2014/10/28 by Irmgard Bischofberger, Bischofberger, Irmgard, Radha Ramachandran +3
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1410.7623
openalex publication_date 2014/10/28 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
The displacement of a more viscous fluid by a less viscous one in a quasi-two\ndimensional geometry leads to the formation of complex fingering patterns. This\nfingering has been characterized by a most unstable wavelength, \λc,\nwhich depends on the viscosity difference between the two immiscible fluids and\nsets the characteristic width of the fingers. How the finger length grows after\nthe instability occurs is an equally important, but previously overlooked,\naspect that characterizes the global features of the patterns. As the lower\nviscosity fluid is injected, we show that there is a stable inner region where\nthe outer fluid is completely displaced. The ratio of the finger length to the\nradius of this stable region depends only on the viscosity ratio of the fluids\nand is decoupled from \λc.\n