Effective coordination number percolation

Figure 12. The effective coordination numbers /r, and enhancement exponents 7, versus 9 for —10 < 9 < 10 of SAW configurations on the backbone of the critical percolation cluster in d = 2 (adapted from Ref. [74]). The values for fi and 7 on regular square lattice are marked by arrows, clearly showing that lim, joo % is larger than 7 on regular square lattice. The inset shows p, versus 9 for —2 < g < 2 in d = 2, in good agreement with the theoretical result p, = no(l + qa IT) (continuous line), suggested for jqj 0, with Ho = 1.456 and cto = 0-45 [75].

In general, different lattices with the same dimensionality and coordination number, e.g. the hexagonal and Voronoi polygon, exhibit similar behavior [40]. More importantly, the effective diffusion coefficient on these lattice structures can be closely approximated by selecting a Bethe lattice with an appropriate effective coordination number For example, three-dimensional cubic and Voronoi polyhedron lattices, with coordination numbers of 6 and 16, have the same effective diffusion coefficient behavior as Bethe lattices with coordination number of 5 and 7 [44]. Therefore, the effective diffusion coefficient and tortuosity trends shown in Figure 6 are applicable to percolation lattices with widely different geometries. Prediction of the effective diffusivity of a given real lattice follows directly from selection of an effective Bethe coordination number. 

Contamination, 7 35 Continuity, 437-439 Continuous random network, 574, 621 Continuum percolation, 322, 328-330, 347 Contraction. See Shrinkage Convective heating, 475, 477 Cooling rale critical, 731 effect on T, 748-751 Coordination number, 255, 266-267, 269, 292, 698, 720... 

---