Percolation segregation

Relative motion can be induced, for example, as a pile is being formed, as particles tumble and slide down a chute. The result of sifting/percolation segregation is usually a side-to-side variation of particles. In the case of a bin, the smaller particles will generally be concentrated under the fill point, with the coarse particles concentrated at the outside of the pile (Fig. 4). 

Percolation segregation is the movement of the small particles through the voids in the static powder bed. 

If effective, this technique would provide a very neat solution to the problem of mixing powders for many processes and would be particularly attractive if very large volumes of material were to be mixed. It presupposes that all the material is in motion and that there is no hold-up of material within the cycle. Segregation is likely to be a problem both on the free surface of the hopper and within the bulk of the material due, in both cases, to percolating segregation. 

Further evidence for microphase separahon has been seen by AFM. As expected, BPSH 00, with no ionic regions, displays no significant features in its AFM image. For BPSH 20, isolated ionic clusters have dimensions of 10-25 nm. These clusters are even more readily discerned from the non-ionic matrix in BPSH 40, but the domains appear to remain relatively segregated from each other. In the case of BPSH 50 and 60, connections between domains are clearly visible, especially in the case of the latter sample. It also should be noted, however, that these samples were in a dehydrated state. Therefore, it might be expected that even in the case of the lower acid content samples, it is likely that some channel formation between ionic domains will still occur upon the uptake of water. This can be clearly seen in its linear conductivity behavior as a function of disulfonated monomer (i.e., the percolation threshold has been reached by at least 20-30% content of disulfonated monomer). 

At the mesoscopic scale, interactions between molecular components in membranes and catalyst layers control the self-organization into nanophase-segregated media, structural correlations, and adhesion properties of phase domains. Such complex processes can be studied by various theoretical tools and simulation techniques (e.g., by coarse-grained molecular dynamics simulations). Complex morphologies of the emerging media can be related to effective physicochemical properties that characterize transport and reaction at the macroscopic scale, using concepts from the theory of random heterogeneous media and percolation theory. 

In this section, we describe the role of fhe specific membrane environment on proton transport. As we have already seen in previous sections, it is insufficient to consider the membrane as an inert container for water pathways. The membrane conductivity depends on the distribution of water and the coupled dynamics of wafer molecules and protons af multiple scales. In order to rationalize structural effects on proton conductivity, one needs to take into account explicit polymer-water interactions at molecular scale and phenomena at polymer-water interfaces and in wafer-filled pores at mesoscopic scale, as well as the statistical geometry and percolation effects of the phase-segregated random domains of polymer and wafer at the macroscopic scale. 

We have studied above a model for the surface reaction A + 5B2 -> 0 on a disordered surface. For the case when the density of active sites S is smaller than the kinetically defined percolation threshold So, a system has no reactive state, the production rate is zero and all sites are covered by A or B particles. This is quite understandable because the active sites form finite clusters which can be completely covered by one-kind species. Due to the natural boundaries of the clusters of active sites and the irreversible character of the studied system (no desorption) the system cannot escape from this case. If one allows desorption of the A particles a reactive state arises, it exists also for the case S > Sq. Here an infinite cluster of active sites exists from which a reactive state of the system can be obtained. If S approaches So from above we observe a smooth change of the values of the phase-transition points which approach each other. At S = So the phase transition points coincide (y 1 = t/2) and no reactive state occurs. This condition defines kinetically the percolation threshold for the present reaction (which is found to be 0.63). The difference with the percolation threshold of Sc = 0.59275 is attributed to the reduced adsorption probability of the B2 particles on percolation clusters compared to the square lattice arising from the two site requirement for adsorption, to balance this effect more compact clusters are needed which means So exceeds Sc. The correlation functions reveal the strong correlations in the reactive state as well as segregation effects. 

Reduction of segregation. When mixtures of powders and granules are mixed, the powder will percolate through the interstitial voids of the granules. By granulating the powder, the segregation can be reduced. 

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