  It is well-known that wettability exerts fundamental control over multiphase
flow in porous media, which has been extensively studied in uniform-wet porous
media. In contrast, multiphase flow in porous media with heterogeneous
wettability (i.e., mixed-wet) is less well-understood, despite its common
occurrence. Here, we study the displacement of silicone oil by water in a
mostly oil-wet porous media patterned with discrete water-wet clusters that
have precisely controlled wettability. Surprisingly, the macroscopic
displacement pattern varies dramatically depending on the details of
wettability alteration -- the invading water preferentially fills strongly
water-wet clusters but encircles weakly water-wet clusters instead, resulting
in significant trapping of the defending oil. We explain this counter-intuitive
observation with pore-scale simulations, which reveal that the fluid-fluid
interfaces at mixed-wet pores resemble an S-shaped saddle with mean curvatures
close to zero. We show that incorporation of the capillary entry pressures at
mixed-wet pores into a dynamic pore-network model reproduces the experiments.
Our work demonstrates the complex nature of wettability control in mixed-wet
porous media, and it presents experimental and numerical platforms upon which
further insights can be drawn.
