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2-D Dynamics of a Jet in a Flowing Soap Film
Adam Cone,Nicolas Vandenberghe,Jun Zhang,Courant Institute,NewYork University
Albert Libchaber,The Rockefeller University
Fluid is
pumped into
the tube at
constant rate
Camera
Soap film
Low pressure
sodium lamp
Fig.a
Fig.b
Fig.c
We study the dynamics of a jet in a flowing soap film.
The liquid film,a thin (~3 µm) sheet of soap solution,flows vertically,
driven by gravity and guided by two nylon threads [1] (Fig.a). We use
film speeds (Ufilm) between 1.40 and 2.50 m/s,as measured by Laser
Doppler Velocimetry. The Reynolds number for the soap film, based on
the channel width (9 cm), is on the order of 50 000.
A liquid jet is introduced through a short tube (15 mm) in the plane of
the soap film. We use the same soap concentration (1.5 % soap in
water) for the jet and the film. The jet flow rate is imposed by a syringe
pump and for the current experiment is set to 4.6 10-8 m3/s. The inner
diameter of the tube outlet is 326 µm; the typical jet speed is thus 0.55
m/s. The Reynolds number for the jet, based on the tube's inner
diameter, is 180.At this flow rate, in the absence of a film, we observe
drops instead of a jet (Fig.b).
We take photographs using a digital camera (exposure time 100 µs,
sensitivity equivalent to 3200 ASA). The photographed area for all
pictures is 4.6 x 3.0 cm. In monochromatic light (low pressure sodium
lamp - wavelength 589 and 589.6 nm), thickness variations are visible in
the film as bright and dark areas as a result of optical interference.
Our main objective is to document the dynamics of a jet that is
'confined' to two dimensions. With increasing film speed, we observe a
transition from a straight (Photo 1) to a wavy jet (Photo 2), with the
traveling waves in the latter state propagating downstream. The
observed wavelength is significantly longer than the wavelength
observed in the vortical wake caused by the tube (Fig.c). At higher film
speed, we observe branching of secondary structures at the wave crests
(Photos 3-4). As the film speed increases further, this system presents
progressively more complex patterns (Photos 5-6).
The straight-to-wavy transition is distinct from the well-documented
Rayleigh instability, which is caused by surface tension and leads to
drop formation [2]. However,similar 'snake modes' have been observed
in a three dimensional liquid jet inside a gaseous jet [3]. Moreover,the
wavy jet ressembles elastic structures which present similar patterns in
soap films [4]. This analogy between viscous jet and elastic structure
dynamics has been observed and modeled for example in a highly
viscous coiling jet [5].
Photo 1; Ufilm = 1.40 m/s Photo 3; Ufilm = 1.80m/s
Photo 4; Ufilm = 1.95 m/s Photo 5; Ufilm = 2.20 m/s Photo 6; Ufilm = 2.50 m/s
Photo 2; Ufilm = 1.65m/s