Rayleigh-Taylor Instability Using Magnetorheological Fluids
A challenge in experimentally studying the Rayleigh-Taylor
instability is to achieve a well-characterized interface geometry
without the use of a separating membrane. These experiments
utilize a magnetorheological (MR) fluid which exhibits
supermagnetism. This property allows the material to be held
static in a magnetic field of sufficient strength, and is then free
to flow as a liquid when the field is removed. The MR fluid is
prepared by dispersing carbonyl iron particles (10-6 m in
diameter) in mineral oil or hexane and particle agglomeration is
minimized with the addition of a minute amount of surfactant.
Depending on the volume fraction of iron particles and the carrier
fluid, the density of the MR fluid may be chosen from the range &rhoH=[1.8 ... 2.7] kg/m3.
To prepare an interface with a prescribed perturbation, water is
placed in a test section with a sinusoidal mold, frozen, the mold is
removed, MR fluid is poured on top of the ice, a
magnetic field is applied, and the ice is melted. Two banks of
round, permanent magnets are used to hold the interface shape until
the experiment commences at which time the test section is flipped and the
magnet banks are retracted.
The instability is diagnosed optically or with X-rays using the
experimental setups shown below. Originally, the optical
technique was used and measurements were limited to the spike growth
since a thin film of opaque MR fluid remained on the test section
walls obscuring the observation of bubble growth. The X-ray
technique allows for spike and bubble growth observation and also
provides a way to obtain density field measurements in addition to
the geometrical ones.
Images from experiments with a single perturbation, or bump, on
the interface are shown below.
This MR fluid over water experiment has an Atwood number of moderate
magnitude, A=0.46, and
this density ratio of heavy and light fluids is defined as A=(&rhoH-&rhoL)/(&rhoH+&rhoL).
The growth of the spike tip is
observed with both the optical and X-ray techniques. The
optical technique provides much better contrast; however, the X-ray
technique reveals the characteristic roll-up at the spike location
along with the lighter fluid pushing up, or bubbling, into the heavy
fluid on each side of the spike.