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Numerical simulations of mercury injection using three-dimensional resistor networks demonstrate that the electrical resistance decreases in stepwise fashion with increasing occupation probability near the resistance percolation threshold. The power-law nature of the resistance-step distribution and the value of the exponent are consistent with results on porous materials obtained during mercury injection in the presence of a gravitational gradient. These studies include the effects of gravity and a distribution of pore sizes. The results provide a direct connection between the configuration of the injected mercury and the geometry of a percolation cluster in both the standard and the graded percolation problems.
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Katz et al. (1988) studied this question.
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