Applications Of Percolation TheoryOver the past two decades percolation theory has been used to explain and model a wide variety of phenomena that are of industrial and scientific importance. Examples include characterization of porous materials and reservoir rocks, fracture patterns and earthquakes in rocks, calculation of effective transport properties of porous media permeability, conductivity, diffusivity, etc., groundwater flow, polymerization and gelation, biological evolution, galactic formation in the universe, spread of knowledge, and many others. Most of such applications have resulted in qualitative as well as quantitative predictions for the system of interest. This book attempts to describe in simple terms some of these applications, outline the results obtained so far, and provide further references for future reading. |
Contents
1 Connectivity as the essential physics of disordered systems | 1 |
2 Elements of percolation theory | 8 |
3 Characterization of porous media | 23 |
4 Earthquakes and fracture and fault patterns in heterogeneous rock | 41 |
5 Singlephase flow and transport in porous media | 56 |
6 Hydrodynamic dispersion and groundwater flow in rock | 81 |
7 Twophase flow in porous media | 101 |
8 Transport reaction and deposition in evolving porous media | 127 |
9 Fractal diffusion and reaction kinetics | 150 |
10 Vibrations and density of states of disordered materials | 164 |
11 Structural mechanical and rheological properties of branched polymers and gels | 177 |
12 Morphological and transport properties of composite materials | 203 |
13 Hopping conductivity of semiconductors | 238 |
14 Percolation in biological systems | 257 |
| 268 | |
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Common terms and phrases
agreement applications assumed average behavior bonds calculated called cells close cluster completely composite conductivity connected Consider constant correlation curves defined density dependence developed diffusion dimension direction discussed discussed in Chapter disordered dispersion displacement distribution effective elastic equation estimate et al example experimental data experiments field Figure finite flow fluid forces fractal fraction fracture frequency function given grains imbibition important increase indicate interested lattice length Lett macroscopic mean measured medium metal method obtain particles percolation model percolation networks percolation threshold permeability phase Phys polymers pore pore space porosity porous media predictions pressure probability problem properties radius random reaction regime region represents rock Sahimi sample sample-spanning scaling shows similar simulations solid solution spheres structure studied surface theory three-dimensional transport usually various volume