  Slow flow of a single fluid through a porous medium is well understood on a
macroscopic level through Darcy's law, a linear relation between flow rate and
a combination of pressure differences, viscosity, and gravitational forces.
Two-phase flow is complicated by the interface separating the fluids, but
understanding of two-dimensional, two-phase flow has been obtained from
experiments using transparent cells. In most three-dimensional media, however,
visual observation is difficult. Here, we present preliminary results of
experiments on a model medium consisting of randomly packed glass spheres, in
which one fluorescent liquid invades another. By refractive index matching and
scanning with a sheet-shaped laser beam, we obtain slices of the flow patterns,
which we combine into three-dimensional pictures. We observe a compact region
of invading fluid, surrounded by finger-like protrusions. The compact region
becomes more dominant with increasing invader flow rate. The patterns are
theoretically analyzed in terms of the interplay between gravitational,
viscous, and capillary forces.
