Diffusion coefficient of water

Diffusion of the molecular gases can be compHcated by reactions with the glass network, especially at the sites of stmctural defects. The diffusion coefficient of water, for example, shows a distinct break around 550°C (110). Above 550°C, the activation energy is approximately 80 kj /mol (19 kcal/mol), but below 550°C, it is only 40 kJ/mol (9.5 kcal/mol). Proposed explanations for the difference cite the fact that the reaction between water and the sihca network to form hydroxyls is not in equiUbrium at the lower temperatures. 

The values for the lipid molecules compare well (althoughJgiey are still somewhat larger) with the experimental value of 1.5x10 cm /s as measured with the use of a nitroxide spin label. We note that the discrepancy of one order of magnitude, as found in the previous simulation with simplified head groups, is no longer observed. Hence we may safely conclude that the diffusion coefficient of the lipid molecules is determined by hydrodynamic interactions of the head groups with the aqueous layer rather than by the interactions within the lipid layer. The diffusion coefficient of water is about three times smaller than the value of the pure model water thus the water in the bilayer diffuses about three times slower than in the bulk. 

Fig. 2.7.5 Two-dimensional D—T2 map for Berea sandstone saturated with a mixture of water and mineral oil. Figures on the top and the right-hand side show the projections of f(D, T2) along the diffusion and relaxation dimensions, respectively. In these projections, the contributions from oil and water are marked. The sum is shown as a black line. In the 2D map, the white dashed line indicates the molecular diffusion coefficient of water,...

Farng and Nelson [1] applied the capillary method to the determination of the diffusion coefficient of salicylic acid in the presence of polyelectrolytes. The reported variability in terms of the coefficient of variation ranged from 0.89% to 8.3%. Stout et al. [2] showed the tube method to be useful for determining diffusion coefficients of water-insoluble pharmaceuticals such as sulfonamides and steroids. The coefficient of variation associated with the diffusion coefficient for sulfisoxazole is 5.5%. 

DWi = diffusion coefficient of water in air Xw = mole fraction of water vapor in air at a point x... 

Figure 31. Diffusion coefficient of water in a DPPC bilayer as a function of position. Results of MD simulations of Marrink and Berendsen [129]. Redrawn by permission of the American Chemical Society...

These studies showed that sulfonate groups surrounding the hydronium ion at low X sterically hinder the hydration of fhe hydronium ion. The interfacial structure of sulfonafe pendanfs in fhe membrane was studied by analyzing structural and dynamical parameters such as density of the hydrated polymer radial distribution functions of wafer, ionomers, and protons water coordination numbers of side chains and diffusion coefficients of water and protons. The diffusion coefficienf of wafer agreed well with experimental data for hydronium ions, fhe diffusion coefficienf was found to be 6-10 times smaller than the value for bulk wafer. 

While D issuing from these experiments is not strictly the diffusion coefficient of water per se, but rather that of H throughout the ensemble of environments in the hydration microstructure, these authors rationalized that it could in fact be identified with D at both high and low water contents. It should be appreciated that self-diffusion coefficients measured in this way reflect fundamental hopping events on a molecular scale. 

The self-diffusion coefficient of water in Nafion, as measured by PFG is shown in... 

For comparison purposes, the proton mobility. Do (for Nafion solvated with water), which is closely related to the self-diffusion coefficient of water, is also plotted. At low degrees of hydration, where only hydrated protons (e.g., H3O+) are mobile, it has a tendency to fall below the water diffusion coefficient (this effect is even more pronounced in other polymers), which may be due to the stiffening of the water structure within the regions that contain excess protons, as discussed in Section 3.1.1. . Interestingly, the proton mobility in Nafion solvated with methanol (Da(MeOH) in Figure 14a) is even lower than the methanol self-diffusion (Z ieon). This may... 

From the formation reaction of protonic defects in oxides (eq 23), it is evident that protonic defects coexist with oxide ion vacancies, where the ratio of their concentrations is dependent on temperature and water partial pressure. The formation of protonic defects actually requires the uptake of water from the environment and the transport of water within the oxide lattice. Of course, water does not diffuse as such, but rather, as a result of the ambipolar diffusion of protonic defects (OH and oxide ion vacancies (V ). Assuming ideal behavior of the involved defects (an activity coefficient of unity) the chemical (Tick s) diffusion coefficient of water is... 

L22 and L33 are related to the self-diffusion and chemical diffusion coefficients of water and methanol ... 

Upon comparison of eq 32 to 28, it is seen that the proton—water interaction is now taken into account. This interaction is usually not too significant, but it should be taken into account when there is a large gradient in the water (e.g., low humidity or high-current-density conditions). Upon comparison of eq 33 to 31, it is seen that the equations are basically identical where the concentration and diffusion coefficient of water have been substituted for the chemical potential and transport coefficient of water, respectively. Almost all of the models using the above equations make similar substitutions for these variables 15,24,61,62,128... 

Haller W. (1963) Goncentration-dependent diffusion coefficient of water in glass. Phys. Chem. Glasses 4, 217-220. 

Tomozawa M. (1985) Concentration dependence of the diffusion coefficient of water in Si02 glass. Am. Ceram. Soc. C, 251-252. 

In Fig. 42, the full-width at half maximum of the (narrower) exchange propagator provides an estimate of the effective diffusion coefficient of water molecules moving between the pore space of the catalyst and the inter-particle space of the bed. In this example, the value is 2 x lO- m s which gives a lower limit to the value for the mass transfer coefficient of 4x 10 ms This value was obtained by defining a mass transfer coefficient as Djd where d is a typical distance traveled to the surface of the catalyst that we estimate as half a typical bead dimension (approximately 500 pm). This value of the mass transfer coefficient is consistent with the reaction occurring under conditions of kinetic as opposed to mass transfer control. 

Figure 5. Experimental self-diffusion coefficient of water molecules in NaX as a function of reciprocal temperature, (a) Mean diameter of the zeolite crystals 3 pm ...

We wish to estimate the time it takes to evaporate a puddle of water. The depth of the puddle is 0.08 inches and covers a surface area of 2 ft2. Both the surr.ounding air (which is stagnant) and the water are at a constant temperature of 77°F. The absolute humidity is 0.001 lb water/lb dry air. Assume the evaporation to occur, through stagnant gas film that is 0.28 inches thick. The gas diffusion coefficient of water vapor at these conditions is 0.259 cm2/sec. 

D — gaseous diffusion coefficient of water through air, 0.208 sq. cm. per second Dm = diffusivity of water vapor in air... 

Tanner [49] measured diffusion coefficients of water in three different types of frog muscle cells. He used a variety of magnetic field gradient techniques so as to cover a wide range of diffusion times A= 1 ms to 1 s. The time dependence of the diffusion coefficient was analyzed to obtain the intracellular diffusion coefficients and estimates of the permeability of the cell membranes. In restricted diffusion studies three 90 degree r.f. pulse sequences (stimulated echo) are often used which provides PG-NMR experiments with long diffusion times to explore the dependence of diffusion time on the echo attenuation [49]. 

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