Fig. 1.

We conduct radial fluid–fluid displacement experiments by injecting water into viscous silicone oil in quasi-2D microfluidic flow cells patterned with vertical posts. (A) The core of the flow cell is made of a photocurable polymer (NOA81) patterned with circular posts of height $b=$ 100 μm. The flow cell has porosity $\varphi =0.45$, pore volume $V=0.38$ mL, and intrinsic permeability $k\approx 2.4\times {10}^{-10}$ m². (B) The flow cell is initially saturated with a viscous silicone oil (${\eta }_{\text{oil}}=340$ mPa $\cdot$ s) and placed in a bath of the same fluid to avoid capillary edge effects. We inject water into the center of the flow cell at a constant rate Q. A pressure sensor records the injection pressure throughout the experiment. We image the experiment from above with a CMOS camera, measuring the gap-averaged water saturation at high spatial and temporal resolution from calibrated light intensity. (C) We design the pattern of posts to introduce disorder, but such that it is macroscopically homogeneous at the scale of the flow cell. Here, we show the spatial distribution of pore-throat sizes, which range from 80 to 900 μm (SI Appendix, Fig. S1).