Fickian diffusion coefficients

The needed Fickian diffusion coefficient is then derived by equating Eqs. 12.166 and 12.168, and solving for D km (the m in the subscript designates mixture), yielding [72,... 

Evaluate the four multicomponent Fickian diffusion coefficients D km obtained from Eq. 12.169. 

Dj Fickian diffusion coefficient of species i, m /s e Restitution coefficient... 

To convert the intra(self-)diffusion coefficients (Dseif) to inter(Fickian)diffusion coefficients (Dchem). Zawodzinski and co-workers [64] have corrected the selfdiffusion coefficients they measured for water activity coefficient variations along the membrane thickness dimension and for the effects of swelling of the polymer [87]. The resulting Dchem for water in the Nafion membrane was 2 x lOr cm /s at 30 °C and did not exhibit a strong dependence on water content (however, recent reevalua-... 

However, the multicomponent Fickian diffusivities, Dgy, do not correspond to the approximately concentration independent binary diffusivities, Dsr, which are available from binary diffusion experiments or kinetic theory determined by the inter-molecular forces between s —r pair of gases. Instead, these multicomponent Fickian diffusion coefficients are strongly composition dependent. 

TABLE 2.14 Fickian Diffusion Coefficients [(m2/s) x 10"] at Atmospheric Pressure... 

High-intensity electric field pulses accelerated osmotic dehydration of carrot [18], A Fickian diffusion coefficient for water and solute increased exponentially with electric field strength. This effect was attributed to increased cell wall permeability, which was also manifested by the softening of product. 

The Fickian diffusion coefficient is assumed to be independent of coverage degree. 

Tapping mode atomic force microscopy Water molecules per acid site, H2O/SO3H Fickian diffusion coefficient of water Self-diffusion coefficient of water Proton mobility Electroosmotic drag coefficient Bulk membrane proton resistance Uncompensated resistance Glass transition temperatme Water volume fraction... 

The variation in literature values of Dchem has been addressed in a study of water transport though Nafion membranes [222]. Measurements of the diffusion of water were conducted wherein the membrane was exposed to liquid water on one side and dry flowing nitrogen on the other side, and water flux measurements were made across a Nafion 115-H membrane at 80 °C. Based on comparisons of their experimental data, the most accurate expression for the dependence of the Dchem ou water content was exhibited using Fickian diffusion coefficient data obtained from [208]. The following expression was developed, where Dchem has units of cm s ... 

Then, there is the very serious difficulty that empirical extension of Tick s law to systems with more than two components leads to logical inconsistencies and major calculation difficulties tTaylor and Krishna. 1993 Wesselingh and Krishna. 2QQQ1 For example, in ternary systems, the Fickian diffusion coefficient is not symmetrical, Dy Djy, which means that additional constants are required. In addition, the values of... 

For the limiting case of an ideal ternary that is quite dilute in one component (arbitrarily called component A), an effective Fickian diffusion coefficient for the dilute component can be calculated. 

Modified Fick model, also known as mixed diffusion approach is the simplest of all approaches. It is easy to program and is less computationally expensive. In this method an equivalent Fickian diffusion coefficient is derived by considering the mixture diffusion coefficient Dktn acting in series with Knudsen diffusion coefficient Dkn as follows... 

Bulk liquid Fickian diffusion coefficient of solute i (m s )... 

The (Fickian) diffusion coefficient of a chemical within a polymer is governed by two sets of properties. The first comes from the polymer itself its free volume and its ability to undergo main-chain segmental motion. The second comes from the chemical its molecular size, its degree of branching, and its general stiffness. The compatibilities of polymer/ chemical are not, surprisingly, reflected directly in the diffusion constant. 

Beyond a diffusion distance of OARg, the normal Fickian diffusion coefficient of kicks in, note the break point in Figure 5.12. Of course, at this point, considering diffusion from both sides, a total interdiffusion of 0.81 ghas taken place. This means that the film is substantially completely interdiffused, and its tensile strength will be approaching its full value, see Section 11.5.4. Note that while the slopes in Figure 5.12 theoretically should have been exactly 0.25 and 0.50 before and after the break point, respectively, some experimental error was observed due to the paucity of experimental points. 

The maximum degree of polymerization of a growing MMA chain radical with a sulfate or sulfonate end-group in aqueous solution is on the order of 65 to 75 units, according to the APO data in Table I. From the time required to polymerize to this chain length and from the Fickian diffusion coefficient, it is possible to calculate the distance, L, a growing radical will diffuse before it precipitates out to form a primary particle. This is required in order to calculate the particle formation rate and final number of particles as described in the preceding paper. 

Einstein s diffusion law relates the average distance travelled in Brownian motion, L, to the time by means of the Fickian diffusion coefficient (in this case an average value, since the radical is... 

Time Dependence of the Diffusion Coefficient, D. The value for D we have chosen is a time average one. The oligomeric radicals involved of course grow from monomeric species to much larger ones, with a concomitant decrease in the Fickian diffusion coefficient with time. However, since L must be a constant, average value in our equations, its time dependence is not involved. Current work is directed towards finding a more reliable average value for... 

The flux, J, computed by the molecular dynamic model was also apphed to calculate the Fickian diffusion coefficients, D, and the Onsager coefficient, L, by using the matrices... 

In response to the disadvantageous lack of symmetry argument, Curtiss [25] made an alternative generalized Fickian diffusion coefficient definition proposal in 1968 ... 

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