Percolation defined

Leachate in landfills. Leachate may be defined as hquid that has percolated through sohd waste and has extracted dissolved or suspended materials from it. In most landfills, the liqiiid portion of the leachate is composed of the liquid produced from the decomposition of the wastes and liquid that has entered the landfill from external sources, such as surface drainage, rainfall, groundwater, and water form underground springs. Representative data on chemical characteristics of leachate are reported in Table 25-72. 

The percolation parameters (p — Pc) associated with the disentanglement process are derived as follows p is the normalized entanglement density defined as... 

Its main features are given by the use of a stream of inert carrier gas which percolates through a bed of an adsorbent covered with adsorbate and heated in a defined way. The desorbed gas is carried off to a detector under conditions of no appreciable back-diffusion. This means that the actual concentration of the desorbed species in the bed is reproduced in the detector after a time lag which depends on the flow velocity and the distance. The theory of this method has been developed for a linear heating schedule, first-order desorption kinetics, no adsorbable component in the entering carrier gas (Pa = 0), and the Langmuir concept, and has already been reviewed (48, 49) so that it will not be dealt with here. An analysis of how closely the actual experimental conditions meet the idealized model is not available. 

The advantages of this type of system are obvious the pore space is of sufficient complexity to represent any natural or technical pore network. As the model objects are based on computer generated clusters, the pore spaces are well defined so that point-by-point data sets describing the pore space are available. Because these data sets are known, they can be fed directly into finite element or finite volume computational fluid dynamics (CFD) programs in order to simulate transport properties [7]. The percolation model objects are taken as a transport paradigm for any pore network of major complexity. 

O2 diffusion through the membrane seems to be limited by the percolation network of the diffusion path, which is not only defined by the amount of water in the membrane, but also by the different chemical structure of the membranes. It is difficult to make comparisons of gaseous diffusion behavior among polymers with different structures because polymer morphology can change drastically without appreciable changes in density, and the presence of water and the hydrogen bonds formed between polymer-water moieties also has major effects on system properties. However, some points can be made from these particular studies. 

Accumulation of salt in the root zone can be prevented by allowing a certain amount of water to percolate through the root zone. This is known as the leaching requirement, and is defined as the leaching fraction, LF, such that ... 

Thus, in summary, self diffusion measurements by Lindman et a (29-34) have clearly indicated that the structure of microemulsions depends to a large extent on the chain length of the oosurfactant (alcohol), the surfactant and the type of system. With short chain alcohols (hydrophilic domains and the structure is best described by a bicontinuous solution with easily deformable and flexible interfaces. This picture is consistent with the percolative behaviour observed when the conductivity is measured as a function of water volume fraction (see above). With long chain alcohols (> Cg) on the other hand, well defined "cores" may be distinguished with a more pronounced separation into hydrophobic and hydrophilic regions. 

The percolation model, which can be applied to any disordered system, is used for an explanation of the charge transfer in semiconductors with various potential barriers [4, 14]. The percolation threshold is realized when the minimum molar concentration of the other phase is sufficient for the creation of an infinite impurity cluster. The classical percolation model deals with the percolation ways and is not concerned with the lifetime of the carriers. In real systems the lifetime defines the charge transfer distance and maximum value of the possible jumps. Dynamic percolation theory deals with such case. The nonlinear percolation model can be applied when the statistical disorder of the system leads to the dependence of the system s parameters on the electrical field strength. 

We study here the A + 5B2 —> 0 reaction upon a disordered square lattice on which only a certain fraction S of lattice sites can be accessed by the particles (the so-called active sites). We study the system behaviour as a function of the mole fractions of A and B in the gas phase and as a function of a new parameter S. We obtain reactive states for S > Sq where Sq is the kinetically defined percolation threshold which means existence of an infinite cluster of active sites. For S < Sq we obtain only finite clusters of active sites exist. On such a lattice all active sites are covered by A and B and no reaction takes place as t —> 00. 

For S > Sc we obtain an infinite cluster for which in principle a reactive state exists. We use this fact to define the percolation threshold in a kinetic way for the particular reaction at hand as the transition point from the reactive (Rco2 > 0) to the non-reactive (Rco2 — 0) state. As we have shown above, this transition happens in such a way that the kinetic phase transition points of 2/1 and are approaching each other if S —> Sc [25]. At S = Sc the... 

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. 

Percolation simulations on a computer on the other hand demonstrate nicely the formation of a well defined surface43"45. The prediction of the gel point still remains poor probably the extent of ring formation is overestimated in the presently used simplest models for percolation. 

Chromatography may be defined as a physical method of separation in which the components to be separated are partitioned between two phases. One of these is stationary(solid or liquid), the -other being mobile(liquid or gas) percolates thru stationary phase(Refs 58, 77 78)... 

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