Dynamics of liquid rope coiling

Abstract

We present a combined experimental and numerical investigation of the coiling of a liquid "rope" falling on a solid surface, focusing on three little-explored aspects of the phenomenon: The time dependence of "inertio-gravitational" coiling, the systematic dependence of the radii of the coil and the rope on the experimental parameters, and the "secondary buckling" of the columnar structure generated by high-frequency coiling. Inertio-gravitational coiling is characterized by oscillations between states with different frequencies, and we present experimental observations of four distinct branches of such states in the frequency-fall height space. The transitions between coexisting states have no characteristic period, may take place with or without a change in the sense of rotation, and usually (but not always) occur via an intermediate "figure of eight" state. We present extensive laboratory measurements of the radii of the coil and of the rope within it, and show that they agree well with the predictions of a "slender-rope" numerical model. Finally, we use dimensional analysis to reveal a systematic variation of the critical column height for secondary buckling as a function of (dimensionless) flow rate and surface tension parameters.

Spontaneous generation of spiral waves by a hydrodynamic instability

“…At relatively low heights corresponding to the lower-frequency part of the gravitational regime [20][21][22][23], the center of coiling precessed and some irregular bubbles were formed. At somewhat greater heights, the bubble pattern became more regular and some rather unclear spiral patterns were observed.…”

“…Because the coiling period is much shorter than the time required for an individual coil to coalesce completely with its predecessor, the coiling filament forms a tall liquid tube that builds up, buckles under its own weight at a critical height, and starts rebuilding again with a characteristic period [23]. In this regime we observed bubbles of two different sizes: bubbles smaller than the filament radius that form with a period comparable to that of the coiling; and larger bubbles with sizes comparable to that of the liquid tube that form during the secondary buckling.…”

“…1) [17][18][19]. In previous papers we investigated how the frequency and radius of the coiling depends on the orifice diameter, the height of fall, the flow rate, and the fluid viscosity, and we showed that coiling traverses four different dynamical regimes as the fall height increases [20][21][22][23][24]. Here we report that in a limited portion of the parameter space, air bubbles become trapped between successive coils and are then advected radially away to form surprising and very regular spiral patterns.…”

Bending-filament model for the buckling and coiling instability of a viscous fluid rope

“…Most of experimental works on fluid rope coiling discuss coiling frequency as a function of the fall height [1,2,3,4,5] or the rope's radius [6]. Let us compare the coiling frequency of the present model with the experiments.…”

“…Backing and coiling instabilities of fluid jets are examples of such systems, and have been studied for several decades in the laboratory [1,2,3,4,5,6]. A fluid rope and coiling can also be observed in daily life, such as when honey is poured from a teaspoon onto toast.…”