Stability Transition in Gap Expansion-Driven Interfacial Flow

Phys Rev Lett. 2024 Jul 19;133(3):034003. doi: 10.1103/PhysRevLett.133.034003.

Abstract

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.