Slowing-down diffusion theory

Apart from this limitation, the principal restriction in the use of the Fermi age model is due to the large number of conditions which must be satisfied by the physical system if the model is to be valid (see Sec. 7.3i). However, even with this shortcoming, the model is still very useful for preliminary studies and for gaining insight into the essential features of many reactor problems. The Fermi age or continuous-slowing-down diffusion theory, then, offers some generality without introducing excessive computational difficulties. 

The appropriate time-dependent differential equations for the com-bined-slowing-down diffusion theory may be obtained by recognizing that the time rate of change of the neutron density is given by the difference between the rates of disappearance and appearance of neutrons from sinks and sources. Thus we write... 

D also depends on the presence of crystallites slowing down diffusion. Starting from a classical theory very often used for the diffusion of gases in PE [92,93] ... 

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

As corrosion products develop, the rate of diffusion of O2 reduces and, in theory, the (general wastage) corrosion rate slows down, but in practice the presence of deposits tends to promote various forms of localized corrosion involving oxygen, such as tuberculation. 

One explanation for anomalous diffusion in Hamiltonian dynamics is the presence of self-similar invariant sets or hierarchical structures formed in phase space that play the role of partial barriers. They slow down the normal diffusion. A different explanation for intermittent behavior is given by the existence of deformed and approximate adiabatic invariants in phase space. They are shown in terms of elaborated perturbation theories such as the KAM and Nekhoroshev theorems. 

Experimentally, the resistance at the interface has been shown to be negligible for most cases of mass transfer where chemical reactions do not occur, such as absorption of common gases from air to water and extraction of organic solutes from one phase to another. However, there are some exceptions. Certain surface-active compounds may concentrate at the interface and cause an interfacial resistance that slows down the diffusion of solute molecules. Theories to predict when interfacial resistance may occur are still obscure and unreliable. 

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