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.
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ABSTRACT: The behaviour of a viscous thread as it falls onto a moving belt is analysed in the asymptotic limit of a slender thread. While the bending resistance of a slender thread is small, its effects are dynamically important near the contact point with the belt, where it changes the curvature and orientation of the thread. Steady flows are shown to fall into one of three distinct regimes, depending on whether the belt is moving faster than, slower than or close to the same speed as the free-fall velocity of the thread. The key dynamical balances in each regime are explained and the role of bending stresses is found to be qualitatively different. The asymptotic solutions exhibit the ‘backward-facing heel’ observed experimentally for low belt speeds, and provide the leading-order corrections to the stretching catenary in theory previously developed for high belt speeds. The asymptotic stability of the thread to the onset of meandering is also analysed. It is shown that the entire thread, rather than the bending boundary layer alone, governs the stability. A balance between the destabilising reaction forces near the belt and the restoring force of gravity on the remainder of the thread determines the onset of meandering, and an analytic estimate for the meandering frequency is thereby obtained. At leading order, neutral stability occurs with the belt moving a little more slowly than the free-fall velocity of the thread, not when the lower part of the thread begins to be under compression, but when the horizontal reaction force at the belt begins to be slightly against the direction of belt motion. The onset of meandering is the heel ‘losing its balance’.Journal of Fluid Mechanics 05/2011; 674:489 - 521. · 2.29 Impact Factor
Article: Coiling of yield stress fluids.[Show abstract] [Hide abstract]
ABSTRACT: We present an experimental investigation of the coiling of a filament of a yield stress fluid falling on a solid surface. We use two kinds of yield stress fluids, shaving foam and hair gel, and show that the coiling of the foam is similar to the coiling of an elastic rope. Two regimes of coiling (elastic and gravitational) are observed for the foam. Hair gel coiling, on the other hand, is more like the coiling of a liquid system; here we observe viscous and gravitational regimes. No inertial regime is observed for either system because of instabilities occurring at high flow rates or the breakup of the filament from large heights.Physical Review E 05/2011; 83(5 Pt 2):056327. · 2.31 Impact Factor
Article: Liquid Rope CoilingAnnual Review of Fluid Mechanics 01/2012; · 12.60 Impact Factor