Diffusivity typical values

Equation 5 Knox equation, with reduced plate height, h reduced velocity (m dpID ), V, coefficient B, describing axial diffusion (typical value 2) coefficient A, describing bed homogeneity (typical value 1-2) and coefficient C, describing mass transfer (typical value 0.05). 

Fig. 1. LED pulse sequence for the measurement of stimulated echoes attenuated by diffusion. Typical values for delays and pulse widths are 5 ms for the gradient pulse widths tg, 2-3 ms for the recovery time tr, 0.1 s for the diffusion time td, and 5 ms for the storage time...

HgCdTe photodiode performance for the most part depends on high quantum efficiency and low dark current density (83,84) as expressed by equations 23 and 25. Typical values of at 77 K ate shown as a function of cutoff wavelength in Figure 16 (70). HgCdTe diodes sensitive out to a wavelength of 10.5 p.m have shown ideal diffusion current limitation down to 50 K. Values of have exceeded 1 x 10 . Spectral sensitivities for... 

Typical values of the energy to form vacancies are for silver, lOSkJmol and for aluminium, 65.5kJmol These values should be compared with the values for the activation enthalpy for diffusion which are given in Table 6.2. It can also be seen from the Table 6.2 that die activation enthalpy for selfdiffusion which is related to the energy to break metal-metal bonds and form a vacant site is related semi-quantitatively to the energy of sublimation of the metal, in which process all of the metal atom bonds are broken. 

The mobilities of ions in molten salts, as reflected in their electrical conductivities, are an order of magnitude larger than Arose in Are conesponding solids. A typical value for diffusion coefficient of cations in molten salts is about 5 X lO cm s which is about one hundred times higher Aran in the solid near the melting point. The diffusion coefficients of cation and anion appear to be about the same in Are alkali halides, wiAr the cation being about 30% higher tlrair Are anion in the carbonates and nitrates. 

Table 4-1 lists some rate constants for acid-base reactions. A very simple yet powerful generalization can be made For normal acids, proton transfer in the thermodynamically favored direction is diffusion controlled. Normal acids are predominantly oxygen and nitrogen acids carbon acids do not fit this pattern. The thermodynamicEilly favored direction is that in which the conventionally written equilibrium constant is greater than unity this is readily established from the pK of the conjugate acid. Approximate values of rate constants in both directions can thus be estimated by assuming a typical diffusion-limited value in the favored direction (most reasonably by inspection of experimental results for closely related... 

Typical values of self-diffusion coefficients and mutual diffusion coefficients in aqueous solutions and in molten salt systems such as (K,Ag)N03 are of the order... 

The above data relate to very pure iron samples with low dislocation densities. In real steels the trapping effects result in much lower apparent diffusivities, which are dependent on the metallurgical state of the steel, as well as its chemical composition. Typical values for the apparent diffusion coefficient of hydrogen in high-strength alloy steel at room temperature are in the region of 10" mVs. 

There is considerable compensation in these equations that tends to make the change in k less severe than noted. A molecule more mobile than most is probably smaller. It has a higher diffusion coefficient, but a smaller encounter probability. If one partner is especially small and mobile, the rate constant may exceed the typical values by a small factor. On the other hand, even when this size difference is allowed for, the rate constants for a few reactions are higher than one can account for in these terms. 

Optimization requires that a-rtjl have some reasonably high value so that the wall temperature has a significant influence on reactor performance. There is no requirement that 3>AtlR be large. Thus, the method can be used for polymer systems that have thermal diffusivities typical of organic liquids but low molecular diffusivities. The calculations needed to solve the optimization are much longer than those needed to solve the ODEs of Chapter 6, but they are still feasible on small computers. 

It is a typical feature of the diffusion processes at electrodes of small size, which are reached by converging diffusion fluxes, that a steady state can be attained even without convection (e.g., in gelled solutions). Such electrodes, which have dimensions comparable to typical values of 8, are called microelectrodes. 

Figure 3.39. Typical value.s for the diffusion coefficient as a function of pore size.

In the presence of an electric field the drift length is the mobility-lifetime product times the electric field A.mfp = prE [576]. With typical values of pz and E the mean free path usually exceeds by far the thickness of the solar cell, and virtually all photogenerated carriers can be collected. However, under certain operating conditions, field-free regions in the / -layer may exist, and the collection efficiency is decreased because the diffusion lengths of the carriers are much smaller than the thickness of the solar cell [11, 577]. 

