Scaling of cluster mass between two lines in 3d percolation

We consider the cluster mass distribution between two lines of arbitrary orientations and lengths in porous media in three dimensions, and model the porous media by bond percolation at the percolation threshold pc. We observe that for many geometrical configurations the mass probability distribution presents power law behavior. We determine how the characteristic mass of the distribution scales with such geometrical parameters as the line length, w, the minimal distance between lines, r, and the angle between the lines, θ. The fractal dimensions of the cluster mass are independent of w,r, and θ. The slope of the power-law regime of the cluster mass is unaffected by changes in these three variables; however the characteristic mass of the cluster depends upon θ. We propose new scaling functions that reproduce the θ dependence of the characteristic mass found in the simulations.