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The displacement of a more viscous fluid by a less viscous one in a quasi-twodimensional geometry leads to the formation of complex fingering patterns. Thisfingering has been characterized by a most unstable wavelength, $\lambda_c$,which depends on the viscosity difference between the two immiscible fluids andsets the characteristic width of the fingers. How the finger length grows afterthe instability occurs is an equally important, but previously overlooked,aspect that characterizes the global features of the patterns. As the lowerviscosity fluid is injected, we show that there is a stable inner region wherethe outer fluid is completely displaced. The ratio of the finger length to theradius of this stable region depends only on the viscosity ratio of the fluidsand is decoupled from $\lambda_c$.

An island of stability in a sea of fingers: emergent large-scale features of the viscous flow instability