  Capillary fingering is a displacement process that can occur when a
non-wetting fluid displaces a wetting fluid from a homogeneous disordered
porous medium. Here, we investigate how this process is influenced by a pore
size gradient. Using microfluidic experiments and computational pore-network
models, we show that the non-wetting fluid displacement behavior depends
sensitively on the direction and the magnitude of the gradient. The fluid
displacement depends on the competition between a pore size gradient and
pore-scale disorder; indeed, a sufficiently large gradient can completely
suppress capillary fingering. By analyzing capillary forces at the pore scale,
we identify a non-dimensional parameter that describes the physics underlying
these diverse flow behaviors. Our results thus expand the understanding of flow
in complex porous media, and suggest a new way to control flow behavior via the
introduction of pore size gradients.
