Diffusion constants typical values

The Peclet number shows the relative importance of mass (or heat) transport by convection as compared to molecular (gas-phase) diffusion. Again, typical values of Pe are around unity, implying that the flow is quite diffusive. The Peclet number is independent of pressure, when everything else is held constant. 

The performance of the dmg dehvery system needs to be characterized. The rate of dmg release and the total amount of dmg loaded into a dmg dehvery system can be deterrnined in a dissolution apparatus or in a diffusion ceU. Typically, the dmg is released from the dmg dehvery system into a large volume of solvent, such as water or a buffer solution, that is maintained at constant temperature. The receiver solution is weU stirred to provide sink conditions. Samples from the dissolution bath are assayed periodically. The cumulative amount released is then plotted vs time. The release rate is the slope of this curve. The total dmg released is the value of the cumulative amount released that no longer changes with time. 

The proportionality constant in this equation, D, is called the diffusion constant. A typical solute has D 1 X 10 9 m2 s . Values of D do not vary greatly with the solute but are inversely proportional to the viscosity of the solvent. 

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. 

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... 

What Would Make a Sweep Rate Too Slow One general criterion that can be taken here is that the time in which (nDT)l/2 = 8, an assumption used in the theory ofpotentiodynamic transients, remains valid. It is an experimental fact that 8 at an electrode in a still solution for a long time (> 10 s, say) is about 0.05 cm and constant because natural convection stirs the solution and wipes out the concentration gradient set up by diffusion alone. Hence, one can assume that the limit of validity of 8,= (jiDt)m is a time at which becomes 8 equal to 0.05 cm. Using a typical value of D (= 3 x 10-5 cm2 s-1), one obtains... 

Typical values of R and D are 0.5 nm and 10-9 m2 s-1. The time dependence of the density distribution is shown in Fig. 1 for these parameters. As reaction proceeds, the density (or concentration) of reactant B in the immediate vicinity of A decreases. The time scale over which this reduction is most noticeable is R2/D 1 ns. This is the mean time it takes for a reactant to diffuse a distance R. Initially, the concentration of B around A is constant. As reaction begins, B diffuses towards A and reaction becomes rapid at times R2/D. Most depletion of the density at this time has occurred at short distances ( i2— 2R). At later times, more depletion of the density occurs at larger distances. Ultimately, after a time 100 R2/D little further change to the density distribution occurs. B now diffuses towards A at a rate which sustains a constant density distribution a steady-state is established and it has a distribution... 

In the cases above, a two-parameter model well represents the data. A model with more parameters would be more flexible, but by using a partition constant, K, or a desorption rate constant ka and k, , for the mass-transfer coefficients, the data are well described (see Figs. 3.4-15 and 3.4-13). While K would be a value experimentally determined, kp can be estimated from eqn. (3.4-97) with the external mass-transfer coefficient, km, estimated from the correlation of Stiiber et al. [25] or from that of Tan et al. [27], and the effective diffusivity from the Wakao Smith model [36], Typical values of kp obtained by fitting the data of Tan and Liou are shown in Fig. 3.4-16. As expected, they are below the usual mass-transfer correlations, because internal resistance diminishes the global mass transfer coefficient. These data correspond to the regeneration of spent activated carbon loaded with ethyl acetate, using high-pressure carbon dioxide, published by Tan and Liou [45]. 

The kinematic viscosity considered in the simulations was that of water. Here, as diffusion constant D a value of 10 10 m2 s, a typical value for diffusion of small proteins in aqueous solutions, was taken. 

From Eq. (11), an obviously desirable characteristic for thermoelectric materials is to have low thermal conductivity k. The thermal diffusivity constant, Dt, of ErB44Si2 has been found to have small values of Dt < 1.1 x 10 2 cm 2/s (Mori, 2006c). These values are significantly smaller than what has been observed for boron carbide samples (Wood et ah, 1985). Although no data exists for the sound velocities of ErB44Si2, the velocities are probably high since borides are typically hard materials. Therefore, the small values of Dt indicate extremely short phonon... 

It is important to know for which A the transition from the time dependent Deff to the constant Dtort occurs. Using the relationship = 6D0A with D0 10"n m2/s, which is a typical value for polymers, and A between 10 2 and 1 second, the range accessible for most PFGE experiments, one finds ()1/2= 0.8-8 pm. Consequently, the PFGE experiment is able to detect in a material diffusion barriers if the space between these barriers has dimensions in this range. 

For packed columns, typical values [701] are h = 3 and v= 3, so that h/ v= 1. For open columns typically h = 1.5 and v= 5, so that /i/ v= 0.3. Consequently, capillary columns will lead to analysis times that are about three times shorter (for dp— dc) for the same separation (N and k constant). Therefore, in principle, capillary columns are superior to packed columns. Unfortunately, capillary columns cannot always be used. This arises from the occurrence of the diffusion coefficient (Dm) in eqn.(7.6). Typically, Dm is 10,000 times larger in gases than it is in liquids. This necessitates the use of very small particles (typically 5-10 pm) in HPLC columns. If we compare packed and capillary columns with dp= which is a reasonable assumption for GC [702], then capillary columns with very small internal diameters need to be considered for LC [703]. Such very narrow columns impose extreme demands on the instrumentation, and at present open tubular columns cannot be used for practical LC separations. 

It is straightforward that under high positive polarization, the current levels off to a constant being the sum of jo and /ph. Since the charge carriers to be transferred across the interface are minority carriers, j0 is usually of very small magnitude and depends on material properties such as diffusion coefficient and the diffusion length of minority carriers, as expressed in (16.30). For instance, using typical values of the parameters in (16.30) for Si electrodes, the dark current density jo is found to be in... 

For dye K2, the kq value decreases by 40 times on passing from an aqueous solution to a complex with DNA. Similarly, kq obtained upon quenching of the triplet state of dye K1 bound to DNA is much lower than the values of the constants typical for the mechanism of acceleration of the intersystem crossing to the groimd state ( 1 x 10 1 mol s ). The possible reason for these phenomena is bulky substituents in the polymethine chain (OCH3 and SCH3), which create additional spatial hindrances to quencher molecules upon complexation with DNA. Hence, diffusion of the quencher to the triplet molecules is strongly impeded (ka and k ... 

The primary variable that determines whether the controlling resistance is in the liquid or gas film is the H or Henry constant. As shown in Figure 5.15, and as is apparent from equation 39, for small values of H the water phase film controls the transfer, and for high values of H the transfer is controlled by the air phase film. Gas transfer conditions that are liquid film controlled sometimes are expressed in terms of thickness, Zw, of the water film. As indicated by equation 38, this can be done from a measured value of (or K,o,) and the diffusion coefficient of the substance Zw decreases with the extent of turbulence (current velocity, wind speed, etc.). Typical values for are in the range of micrometers for seawater, a few hundred micrometers in lakes and up to 1 nun in small wind-sheltered water bodies (Brezonik, 1994). 

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