Flexible Filaments in Flowing Soap Film 

 

 
  We study here the dynamics of flexible filaments (silk threads) in a flowing soap film. For a single filament held at its upstream end and otherwise unconstrained, we found two distinct , stable dynamical states: a "stretched-straight" state, and a flapping state. The stretched-straight state is proven experimentally to be linearly stable. In this state, the filament is immobile and aligned in the flow direction, and sheds a small von Karman vortex street downstream from its free end. In the flapping state, the filament executes a sinuous motion with waves traveling downstream along its length in a manner akin to the flapping of a flag in the wind. We also study the side by side interaction between two coupled filaments. Four different dynamical states are observed, depending on the distance between the filaments: a steady state, an in-phase flapping state, an out-of-phase flapping state, and a decoupled flapping state. [Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. by Zhang, Childress, Libchaber and Shelley, Nature, 408, 835, (2000)]  
 
The setup for the flowing soap film: The typical thickness of the soap film is 3-4 microns and the speed is about 200 cm/sec. We use the commercial soap "Dawn" and mix it with distilled water at a 1.5% concentration. The flow can run (on a good day) for hours without breaking. In this figure, H is the upper container, S the stopcock which regulates the flux (thus the flow speed), N the two nylon lines on which the soap film is formed as it flows, T four tension lines to separate the two nylon lines, L is the lower container and F the silk filament (exaggerated in size).
 
 
A stretched-straight state: The filament is stable under  small disturbances. A vortex street similar to von Karman street is shed behind the free end. The filament is stationary. However, if the external disturbances are big enough,  the filament will jump to a "flapping state" [see image below] . The flow is visualized with a low pressure sodium lamp from the interference pattern. The bifurcation from "straight" to "flapping" state can be shown experimentally to be subcritical. 
 
 
The flapping state: the filament executes an oscillatory motion with a wave traveling downstream. The thin wake generated from the free end is now modified and displaced in concert with the flapping motion. This state is stable under finite disturbances, but it can be forced back to the "stretched-straight" state by holding it taut.
 
 
The free end of the filament executes a "figure-eight " motion due to the fact that the filament is inextensible and the flapping motion is a traveling wave moving along in the free stream direction. 
 
 
Comparison of the wakes of (1) cylinder, (2) fish tail ,and (3) flexible filament. Notice that the vortex streets are significantly different.
 
 
Two filaments are inserted side-by-side in the running soap film . The interaction is mediated through the fluid. Two phase-locked states are discovered. In one, both filaments are flapping in phase, and in the other the filaments flap 180 degrees out of phase. As the coupling distance is increased, each filament starts to flap independently. A "stretched-straight" state is also observed, where both filaments stay stationary (not shown).
 
 


"Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind"
Zhang, Childress, Libchaber and Shelley
Nature, 408, 835, (2000)
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