Issue 37, 2015

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

Abstract

The displacement of a more viscous fluid by a less viscous one in a quasi-two dimensional geometry leads to the formation of complex fingering patterns. This fingering has been characterized by a most unstable wavelength, λc, which depends on the viscosity difference between two immiscible fluids and sets the characteristic width of the fingers. How the finger length grows after the instability occurs is an equally important, but previously overlooked, aspect that characterizes the global features of the patterns. Long after the instability onset, once the fingers are growing in a nearly steady-state regime, there is a stable inner region where the outer fluid is completely displaced. We show that the ratio of the finger length to the radius of this stable region depends only on the viscosity ratio of the fluids and is decoupled from λc.

Graphical abstract: An island of stability in a sea of fingers: emergent global features of the viscous-flow instability

Supplementary files

Article information

Article type
Paper
Submitted
21 Apr 2015
Accepted
05 Aug 2015
First published
13 Aug 2015

Soft Matter, 2015,11, 7428-7432

Author version available

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

I. Bischofberger, R. Ramachandran and S. R. Nagel, Soft Matter, 2015, 11, 7428 DOI: 10.1039/C5SM00943J

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