Fickian diffusion equation

Sorption Rates in Batch Systems. Direct measurement of the uptake rate by gravimetric, volumetric, or pie2ometric methods is widely used as a means of measuring intraparticle diffusivities. Diffusive transport within a particle may be represented by the Fickian diffusion equation, which, in spherical coordinates, takes the form... 

The development of the theory of solute diffusion in soils was largely due to the work of Nye and his coworkers in the late sixties and early seventies, culminating in their essential reference work (5). They adapted the Fickian diffusion equations to describe diffusion in a heterogeneous porous medium. Pick s law describes the relationship between the flux of a solute (mass per unit surface area per unit time, Ji) and the concentration gradient driving the flux. In vector terms. 

The analysis of the ZLC desorption curve involves solving Fickian diffusion equation with appropriate initial and boundary conditions (9). The solution of the desorption curve for spherical geometry is given as ... 

For the distributed-parameter skin compartment model, the concentration Csc is calculated by discretizing the stratum corneum compartment into a set of iV -i-2 equidistant nodes and using the central difference formula. This results in the representation of the one-dimensional Fickian diffusion equation to calculate mass flux at any depth within the stratum corneum (46) ... 

The self part Gs(r,f) of the van Hove correlation function represents the probability that a proton, which was at the origin at time 0, will be at position r at time t. For a particle undergoing a translational diffusion with diffusion coefficient D, Gs(r,0 therefore obeys the Fickian diffusion equation... 

Ritger and Peppas proposed an equation for the release of fruit extract by-products from PLGA NP. This model could be seen as a generalised form of the Fickian diffusion Equation 6.1 [23] ... 

This equation describes the transient flow of an ideal gas in a porous medium. The above equation has a similar form to the standard Fickian diffusion equation... 

Substituting eq. (9.2-2a) into eq. (9.2-lb), we obtain the familiar looking Fickian diffusion equation written in terms of only the gas phase concentration... 

The linear Fickian diffusion equation (9.2-3) has the form (written in nondimensional form)... 

Unfortunately, because of the conplexity of the flow fields in most separators, reactors, and other devices where interfacial mass transfer occurs, solution of the Fickian diffusion equations for binary systems is not usually feasible. In these cases we typically use the empirical linear driving-force model for mass transfer that was briefly introduced in Section 1.3. This equation [a modification of Eq. ri-411 is... 

The diffusion coefficients determined in the conventional manner also were substituted into the analytical solutions of the purely Fickian diffusion equations for permeation, sorption and desorption into flat membrane [8]. 

This equation was used to predict diffusion of erucamide in polyamide-12, PA-12, at three temperatures. Film containing 15 wt% erucamide was placed between erucamide-free films and diffusion was carried out under isothermal conditions. Figures 7.1 and 7.2 show some data. Experimental points (Figure 7.1) obtained from gas chromatographic determination of concentration of erucamide confirm that the concentration profile calculated from a simple Fickian diffusion (equation 7.1) is correct. 

In some cases the Fickian model does not accurately represent moisture uptake in adhesives. This is illustrated in O Fig. 31.12a, which shows the uptake plot for an epoxide immersed in water at SO C. The experimental data appears to indicate Fickian diffusion however, the best fit of the Fickian diffusion equation to the data indicates equilibrium is reached more slowly than predicted by Fickian diffusion. This type of behavior is sometimes termed pseudo-Fickian behavior. In general, anomalous behavior is seen at high temperatures and humidity. 

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