TY - JOUR

T1 - Shape and stability of a viscous thread

AU - Bohr, Tomas

AU - Senchenko, Sergey

N1 - Copyright 2005 American Physical Society

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.71.056301

DO - 10.1103/PhysRevE.71.056301

M3 - Journal article

C2 - 16089643

VL - 71

SP - 056301

JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

SN - 2470-0045

IS - 5

ER -