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.
- SourceAvailable from: damtp.cam.ac.uk[Show abstract] [Hide abstract]
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: Buckling of liquid columns.[Show abstract] [Hide abstract]
ABSTRACT: Under appropriate conditions, a column of viscous liquid falling onto a rigid surface undergoes a buckling instability. Here we show experimentally and theoretically that liquid buckling exhibits a hitherto unsuspected complexity involving three different modes-viscous, gravitational, and inertial-depending on how the viscous forces that resist bending of the column are balanced. We also find that the nonlinear evolution of the buckling exhibits a surprising multistability with three distinct states: steady stagnation flow, "liquid rope coiling," and a new state in which the column simultaneously folds periodically and rotates about a vertical axis. The transitions among these states are subcritical, leading to a complex phase diagram in which different combinations of states coexist in different regions of the parameter space.Physical Review Letters 02/2010; 104(7):074301. · 7.73 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics. Inviscid, and viscous Newtonian jets have been studied in great detail; buckling instability in viscous jets leads to regular periodic coiling of the jet that exhibits a non-trivial frequency dependence with the height of the fall. Very few experimental or theoretical studies exist for continuous viscoelastic jets beyond the onset of the first instability. Here, we present a systematic study of the effects of viscoelasticity on the dynamics of free surface continuous jets of surfactant solutions that form worm-like micelles. We observe complex nonlinear spatio-temporal dynamics of the jet and uncover a transition from periodic to doubly-periodic or quasi-periodic to a multi-frequency, possibly chaotic dynamics. Beyond this regime, the jet dynamics smoothly crosses over to exhibit the "leaping shampoo effect" or the Kaye effect. This enables us to view seemingly disparate jetting dynamics as one coherent picture of successive instabilities and transitions between them. We identify the relevant scaling variables as the dimensionless height, flow rate, and the elasto-gravity number and present a regime map of the dynamics of the jet in terms of these parameters.12/2010;