*2.2. Displacement Experiment*

We performed the fluid displacement under hydrodynamically stable conditions, i.e., a more viscous fluid displaced a less viscous one. The schematic for the fluid displacement is shown in Figure 4. Hele-Shaw cells were used instead of porous media because the Hele-Shaw cell consists of a thin gap between two parallel glass plates and is the simplest two-dimensional model of porous media. The gap between the Hele-Shaw cells was fixed at 0.3 mm. First, we filled up the cell with the less viscous Na2SO4 solution and then injected the more viscous PEG solution into the cell using a syringe pump. The PEG solutions were dyed blue to visualize the experimental process. The displacement experiments were recorded by a video camera from the bottom. The injection flow rate of the more viscous liquid was fixed as 3.35 mL/h. All experiments were performed at room temperature (25 ± 1 ◦C) and atmospheric pressure (approx. 1 atm).

**Figure 4.** The schematic for the hydrodynamically stable displacement.
