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 a of the front between the fluids is found to scale with the dimensionless Bond number Bo (ratio between gravitational and capillary forces) as CT~BO~^^^, as predicted by theory. The external perimeter of the invaded structure is shown to be fractal with the fractal dimension Z)^ -1.34 for length scales smaller than the front width.PACS numbers: 47.55.Mh, 05.40.+J, 47.55.Kf, 64.6aAk Slow fluid-fluid displacement in a porous medium under the influence of gravitational forces is important in oil production, in hydrology, in chemical engineering, and in the physics of disordered media. Front structures observed in two-phase flow exhibit patterns that range from compact to disordered and ramified [1,2]. Commonly studied processes are fast viscous fingering [3-5] dominated by viscous forces (modeled by the diff*usion-limited aggregation algorithm [6]) and slow invasion percolation (IP) [7,8], where capillary forces dominate, which is simulated by the IP algorithm [9,10]. The interfaces between the fluids form fractal fronts [11,12] having no intrinsic length scale.Most systems of practical importance are threedimensional (3D) and include fluids of diff*erent densities. Therefore, it is important to study the eff'ect of gravity on the front structure. Gravity causes hydrostatic pressure gradients in the fluids, and introduces a length scale that leads to crossover phenomena. If the less-dense fluid is on top of the heavier fluid, gravity eff'ects stabilize the front. In quantitative terms the competition between gravity and capillary forces is described by the dimensionless Bond number: Bo=ga^Ap/7, where g is the acceleration of gravity, cf is a typical pore size, Ap is the fluid density diff*erence, and / is the fluid interface tension.Little experimental information on gravity eff'ects is available and experiments with a systematic variation of Bo are needed. Clement and co-workers [13] performed 3D IP experiments. Nonwetting Woods metal was slowly injected from below into a column of crushed glass. Horizontal cuts of the solid material were analyzed to determine the spatial correlations of the metal and the fractal character of the front was studied. However, they used only one value of Bo.Here we present two-dimensional (2D) experiments where, for the first time, Bo was varied systematically by tilting the plane of the experimental model from the horizontal plane. The resulting invasion front geometry was studied quantitatively and compared to theory and 2D computer simulations. Figure 1 shows pictures of experiments and results from simulations at two diff^erent We found (Fig. 2) that the front width scales asThe exponent 0.57, consistent with the theoretical prediction of f, will be discussed below. We also found that the fronts between the two fluids had a fractal dimension ^exp~L34, consistent with the...
