The concept of percolation is important for many aspects of science and technology . For materials, percolation really only applies to a random material, made up of two or more phases.
Through some process, one or more phases are being randomly built up, for example through being the products of chemical reaction, or randomly consumed, via being the reactant in a chemical reaction. At any instant of time, a phase is either topologically connected throughout the microstructure, or topologically disconnected. If connected, then a hypothetical ant could walk from one side of the material to the other along this phase. If disconnected, then the ant would have to "jump" some gaps between parts of the phase in order to proceed along it. When a phase goes from being disconnected to connected, or vice versa, so that there is a change in topology, then we call this point a percolation threshold, and denote the volume fraction of the phase at this point with a subscript "c."
Percolation obviously has a strong influence on transport. When a material only has one phase that is active in transport, then when that phase is percolated, the material has a non-zero transport property. When that phase is disconnected, then the material has a zero transport property. When two or more phases are active in transport, for example electrical conductivity, then the contrast between the conductivity of each kind of material matters, as well as their relative connectedness.
Since the hydration model is digitally based, it is easy to check whether any given phase or combination of phases is percolated using a modified burning algorithm . This algorithm computes whether or not a phase is percolated. If the phase is percolated, the algorithm also computes how much of the phase is percolated, and how much is isolated. In this paper, the "Fraction Connected" is reported in many of the percolation figures, which is numerically equal to the fraction of the phase in question that is percolated.