Diffusion Fick formulae

The choice of vx is a matter of convenience for the system of interest. Table 1 summarizes the various definitions of vx and corresponding, /Y, commonly in use [3], The various diffusion coefficients listed in Table 1 are interconvertible, and formulas have been derived. For polymer-solvent systems, the volume average velocity, vv, is generally used, resulting in the simplest form of Jx,i- Assuming that this vv = 0, implying that the volume of the system does not change, the equation of continuity reduces to the common form of Fick s second law. In one dimension, this is... 

The most widely used unsteady state method for determining diffusivities in porous solids involves measuring the rate of adsorption or desorption when the sample is subjected to a well defined change in the concentration or pressure of sorbate. The experimental methods differ mainly in the choice of the initial and boundary conditions and the means by which progress towards the new position of equilibrium is followed. The diffusivities are found by matching the experimental transient sorption curve to the solution of Fick s second law. Detailed presentations of the relevant formulae may be found in the literature [1, 2, 12, 15-17]. For spherical particles of radius R, for example, the fractional uptake after a pressure step obeys the relation... 

Fiber-reinforced polymer systems, 38 Fickian diffusion, 665 Fick s law, 663,684 Field flow fractionation, 20 Filled polymers, 38 First normal stress coefficient, 545 difference, 640 First-order transition, 27,152 Flame-retardant additives, 861 Flammability, 847 Flashing, 804 Flash line region, 807 Flexibility of a chain molecule, 246 Flexible polymer molecules, 706 Flexural deformation under constant load, 825 Flexural formulas, 826 Flexural rigidity, 877 Floor temperature, 751 Flory-Huggins... 

Relative recovery can be mathematically expressed by Fick s law of diffusion as modified by Jacobson (Jacobson et al., 1985). In this relationship, recovery is the ratio of the concentration in the perfusate to the concentration extracellular. For the mass recovery, an expression similar to a Michaelis-Menten formula for enzymatic reactions was derived (Ekblom et al., 1992). A number of other mathematical models for quantitative microdialysis have been proposed and are reviewed elsewhere (Justice 1993 Kehr, 1993b). 

We will describe oxygen flux through the GDL by Fick s formula with the effective diffusion coefficient D. Physically, in a dry GDL, D corresponds to a binary diffusion coefficient of oxygen corrected for porosity-tortuosity. When the GDL is partially flooded Z) should be corrected for liquid saturation. A more rigorous approach is based on Stefan-Maxwell relations, which take into account the effect of fluxes of the other mixture components on... 

Diffusion when the motion of particles caused by difference of concentration is represented by Fick s first law. The respective formula proposed by CEB-FIP (1990) is derived in the following form for the amount of transported mass Q as a function of difference of concentration c - cf)... 

The three points thus give us a new point at the next time. Compare this with the box-method expression, Eq. 3.5 they are identical. In fact, one might say that the box-method derives Fick s second diffusion equation in discrete form. Although Eqs. 3.5 and 3.26 are identical, it is clear that the point method derivation is much faster with only a little practice, the discretisation formulae 3.10 to 3.13 are easily memorised and expressions like Eq. 3.26 can be written down straight from the diffusion equation. Furthermore, it will be seen that if the... 

As a first approach to calculate the combined bulk and Knudsen diffusive flux using a Fickian flux formulation, the Bosanquet formula [11] has been suggested in literature [11,70,151]. In this approach, the Fick form formulation uses a diffusivity computed as the reciprocal additivity of the diffusion coefficients in the ordinary and Knudsen diffusion regimes. 

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