Diffusion constant ratio

Figure 19. Low-salinity paths showing the effect of varying the diffusion constant ratio in the microemulsion path 1 represents D(brine)/D(oil) = 5.0 path 2 represents D(brine)/D(oil)= 1.0.

One can thus see that many factors control the relative behaviour of the isotopes in solution, diffusion, and permeation in metals. The solubility ratio combines the effects indicated above the diffusion constant ratio involves differences in the zero-point energies of dissolved hydrogen and deuterium... 

The amplitude of the elastic scattering, Ao(Q), is called the elastic incoherent structure factor (EISF) and is determined experimentally as the ratio of the elastic intensity to the total integrated intensity. The EISF provides information on the geometry of the motions, and the linewidths are related to the time scales (broader lines correspond to shorter times). The Q and ft) dependences of these spectral parameters are commonly fitted to dynamic models for which analytical expressions for Sf (Q, ft)) have been derived, affording diffusion constants, jump lengths, residence times, and so on that characterize the motion described by the models [62]. 

Diffusion constants are enhanced with the approximate inclusion of quantum effects. Changes in the ratio of diffusion constants for water and D2O with decreasing temperature are accurately reproduced with the QFF1 model. This ratio computed with the QFF1 model agrees well with the centroid molecular dynamics result at room temperature. Fully quantum path integral dynamical simulations of diffusion in liquid water are not presently possible. 

A az, s ) and solvent (k, s ) to a carbocation intermediate of solvolysis are first determined from the ratio of the yields the azide ion and solvent adducts (equation (1)). The value for may then be calculated from this product rate constant ratio M ), and az = 5 X 10 s for the diffusion limited... 

Sect. 6 a Aa T Do Fsh T X A M R De final radius of cylindrical gel after swelling displacement relaxation time for swelling collective diffusion constant shear energy trace of the strain tensor u,k swelling rate ratio total change of the radius of the gel longitudinal modulus ratio of the shear modulus to the longitudinal modulus effective collective diffusion constant... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

Finally, various attempts have been reported to interpret the kinetics of radiation grafting. The study by Mock, and Vanderkooi (123) concerned the mutual radiation grafting of styrene from the vapor phase to ethyl cellulose film at 50° C. The radical flux was determined separately using electron spin resonance. The kinetic scheme rigorously took account of the diffusion controlled nature of the reaction and the appropriate diffusion constants were separately determined (124). The value for the ratio of for the graft polymerization was determined as... 

The rotational diffusion constant in water at 25° and neutral pH as measured by electric birefringence (258) is 230 X 105 sec-1 or 0.73 X HT8 sec as a relaxation time. For a hydrodynamic ellipsoid of dimensions 66 X 22 A and a molecular weight of 14,000, the calculated relaxation tilde is 0.72 X 10-8 sec. However, the apparent asymmetry of the molecule from the X-ray structure corresponds to an axial ratio of no more than 2 1 rather than 3 1. 

Stolwijk has reported a mathematical model that describes the initial flux as a function of the diffusion constant of the complex (/)M), the product (Kcx) of the association constant of the complex in the membrane and the partition ratio of the salt, the concentration of salt (a) in the aqueous phase and of the carrier (L0) in the membrane phase, and the thickness of the membrane (d) ... 

M 67] [P 59] The mixing efficiency was calculated for various diffusion constants, ranging from 2 10 7tol0 10 7m2s 1 [59], A meandering ratio of4 was assumed... 

Figure 1.140 Mixing efficiency versus diffusion constant for one zig-zag micro mixer (lines) with s = 400 pm and one straight-channel micro mixer (dashed lines), reference case B, at three different Re values (top). Mixing factor, the ratio between the mixing efficiency of comparable zig-zag and straight-channel micro mixers, versus diffusion constant (bottom) [59] (by courtesy of ACS).

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