  We use confocal microscopy to directly visualize the simultaneous flow of
both a wetting and a non-wetting fluid through a model three-dimensional (3D)
porous medium. We find that, for small flow rates, both fluids flow through
unchanging, distinct, connected 3D pathways; in stark contrast, at sufficiently
large flow rates, the non-wetting fluid is broken up into discrete ganglia. By
performing experiments over a range of flow rates, using fluids of different
viscosities, and with porous media having different geometries, we show that
this transition can be characterized by a state diagram that depends on the
capillary numbers of both fluids, suggesting that it is controlled by the
competition between the viscous forces exerted on the flowing oil and the
capillary forces at the pore scale. Our results thus help elucidate the diverse
range of behaviors that arise in two-phase flow through a 3D porous medium.
