Diffusion non-Fickian

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... 

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 some polymers exhibit non-Fickian diffusion below the Tg, many of these become Fickian as the temperature is raised to above the Tg. 

Polymers may exhibit non-Fickian diffusion below the Tgt but a transition to Fickian diffusion is noted as the temperature is raised above the Tr The permeability of a gas, such as oxygen, is much greater through a silicone membrane than through a polyvinyl alcohol (PVA) membrane. Permeability of specific gases may be controlled by the use of composite membranes. 

Frisch, H.L., Multicomponent non-Fickian diffusion through inhomogeneous polymer membranes, J. Polym. Sci., A2 1115 (1964). 

Non-Fickian diffusion, 696 Non-functional structural groups, 129 Non-linear optics, 347 Non-Newtonian viscosity, 554 Non-redox doping, 345 Non-relaxed dielectric constant, 325 Normal... 

Moreover the electrodiffusion potential gradient is likely to cause electroosmotic transfer of the solution, whose local content is not in equilibrium with that of the counterions [5]. In this case, as it is pointed out in Ref. 5, the ion mobility and concentration depend on the prior history of the process which can bring about non-Fickian diffusion. The application of Nemst-Planck equations to the real system may require inclusion of additional terms that account for the effect of activity coefficient gradients which may be important in IE with zeolites [4,5]. 

Edwards DA. Non-Fickian diffusion in thin pol3uner films. J. Polym. Set, B Polym. Phys. 1996 34 981-997. 

It has long been known that, when the network of pores is fractal, diffusion by molecular movement in this network differs from the transport in media with properties independent of scale. In particular, diffusion of solutes in a fractal pore network does not obey Fick s law, and anomalous, or non-Fickian diffusion takes place instead (Gefen at al., 1983). When Fick s second law... 

The movement of solute particles in soils does not generally follow Brownian motion because soil at any scale consists of correlated units. A particle traveling faster than the mean at some instant is likely to still be traveling faster than the mean some later time (Benson, 1998). One may say that particles have a memory , and the memory of particles is the critical feature required for the occurrence of non-Fickian diffusion (Kin/clhach. 1987). Further, the underlying distribution... 

Tomozawa M, Molinelli J (1984) Non-fickian diffusion of water in glass. Rivista della Staz Sper Vetro 5 33-37... 

Various types of coupled non-linear Fickian diffusion processes were numerically simulated using the free-volume approach given by equation [12.8], as well as non-Fickian transport. The non-Fickian transport was modeled as a stress-induced mass flux that typically occurs in the presence of non-uniform stress fields normally present in complex structures. The coupled diffusion and viscoelasticity boundary value problems were solved numerically using the finite element code NOVA-3D. Details of the non-hnear and non-Fickian diffusion model have been described elsewhere [14]. A benchmark verification of the linear Fickian diffusion model defined by equations [12.3]-[12.5] under a complex hygrothermal loading is presented in Section 12.6. 

Polymeric network topology heavily reflects on drug diffusion as it concurs in determining the drug diffusion coefficient as later on discussed. Additionally, polymeric network can also be responsible for a non-Fickian diffusion. Indeed, in the presence of a very complex topology. 

STUDY OF NON-FICKIAN DIFFUSION ANOMALIES THROUGH TIME LAGS. I. SOME TIME-DEPENDENT ANOMALIES. 

Fickian and non-Fickian diffusion may oecur during plasticizer ineorporation, fusion and gelation... 

The problem of gas diffusion in, and permeation through, inhomogeneous polymers is more complex, but has been considered by a number of investigators [3,5,6,10]. The diffusion coefficient is then also a function of position. When the polymer is highly plasticized (i.e., swelled) by the penetrant, the diffusion coefficient may also become a function of time and of sample history. Such non-Fickian diffusion has also been smdied [3,5,11-16]. 

Although Fickian diffusion has been used to describe the diffusion mechanism of liquid through the rubbery material because of its simplicity and mathematical tractability, most of the rubber-solvent systems do not fit such a simplified explanation. Then, non-Fickian diffusion was developed. The case of non-Fickian diffusion was investigated using the following equation ... 

Figure 27.2 Different types of non-Fickian diffusion (a) classical, (b) two steps, (c) sigmoidal, (d) Case II.

Whereas the value of n equals 0.5, the mechanism of diffusion described by Case I of Fickian model, when n values range between 0.5 and 1 that exhibits anomalous transport model and when n value equals 1, Case II of non-Fickian model is used to determine. Fickian model describing the rate of diffusion of penetrant molecule is much less than the relaxation rate of polymer chains while Case II of non-Fickian diffusion representing rate of diffusion is rapid than relaxation process. For the anomalous transport model, both solvent diffusion rate and polymer relaxation rate are comparable. Figure 27.2 shows various types of non-Fickian model anomalous transport and Case II of non-Fickian are included in this group. ... 

For diffusion of liquid through rubbery polymer composites, Fickian and non-Fickian diffusion theories are frequently used to describe the mechanism of transport, but for gas or vapour, other models have been developed to fit experimental data of diffusion profiles. The models of gas transport include Maxwell s model," free volume increase mechanism," solubility increase mechanism," nanogap hypothesis," Nielsen model, " " Bharadwaj model, ° Cussler model " " and Gusev and Lusti model, " etc. 

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