Fluid-fluid displacement in mixed-wet porous media

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.