Diffusion-like processes

The fact that the mean square displacement is proportional to the number of steps is typical for diffusion-like processes. It implies for the displacement per unit time... 

Two main types of models are in common use for describing axial mixing in bubble columns. The most commonly used model is the Dispersion Model. Here, a diffusion-like process is superimposed on piston or plug flow. The stirred tanks-in-series model has also been used to describe flow of liquids in bubble columns. Levenspiel (1 ) presents a number of models incorporating various combinations of mixed tanks to model stagnant regions and backflow. 

The mechanism of uptake of fatty acids by the cell is not completely understood. Transport of fatty acids across the endothelial cells, the interstitial space, and the plasmalemma of the parenchymal cells is most likely a diffusion-like process (Van der Vusse et al., 1992). Recent experimental findings indicate that (1) specific membrane proteins are involved in transmembrane transport and (2) the uptake of fatty acids by brain is limited by the blood-brain barrier. 

If reactant velocity does not influence the rate of reaction when an encounter pair is formed (see Sect. 2.4), the effect of velocity may be removed from an analysis of the solute motion. Davies [447] showed that, when the velocity distribution is of no interest, the position and time distribution of a solute is described by the telegrapher s equation. It is a diffusion-like process, but one where the particle has a limiting velocity so that a wave of solute probability spreads out with a... 

The axial dispersion in the liquid phase of a trickle-bed reactor results from transport processes occurring at the particle scale i.e., in each flow trajectory considered as independent, as well from the velocity distribution observed at the bed scale. If we assume that the axial dispersion at the particle scale may be represented by a diffusion-like process, the local mass balance in channel i is given by... 

Busselez et al. [56] used neutron scattering with H/D substitution labeling to examine the structure and dynamics of glassy PVP and water in hydrated PVP systems, from which they identified two types of water motion. Consistent with the earlier simulations, they obtained structural evidence for the existence of water clusters, nanosegregation of PVP side-groups, and swelling and disorder within ring nanodomains in the presence of water. The Q-dependence observed for the relaxation time of water molecules indicated that water relaxation was a diffusive-like process in water-rich domains while between water clusters subdiffusive motions prevailed. 

In a comprehensive treatment of the nucleation and crystallization of glass, it would be necessary to consider spinodal separation into two phases by a diffusion-like process without initial formation of surfaces, and consequently without the surface energy barrier encountered in classical nucleation theory ( ). However, this type of nucleation does not appear to enter into the crystallization we have observed in the Ba0-B203-Al203 system. 

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