Percolating porosity

J. Chadam, E. Merino, P. Ortoleva, and A. Sen "Reactive Percolation Porosity... 

Eor pesticides to leach to groundwater, it may be necessary for preferential flow through macropores to dominate the sorption processes that control pesticide leaching to groundwater. Several studies have demonstrated that large continuous macropores exist in soil and provide pathways for rapid movement of water solutes. Increased permeabiUty, percolation, and solute transport can result from increased porosity, especially in no-tiUage systems where pore stmcture is stiU intact at the soil surface (70). Plant roots are important in creation and stabilization of soil macropores (71). 

Solution porosity refers to voids formed by the solution of the more soluble portions of the rock in the presence of subsurface migrating (or surface percolating) waters containing carbonic and other organic acids. Solution porosity is also called vugularporosity where individual holes are called vugs. 

Figure 26 shows plots of this constriction factor verses porosity for various values of L. As observed in Figure 21 for the Michaels model of diffusion in such a cell, the percolation limits are seen where the constriction factor goes to zero at = L/(l + L). 

Figure 2.9.3 shows typical maps [31] recorded with proton spin density diffusometry in a model object fabricated based on a computer generated percolation cluster (for descriptions of the so-called percolation theory see Refs. [6, 32, 33]).The pore space model is a two-dimensional site percolation cluster sites on a square lattice were occupied with a probability p (also called porosity ). Neighboring occupied sites are thought to be connected by a pore. With increasing p, clusters of neighboring occupied sites, that is pore networks, begin to form. At a critical probability pc, the so-called percolation threshold, an infinite cluster appears. On a finite system, the infinite cluster connects opposite sides of the lattice, so that transport across the pore network becomes possible. For two-dimensional site percolation clusters on a square lattice, pc was numerically found to be 0.592746 [6]. 

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

Fig. 2.9.13 Qu asi two-dimensional random ofthe percolation model object, (bl) Simulated site percolation cluster with a nominal porosity map of the current density magnitude relative p = 0.65. The left-hand column refers to simu- to the maximum value, j/jmaK. (b2) Expedited data and the right-hand column shows mental current density map. (cl) Simulated NMR experiments in this sample-spanning map of the velocity magnitude relative to the cluster (6x6 cm2), (al) Computer model maximum value, v/vmax. (c2) Experimental (template) for the fabrication ofthe percolation velocity map. The potential and pressure object. (a2) Proton spin density map of an gradients are aligned along the y axis, electrolyte (water + salt) filling the pore space...

Percolation models differ from the zone-refining model essentially by the absence of mixing in the liquid, giving the liquid position-dependent properties. A simplified account of these models was described in Chapter 8. We will now provide a reasonably comprehensive account which may prove useful to the demanding reader, and then examine some properties of the chromatographic effect in a simple configuration. Let

open volume porosity of the medium, pso, and pliq the density of the solid matrix and melt, respectively, vliq the liquid velocity relative to the matrix, and Cso, and CHq the concentration of element i in the matrix and melt, respectively. Let us rewrite equation (8.3.14) as... 

Table 9.7. Ratio v /vHll during percolation of a melt with specific density 2.7 through a porous matrix with specific density 3.4 for different values of partition coefficient D, and porosity

A quite serious problem, however, still obscures most applications of the percolation theory to the transport of magmas. Most major elements, such as Si, Mg, Ca,... can be considered as compatible since their concentration in the peridotite source and the basaltic melt are similar within a factor of 3. Equation (9.4.37) indicates, as would equations (8.3.17) and (8.3.19) in the most general case, that major elements are slower than the liquid, especially for small porosities. But, what is the liquid made of, then The velocity of a medium is the weighted average velocity of its constituents [see equation (8.1.4)]. The basalt velocity is that of Si, Mg, Ca,... weighted by their... 

Porosity characteristics also influence the degradation rate of blends containing intact starch grains. Amylase removal of starch from these films was not highly correlated with starch content, since films whose starch content was above possible "percolation thresholds" (6) were degraded at very different rates when starch content was not very different (Table I). 

Graphites with larger surface areas or greater porosities have a distinctly lower percolation threshold. It is assumed that the conductivity of a compound depends upon the structured agglomerates being sufficiently close to each other, or in direct contact above the percolation point, and on the continuous current pathways created thereby (14-15). 

Downward movement of triazines may occur from percolating water carrying them to lower soil depths. Within well-structured soils with abundant macropores, triazines have been reported to move to deeper depths than in nonstructured soils with fewer pores. Increased permeability, percolation, and solute movement can result from increased porosity -especially in no-tillage systems where there is pore connectivity at the soil surface. Triazines can move to shallow ground-water by macropore flow in sandy soil if sufficient rainfall occurs shortly after they are applied (Ritter et al, 1994a, b). 

The reason to extend the experiments to tooth material was the idea that the matrix would have a less porous structure compared to human haversian bone and be less exposed to diagenetic alteration. While the porosity in human bone is mainly determined by a complicated network between the Haversian system and the Volk-mann canals that are perpendicular to it, especially enamel is a far denser material than human bone and its organic content is significantly less (2% of organic material only). But in contrast to the enamel, dentine has a similar composition of the organic and the inorganic matrix compared to bone, and it has a high microporosity due to nerve canals that start from the pulpa and stop close to the enamel-dentine junction (edj). However, these nerve canals have a smaller diameter than a haversian pore (70 pm) and the canals are orientated parallel and are not connected with each other. So a fluorine ion cannot percolate from one pore to another, as it is the case in a human bone, but it has to overcome the distance from one canal to the next one by diffusion. So the permeability is low and this results in a smaller diffusion rate D. 

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