Shape and stability of a viscous thread

Tomas Bohr, Sergey Senchenko

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Abstract

When a viscous fluid, like oil or syrup, streams from a small orifice and falls freely under gravity, it forms a long slender thread, which can be maintained in a stable, stationary state with lengths up to several meters. We discuss the shape of such liquid threads and their surprising stability. The stationary shapes are discussed within the long-wavelength approximation and compared to experiments. It turns out that the strong advection of the falling fluid can almost outrun the Rayleigh-Plateau instability. The asymptotic shape and stability are independent of viscosity and small perturbations grow with time as exp(Ct(1/4)), where the constant is independent of viscosity. The corresponding spatial growth has the form exp[(z/L)(1/8)], where z is the down stream distance and L similar to Q(2)sigma(-2)g and where sigma is the surface tension divided by density, g is the gravity, and Q is the flux. We also show that a slow spatial increase of the gravitational field can make the thread stable.
Original languageEnglish
JournalPhysical Review E
Volume71
Issue number5
Pages (from-to)056301
ISSN2470-0045
DOIs
Publication statusPublished - 2005

Bibliographical note

Copyright 2005 American Physical Society

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