Although there are differences in the approach curves with the constant-composition model, it would be extremely difficult to distinguish between any of the K cases practically, unless K was below 10. Even for K = 10, an uncertainty in the tip position from the interface of 0. d/a would not allow the experimental behavior for this rate constant to be distinguished from the diffusion-controlled case. For a typical value of Z)Red, = 10 cm s and electrode radius, a= 12.5/rm, this corresponds to an effective first-order heterogeneous rate constant of just 0.08 cm s. Assuming K,. > 20 is necessary... 

Assume that the effective diffusivity for cumene in these particles is equal to 1.2 x 10 3 cm2/sec, which is a typical value for silica-alumina TCC beads (39). 

After obtaining from the measured value of kl by this procedure, one can determine the attachment efficiency in the quasi-free state, rj = fe1f/fed.ff, by the same procedure as for scavenging reactions (see Eq. 10.11 et seq.). Mozumder (1996) classifies the attachment reactions somewhat arbitrarily as nearly diffusion-controlled, partially diffusion-controlled, and not diffusion-controlled depending on whether the efficiency p > 0.5, 0.5 > r > 0.2, or r < 0.2, respectively. By this criterion, the attachment reaction efficiency generally falls with electron mobility. Nearly diffusion-controlled reactions can only be seen in the liquids of the lowest mobility. Typical values of r] are (1) 0.65 and 0.72 respectively for styrene and p-C6H4F2 in n-hexane (2) 0.14 and 0.053 respectively for a-methylstyrene and naphthalene in isooctane (3) 1.8 X 10-3 for C02 in neopentane and (4) 0.043 and 0.024 respectively for triphenylene and naphthalene in TMS. 

Zel = jRT/2nM (M, molar mass) is the electrochemical collision frequency, v is the scan rate and Z), the diffusion coefficient. Taking typical values, Zel = 4 x 103cms-1, Dj = 10-5cm2s-1 leads to a bracketing of the free energy of activation at the peak between 0.385 eV (for v = 0.1Vs-1,... 

Dispersivity is a property that depends on the nature of the sediment or rock in question, as well as the scale on which dispersion is observed. There is no typical value a dispersivity of 1 cm might be observed in a laboratory experiment, whereas a value of 100 m (10 000 cm) might be found to apply in a field study. Dispersion is generally more rapid along the direction of flow than across it, so oil > t. Typical values of the diffusion coefficient D in porous media are in the range 10-7 to 10-6 cm2 s-1. 

All these reactions are thermodynamically favourable in the direction of proton transfer to hydroxide ion but the rate coefficients are somewhat below the diffusion-limited values. In broad terms, the typical effect of an intramolecular hydrogen bond on the rate coefficient for proton removal is to reduce the rate coefficient by a factor of up to ca 105 below the diffusion limit. Correspondingly the value of the dissociation constant of the acid is usually decreased by a somewhat smaller factor from that of a non-hydrogen-bonded acid. There are exceptions, however. 

The effective diffusivity is obtained from D, but must also take into account the two features that (1) only a portion of the catalyst particle is permeable, and (2) the diffusion path through the particle is random and tortuous. These are allowed for by the particle voidage or porosity, p, and the tortuosity, rp, respectively. The former must also be measured, and is usually provided by the manufacturer for a commercial catalyst. For a straight cylinder, rp = 1, but for most catalysts, the value lies between 3 and 7 typical values are given by Satterfield. 

To integrate the equations of motion in a stable and reliable way, it is necessary that the fundamental time step is shorter than the shortest relevant timescale in the problem. The shortest events involving whole atoms are C-H vibrations, and therefore a typical value of the time step is 2fs (10-15s). This means that there are up to one million time steps necessary to reach (real-time) simulation times in the nanosecond range. The ns range is sufficient for conformational transitions of the lipid molecules. It is also sufficient to allow some lateral diffusion of molecules in the box. As an iteration time step is rather expensive, even a supercomputer will need of the order of 106 s (a week) of CPU time to reach the ns domain. 

Typical values for the dimensions of the various layers are included in Figure 1 of Chapter 1. Diffusion layer thicknesses depend on the timescale and hydro-dynamic conditions they will be dealt with in detail in Sections 3 and 4. 

Figure 2 plots the evolution of the incoming fluxes Jm and with time for some typical values from the literature [24,25] and references therein. As expected, the diffusive flux Jm decreases with time and tends towards a steady-state value when converging with Ju. It is noticeable that, in the initial transient, the internalisation flux Ju is much closer to its eventual steady-state... 

We note incidentally that the reaction layer thickness is on the same order as that of the double layer for k+ 1010 s-1 (typical values of the diffusion coefficient are of the order of 10 5 cm2 s 1). It is only for such fast reactions that their kinetics may be perturbed by the strong electric field present in the close vicinity of the electrode.3... 

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