Fickian diffusivities

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 release of steroids such as progesterone from films of PCL and its copolymers with lactic acid has been shown to be rapid (Fig. 10) and to exhibit the expected (time)l/2 kinetics when corrected for the contribution of an aqueous boundary layer (68). The kinetics were consistent with phase separation of the steroid in the polymer and a Fickian diffusion process. The release rates, reflecting the permeability coefficient, depended on the method of film preparation and were greater with compression molded films than solution cast films. In vivo release rates from films implanted in rabbits was very rapid, being essentially identical to the rate of excretion of a bolus injection of progesterone, i. e., the rate of excretion rather than the rate of release from the polymer was rate determining. 

Release of tetracycUne hydrochloride from PCL fibers was evaluated as a means of controlled administration to periodontal pockets (69). Only small amounts of the drug were released rapidly in vitro or in vivo, and poly(ethylene-co-vinyl acetate) gave superior results. Because Fickian diffusion of an ionic hydrochloride salt in a UpophiUc polymer is unlikely, and because PCL and EVA have essentially identical Fickian permeabilities, we attribute this result to leaching of the charged salt by a mechanism similar to release of proteins from EVA (73). Poly-e-caprolactone pellets have been found unsuitable for the release of methylene blue, another ionic species (74,75). In this case, blending PCL with polyvinyl alcohol (75% hydrolyzed) increased the release rate. 

Malek K, Coppens MO. 2003. Knudsen self- and Fickian diffusion in rough nanoporous media. J Chem Phys 119 2801-2811. 

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. 

Transport in the polymeric system is assumed to be by Fickian diffusion, although the diffusivity of the various species depends on the extent of hydrolysis of the polymeric linkages. 

The rate and type of release can be analyzed by the expression Mt/Moo=ktn (76). In the case of pure Fickian diffusion n = 0.5, whereas n > 0.5 indicates anomalous transport, i.e., in addition to diffusion another process (or processes) also occurs. If n = 1 (zero order release), transport is controlled by polymer relaxation ("Case II transport") (76). The ln(Mt/Mco) versus In t plots, shown in Figure 4, give n = 0.47 and 0.67 for samples A-9.5-49 and A-4-56, respectively. Evidently theophylline release is controlled by Fickian diffusion in the former network whereas the release is... 

Permeability A rate of mass transfer, usually expressed per unit surface area. For Fickian diffusion in a membrane, the permeability is proportional to the diffusion coefficient and inversely proportional to the membrane thickness. 

Criteria 1-3 are the cardinal characteristics of Fickian diffusion and disregard the functional form of D(ci). Violation of any of these is indicative of non-Fickian mechanisms. Criterion 4 can serve as a check if the D(ci) dependence is known. As mentioned, it is crucial that the sorption curve fully adhere to Fickian characteristics for a valid determination of D from the experimental data. At temperatures well above the glass transition temperature, 7 , Fickian behavior is normally observed. However, caution should be exercised when the experimental temperature is either below or slightly above 7 , where anomalous diffusion behavior often occurs. 

This solution is valid for the initially linear portion of the sorption (or desorption) curve when MtIM is plotted against the square root of time. These equations also demonstrate that for Fickian processes the sorption time scales with the square of the dimension. Thus, to confirm Fickian diffusion rigorously, a plot of MJM vs. Vt/T should be made for samples of different thicknesses a single master curve should be obtained. If the data for samples of different thicknesses do not overlap despite transport exponents of 0.5, the transport is designated pseudo-Fickian. ... 

In order to improve the predictive power of the Fickian diffusion theory, a concentration dependent diffusion coefficient is used in Eqs. (15) and (16). Equation (16) is then rewritten and solved with the appropriate boundary conditions ... 

Rastogi, N.K., Raghavarao, K.S.M.S., and Niranjan, K. 1997. Mass transfer during osmotic dehydration of banana Fickian diffusion in cylindrical configuration. J. Food Engineer. 31, 423-432. 

Jiang, T.-L., P. Givi, and F. Gao (1992). Binary and trinary scalar mixing by Fickian diffusion - Some mapping closure results. Physics of Fluids A Fluid Dynamics 4, 1028-1035. 

Figure 14 Master curve generated from mean-square displacements at different temperatures, plotting them against the diffusion coefficient at that temperature times time. Shown are only the envelopes of this procedure for the monomer displacement in the bead-spring model and for the atom displacement in a binary Lennard-Jones mixture. Also indicated are the long-time Fickian diffusion limit, the Rouse-like subdiffusive regime for the bead-spring model ( ° 63), the MCT von Schweidler description of the plateau regime, and typical length scales R2 and R2e of the bead-spring model.

The form of the time-dependence can be understood from the anomalous diffusion of a piece of Rouse chain, which displaces in time such that rather than t. As a result the exp(-k Dt) scattering from Fickian diffusers is replaced by The initial structure factor S(k,0) is... 

Early-time motion, for segments s such that UgM(s)activated exploration of the original tube by the free end. In the absence of topological constraints along the contour, the end monomer moves by the classical non-Fickian diffusion of a Rouse chain, with spatial displacement f, but confined to the single dimension of the chain contour variable s. We therefore expect the early-time result for r(s) to scale as s. When all prefactors are calculated from the Rouse model [2] for Gaussian chains with local friction we find the form... 

The major pathway of drug transport across buccal mucosa seems to follow simple Fickian diffusion [17]. Passive diffusion occurs in accordance with the pH-partition theory. Considerable evidence also exists in the literature regarding the presence of carrier-mediated transport in the buccal mucosa [18,19]. Examination of Eq. (1) for drug flux,... 

Drug release from soluble polymers is accompanied by the gradual erosion-type dissolution of the polymer. Therefore, polymer dissolution and drug diffusion may be the overall hybrid mechanism of release. Drug release from nonsoluble hydrogels generally follows Fickian or non-Fickian diffusion kinetics [51]. The mechanism of... 

While the advection-dispersion equation has been used widely over the last half century, there is now widespread recognition that this equation has serious limitations. As noted previously, laboratory and field-scale application of the advection-dispersion equation is based on the assumption that dispersion behaves macroscopically as a Fickian diffusive process, with the dispersivity being assumed constant in space and time. However, it has been observed consistently through field, laboratory, and Monte Carlo analyses that the dispersivity is not constant but, rather, dependent on the time or length scale of measurement (Gelhar et al. 1992),... 

THE BERENS-HQPFENBERG MODEL. The Berens and Hopfenberg model considers the sorption process in glassy polymers as a linear superposition of independent contributions of a rapid Fickian diffusion into pre-existing holes or vacancies (adsorption) and a slower relaxation of the polymeric network (swelling).(lS) The total amount of sorption per unit weight of polymer may be expressed as... 

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