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Percolation theory and the associated conductance networks have provided deepinsights into the flow and transport properties of a vast number ofheterogeneous materials and media. In practically all cases, however, theconductance of the networks' bonds remains constant throughout the entireprocess. There are, however, many important problems in which the conductanceof the bonds evolves over time and does not remain constant. Examples includeclogging, dissolution and precipitation, catalytic processes in porousmaterials, as well as the deformation of a porous medium by applying anexternal pressure or stress to it that reduces the size of its pores. Weintroduce two percolation models to study the evolution of the conductivity ofsuch networks. The two models are related to natural and industrial processesinvolving clogging, precipitation, and dissolution processes in porous mediaand materials. The effective conductivity of the models is shown to followknown power laws near the percolation threshold, despite radically differentbehavior both away from and even close to the percolation threshold. Thebehavior of the networks close to the percolation threshold is described bycritical exponents, yielding bounds for traditional percolation exponents. Weshow that one of the two models belongs to the traditional universality classof percolation conductivity, while the second model yields non-universalscaling exponents.

Percolation and conductivity in evolving disordered media