We investigate interfacial instability in a lifting Hele-Shaw cell by experiments and theory. We characterize the unexplored transition from stable to unstable patterns under a wide range of controlling parameters. Surprisingly, we find that the perturbation growth rate-based criterion for the onset of instability from linear stability theory is too strict by over 3 orders of magnitude. To reconcile this striking discrepancy, we propose a new criterion based on perturbation amplitude, which is in excellent agreement with the experimental results. We further show that the fingering pattern evolves to produce a hierarchical fluid structure and derive a theoretical equation to predict the fingering evolution.

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• Displacement of immiscible fluids
• Fingering instability
• Flows in porous media
• Hele-shaw flows
• Imbibition & injection
• Instability control
• Interfacial flows
• Thin fluid films
• Hele-Shaw cell