“…Multiphase flow in rock fractures is relevant to many subsurface engineering applications including geological carbon sequestration (Teng & Zhang, 2018;Ulven et al, 2014), enhanced oil/gas recovery (Lake, 1989;Morrow & Mason, 2001), and hydraulic fracturing (Song et al, 2019). For such flow of multiple immiscible fluids, fluid-fluid interface instability is a key factor that affects the CO 2 storage capacity, the oil recovery efficiency, and the flow-back (and the disappearance) of fracturing fluids (Edwards et al, 2017). This instability is a classic problem and has been long studied since Hele-Shaw's work over a century ago (Hele-Shaw, 1898).…”