Abstract
Capillary displacement in deterministic and random fractals is explored numerically and analytically using Invasion Percolation (IP) and Eden growth (EG) models. Both compressible and incompressible native fluid cases are studied. It is found that capillary displacements are markedly different for supports having or lacking singly connected links at all scales. It is shown that IP and EG models fill the support if there are links at all scales, for the compressible case. For the incompressible case, on the other hand, a formula is derived which relates the fractal dimension of EG cluster and the dimension of the minimal path and other non-universal quantities. Numerical estimates of the fractal dimension of IP clusters in several supports with links are obtained, and are shown to be different from the corresponding EG values for the incompressible case.
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