Reaction and transport in disordered composite media: Introduction of percolation concepts

Reaction and transport in disordered composites are percolation processes. In this paper, the relevant ideas of percolation theory are laid out and illustrated with the aid of computer simulations. The concepts of percolation theory closely coupled with computer constructs and mathematical modelling provide potent tools for understanding the role of irregular morphology in transient reaction and diffusion processes in disordered composites. Examples given involve diffusion, combustion, and catalysis in porous media, conduction in cellular media, and reaction and conduction in branched polymer systems. The rate at which a combustible porous medium becomes unconsolidated (disintegrates) under combustion is predicted. The effect of porosity on gas penetration and reaction rate in a porous pellet supporting a catalyst is investigated. Transient conduction in cellular systems is studied. Conduction in regular cellular media (squares and hexagons) is compared to conduction in irregular cellular media (Voronoi polygons). The effect of randomly distributed impervious cells and cell-walls is examined. The role of bond coordination number in the molecular weight distribution, gel formation, and electrical conduction of branched polymers is studied. In applications, the percolation threshold and material distributions under conditions near threshold can play a crucial role. The percolation threshold of material i is the volume, area, cell, or cell-wall fraction below which material i exists only in isolated clusters. Analytical results are obtained in some cases, numerical in others.

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