Coordination-number dependent universality in Mixed Wet Percolation

Mixed-wet percolation was introduced recently in the context of two-phase flow in porous media. In this model, the sites of the primal lattice are occupied with a certain probability $p$, and bonds are placed on the dual lattice between two adjacent occupied and unoccupied sites of the primal lattice. The occupied bonds on the dual lattice form perimeter clusters. In this paper, we investigate the scaling properties of the geometric quantities associated with the perimeter clusters of mixed-wet percolation on the dual triangular and dual honeycomb lattices. Although mixed-wet percolation on the dual triangular lattice with a higher coordination number ($z=6$) exhibits ordinary site percolation, the model on the dual honeycomb lattice with a lower coordination number ($z=3$) exhibits the properties of the hull of ordinary site percolation clusters. Such a $z$ dependent breakdown of universality in mixed-wet percolation is rare in the percolation literature. The perimeter clusters in the triangular lattice represent the boundary of the site clusters in the primal lattice, whereas the perimeters in the honeycomb lattice represent their hulls. Because of the low $z$ of the honeycomb lattice, the external and internal perimeters remain isolated. However, the combined external and internal perimeters form cluster boundaries of the site clusters that belong to the site percolation universality class.