Gravity invasion percolation in two dimensions: Experiment and simulation

Abstract

We present experiments and computer simulations of slow drainage in a two-dimensional porous medium. The effect of gravity is systematically varied by tilting the system from the horizontal position. The width \ensuremath{\sigma} of the front between the fluids is found to scale with the dimensionless Bond number Bo (ratio between gravitational and capillary forces) as \ensuremath{\sigma}\ensuremath{\sim}${\mathrm{Bo}}^{\mathrm{\ensuremath{-}}0.57}$, as predicted by theory. The external perimeter of the invaded structure is shown to be fractal with the fractal dimension ${\mathit{D}}_{\mathit{e}}$\ensuremath{\simeq}1.34 for length scales smaller than the front width.