Mean diffusion coefficient

Fig. 22. Diffusion weighted spectral series recorded from TA (a) and SOL b). Diffusion sensitizing gradients with /i-values of 0, 250, 500, 1000 and 2000 s/mm are applied parallel (Gy) and perpendicular (G ) to the muscle axis. In contrast to SOL, TA shows clearly anisotropic signal losses. Mean diffusion coefficients of 20 subjects are given in (c).

This diffusion coefficient is the mean diffusion coefficient for a solid phase loading ranging from c/ to q2-... 

Perfectly mobile equilibria the mean diffusion coefficient... 

In fact, dc0/dt equals the very small value of the difference kpcOL — kpcQ that is virtually zero. It could be decided to neglect this so-cafled source term , but it is much more appropriate to combine eqns. (181a) and (181b) in such a way that (i) the source term is eliminated and (ii) an equation in terms of the total concentration c0t is obtained. To this end, the mean diffusion coefficient is introduced, in this case defined as [11,147]... 

In computer simulations a discrete lattice of sites is considered, each site is occupied by not more than one particle. Particles A are localized in their sites for r seconds and then possess hops. Thus, the mean diffusion coefficient Da = a2/(2dr) could be introduced. We assume that particles B are immobile, Dq = 0, since it permits to reduce greatly simulation time. Moreover, for Da = Dq and d = 1,2 the kinetics turn out to be quite similar. A hop of particle A into the site occupied by particle B results in their instant recombination. 

Dj = mean diffusion coefficient, Di4>i(r) = diffusion coefficient at radius r. 

One can use the relations (1.23) to obtain the mean diffusion coefficient of the centre of mass of the relaxators in equilibrium (Ottinger 1989a)... 

When the diffusion process is not ideal, the diffusion coefficient calculated from Equation 6 for a stationary state process is the mean diffusion coefficient corresponding to a particular concentration difference. Methods of determining the true diffusion coefficient pertaining to a particular concentration were reported by Crank (9). The permeability coefficient calculated from Equation 4 is also a mean value corresponding to a particular vapor pressure difference if the diffusion process is not ideal. 

The column is regarded as being used at its optimum flow which corresponds to Vopt = 3. For the calculation of the matching flow velocity of the mobile phase, a mean diffusion coefficient, D, of the solute molecules in the mobile phase of 1 x 10 m s is assumed. Thus u and F are given by ... 

Trypsin in aqueous solution has been studied by a simulation with the conventional periodic boundary molecular dynamics method and an NVT ensemble.312 340 A total of 4785 water molecules were included to obtain a solvation shell four to five water molecules thick in the periodic box the analysis period was 20 ps after an equilibration period of 20 ps at 285 K. The diffusion coefficient for the water, averaged over all molecules, was 3.8 X 10-5 cm2/s. This value is essentially the same as that for pure water simulated with the same SPC model,341 3.6 X 10-5 cm2/s at 300 K. However, the solvent mobility was found to be strongly dependent on the distance from the protein. This is illustrated in Fig. 47, where the mean diffusion coefficient is plotted versus the distance of water molecules from the closest protein atom in the starting configuration the diffusion coefficient at the protein surface is less than half that of the bulk result. The earlier simulations of BPTI in a van der Waals solvent showed similar, though less dramatic behavior 193 i.e., the solvent molecules in the first and second solvation layers had diffusion coefficients equal to 74% and 90% of the bulk value. A corresponding reduction in solvent mobility is observed for water surrounding small biopolymers.163 Thus it... 

SOLVENT MOBILITIES. One check on the physical significance and the reliability of the data representing the concentration dependence of the diffusion coefficient is to convert these results to solvent mobilities. The values should increase rapidly with increasing concentration and extrapolate to the self-diffusion coefficient for toluene. The procedure for carrying out the calculations was outlined in previous publication (11) and is repeated here in a brief form for convenient reference. The diffusion coefficient obtained directly in the vapor sorption experiment is a polymer, mass-fixed, mean diffusion coefficient, D, in the sorption interval. Duda et. al. (12) have shown that, if the concentration interval is small, the true diffusion coefficient, D, is simply related to the mean diffusion coefficient at a prescribed intermediate concentration in the interval ... 

The effect of the Langmuirian sorption mode per se on migration kinetics is explored further in Fig. 18. The total immobilization limit (F = 0) has been arbitrarily selected in preparing curve (a) of Fig. 18. Clearly, other values of F could be treated as well. The K = 0 limit (Henry s law sorption) gives rise to much more rapid desorption than for K > 0 since the mean diffusion coefficient corresponding to Eq. (27) is equal to Dd when K = 0. For all values of K > 0, D < Dd and desorption is retarded, however total evacuation of the sample is eventually predicted at times which, although non-infinite, are indeed extraordinarily long. 

Such phenomena have been reported for electrode reactions of Cr(EDTA) and Fe(CN)g " in which the viscosity of the solvent (water or dimethyl sulfoxide) is varied by the addition of dextrose or sucrose [64—66]. Solvent friction has also been invoked in reductions of thiophenecarboxylatopenlaamminecobalt(HI) complexes [67] and of metallocenes [68, 69] at Hg electrodes in organic solvents. Of particular interest in the present context are studies by Murray et al. [70, 71] of the reduction kinetics of Co(bpy)3 in a variety of organic solvents, in which kei was found to be proportional to 1/rj, to 1/tl, and to the mean diffusion coefficient D of the reactants over a huge range (11 orders of magnitude) of kei-... 

D is the mean diffusion coefficient of and v kinematic viscosity (see Section 5.3.1), and co = 2nf the angular velocity with/the rotation frequency. In the anodic Tafel region the following equation is obtained ... 

The concentration field looks like it applies to a pure diffusion phenomenon (without migration) for a species (here HCI) with a mean diffusion coefficient, D . 

The progression towards the steady state therefore correlates with the AgNOj diffusion (i.e., the coupled diffusion of both anions and cations), with a mean diffusion coefficient ... 

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