  Transport in multiphase flow through porous media plays a central role in
many biological, geological, and engineered systems. Here, we use numerical
simulations of transport in immiscible two-phase flow to investigate dispersion
in multiphase porous media flow. While dispersion in the main flow direction is
similar to that of a single-phase flow and is governed by the porous media
structure, we find that transverse dispersion exhibits fundamentally different
dynamics. The repeated activation and deactivation of different flow pathways
under the effect of capillary forces lead to intermittent flow patterns,
strongly enhancing dispersion. We show that the transverse dispersion is
controlled by the length scale of fluid clusters, and thus inversely
proportional to the square root of the Bond number, the ratio of the force
driving the flow and the surface tension. This result leads to a new scaling
law relating multiphase flow dynamics to transport properties, opening a range
of fundamental and engineering applications.
