Fractal diffusion

The foregoing treatment can be extended to cases where the electron-ion recombination is only partially diffusion-controlled and where the electron scattering mean free path is greater than the intermolecular separation. Both modifications are necessary when the electron mobility is - 100 cm2v is-1 or greater (Mozumder, 1990). It has been shown that the complicated random trajectory of a diffusing particle with a finite mean free path can have a simple representation in fractal diffusivity (Takayasu, 1982). In practice, this means the diffusion coefficient becomes distance-dependent of the form... 

Fractals, Diffusion, and Relaxation in Disordered Complex Systems A Special Volume of Advances in Chemical Physics, Volume 133, Part A, edited by William T. Coffey and Yuri P. Kalmykov. Series editor Stuart A Rice. 

FRACTALS, DIFFUSION, AND RELAXATION IN DISORDERED COMPLEX SYSTEMS... 

Ngai, K. L., Casalini, R., Capaccioli, S., Paluch, M., and Roland, C. M. (2006) Adv. Chem. Phys. in Chemical Physics Part B, Fractals, Diffusion and Relaxation in Disordered Complex Systems, 133B, 497-582... 

Adv. Chem. Phys. in Chemical Physics Part B, Fractals, Diffusion and Relaxation in Disordered Complex Systems, 133B, 497-582... 

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... 

Fig. 3. The ramified fractal nature of diffuse interfaces is shown for (top) a computer simulated 2-d monomer-monomer interface where the heavy region represents the connected monomers on one side, (middle) a simulated 2-d random coil polymer interface at the reptation time, and (bottom) electrochemically deposited Silver diffusing in polyimide with the unconnected metal atoms removed to show the fractal diffusion front of the connected metal atoms. (Wool and Long)...

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