Revisiting the Saffman—Taylor instability in unstable imbibition

Here, we revisit the classic Saffman--Taylor instability in the imbibition regime, where a more wetting liquid displaces a less wetting and more viscous liquid in a radial Hele-Shaw cell consisting of two plates separated by a small uniform gap. We show that the wetting liquid invades the cell in the form of a thin-film front, which becomes unstable and leads to a viscous fingering pattern. We develop a theoretical model and analyze this front instability using linear stability analysis and nonlinear simulations. We show that the instability here is fundamentally different from the Saffman-Taylor instability in terms of its base state and scaling of the most-unstable wavelength, suggesting that it belongs to a new class of pattern-forming processes.