The motion of a falling liquid filament

When a liquid drop falls from a fluid source with a slow flow rate, it remains attached to the source by an elongating liquid filament until the filament pinches off. For many fluids, this pinch-off occurs first near the end of the filament, where the filament joins to the liquid drop. For other fluids, the filament pinches off at one or more interior points. In this paper, we study the motion of this filament, and we make two points. First, the flow in this filament is not that of a uniform jet. Instead, we show experimentally that a different solution of the Navier–Stokes equations describes the motion of this filament before it pinches off. Second, we propose a criterion for the location of the first pinch-off. In particular, we analyze the linearized stability of the exact solution, both for an inviscid fluid and for a very viscous fluid. Our criterion for pinch-off is based on this stability analysis. It correctly predicts whether a given filament pinches off first near its ends or at points within i...

[1]  Diane M. Henderson,et al.  On the pinch-off of a pendant drop of viscous fluid , 1997 .

[2]  Xiaoguang Zhang,et al.  An experimental study of dynamics of drop formation , 1995 .

[3]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[4]  L. Rayleigh.  On The Instability Of Jets , 1878 .

[5]  S. Bechtel,et al.  Recovery of the Rayleigh capillary instability from slender 1‐D inviscid and viscous models , 1995 .

[6]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[7]  Arthur S. Hathaway,et al.  A COURSE IN MODERN ANALYSIS. , 1903 .

[8]  Shi,et al.  Iterated instabilities during droplet fission. , 1994, Physical review letters.

[9]  P. Hartman.  Ordinary Differential Equations , 1965 .

[10]  F. Bowman,et al.  Introduction to Bessel Functions , 1939 .

[11]  J. Keller,et al.  Surface Tension Driven Flows , 1983 .

[12]  J. Eggers,et al.  Universal pinching of 3D axisymmetric free-surface flow. , 1993, Physical review letters.

[13]  D. Weihs,et al.  Influence of viscosity on the capillary instability of a stretching jet , 1987, Journal of Fluid Mechanics.

[14]  M. Brenner,et al.  A Cascade of Structure in a Drop Falling from a Faucet , 1994, Science.

[15]  D. Weihs,et al.  Stability of a capillary jet with linearly increasing axial velocity (with application to shaped charges) , 1985, Journal of Fluid Mechanics.

[16]  Jens Eggers,et al.  Theory of drop formation , 1995 .

[17]  Howard A. Stone,et al.  An experimental study of transient effects in the breakup of viscous drops , 1986, Journal of Fluid Mechanics.

[18]  L. Rayleigh,et al.  XVI. On the instability of a cylinder of viscous liquid under capillary force , 1892 .

[19]  S. Tomotika.  Breaking up of a Drop of Viscous Liquid Immersed in Another Viscous Fluid Which is Extending at a Uniform Rate , 1936 .

[20]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[21]  R. Schulkes,et al.  The contraction of liquid filaments , 1996, Journal of Fluid Mechanics.

[22]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[23]  D. Peregrine,et al.  The bifurcation of liquid bridges , 1990, Journal of Fluid Mechanics.