  In disordered porous media, two-phase flow of immiscible fluids (biphasic
flow) is organized in patterns that sometimes exhibit fractal geometries over a
range of length scales, depending on the capillary, gravitational and viscous
forces at play. These forces, as well as the boundary conditions, also
determine whether the flow leads to the appearance of fingering pathways, i.e.,
unstable flow, or not. We present here a short review of these aspects,
focusing on drainage and summarizing when these flows are expected to be stable
or not, what fractal dimensions can be expected, and in which range of scales.
We base our review on experimental studies performed in two-dimensional
Hele-Shaw cells, or addressing three dimensional porous media by use of several
imaging techniques. We first present configurations in which solely capillary
forces and gravity play a role. Next, we review configurations in which
capillarity and viscosity are the main forces at play. Eventually, we examine
how the microscopic geometry of the fluid clusters affects the macroscopic
transport properties. An example of such an upscaling is illustrated in detail:
For air invasion in a mono-layer glass-bead cell, the fractal dimension of the
flow structures and the associated scale-ranges, are shown to depend on the
displacement velocity. This controls the relationship between saturation and
the pressure difference between the two phases at the macroscopic scale. We
provide in this case expressions for dynamic capillary pressure and residual
fluid phase saturations.
