeneous steady state. Figure 11 shows the variation oiH(k ) with k for the cases of 8 > 8, and 8 <... 

The splash/tidal zone of bridges and walls represent cylindrical columns immersed in water. These structures involve entry in two dimensions. Chloride ions enter concrete by adsorption at the surface, which is given by an empirical equation. The effective chloride diffusion coefficient is derived from concrete permeability, water/cement ratio, and concrete resistivity. When concentration reaches a critical value in the vicinity of steel, corrosion begins. As shown in Fig. 12.6, a boundary layer exists adjacent to the concrete... 

In both cases, the critical transport parameter is the chloride diffusion coefficient. The diffusion coefficient varies with water to cement ratio and time. In this model, the effective chloride diffusion coefficient is derived from concrete permeabihty, water/ cement ratio, and concrete resistivity. 

The two-site model leads to the definition of the degree of counterion binding, p, as the ratio of counterions to surfactant ions in a surfactant self-assembly. This is a useful but incomplete characterization of the counterion distribution. The value of p can be obtained directly from self-diffusion data because the self-diffusion coefficients of free ions are easily obtainable. For free counterion diffusion a correction is made for the obstruction effect. The micellar D value is obtained as described above or estimated as Dm free. an exact Dm value is not critical. 

DyJll + D J22 — /4D DyA or equivalently at the critical ratio of diffusion coefficients... 

The specific critical hole free volume, is estimated as the specific volume at 0 K, which in turn is obtained from group contribution methods. The ratio of the molar volumes of the jumping units of components i andj, is computed using the values at 0 K. The pre-exponential factor. Do, and the critical energy needed by a molecule to overcome the attractive force, E, are obtained by fitting the Dullien equation for the self-diffusion coefficient to viscosity versus temperature data. Finally, the average hole-free volume per gram of the mixture, VfH/y, can be estimated from those of the individual species ... 

From equations (10), (11) and (12), for an alloy of grain size, d, the ratio (X), critical concentration of B required for external oxidation in material with a grain size d to that when the bulk diffusion coefficient dominates, can be given as ... 

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