Structure of Mix in a Rayleigh-Taylor Unstable Fluid Cell Page: 3 of 9
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, Structure of Mix in a Rayleigh-Taylor..
Structure of Mix in a Rayleigh-Taylor Unstable Fluid
Cell
Marilyn B. Schneider, Guy Dimonte, and Bruce A. Remington
Lawrence Livermore National Laboratory
P. O. Box 808, L-43, Livermore, CA 94550 USA
Abstract: Laser-induced fluorescence is used to image the central plane of the mix region of
two immiscible liquids subject to the Rayleigh-Taylor instability. The familiar bubbles and
spikes display a complex internal structure. This small-scale structure creates a large contact
area whose density is constant in time. The size of the mixing zone, defined in a new way,
grows with coefficient ab >= 0.054.
1. Introduction
The Rayleigh-Taylor (RT) instability[1, 2, 3, 4], occurs during the acceleration of a heavy fluid
by a light fluid. The rate of the instability is parameterized by the acceleration, g, and the
Atwood number, A=(p2 - pi)/(p2 + pi) where pi(p2) is the density of the light (heavy) fluid.
For small initial perturbations, there are linear[2, 6] and non-linear growth phases[5, 7, 8, 9].
Eventually a highly-disordered mixing zone (DMZ) develops, bounded by a bubble front which
penetrates the heavy fluid as ~ abAgt2 and a spike front which penetrates the light fluid as
~ a$Agt2. [10, 11, 12, 13, 14, 15] The coefficient ab is insensitive to A whereas as increases
with A[13, 14].
Experiments[10, 11, 12, 15] using backlit photography obtain values of ab ~ 0.06 - 0.07
that are larger than those found in all 3-D [13, 16] and some 2-D [12, 16, 17] hydrodynamic
simulations, but similar to those found in 2-D simulations which track the interface [18, 19]. The
backlit photography experiments cannot measure the structure within the DMZ. This structure
is important because it determines the constitutive properties in the DMZ such as composition
(or density), energy, effective opacity, and equation of state.
This report describes RT experiments using laser-induced fluorescence (LIF) which image
the DMZ of a cell containing two immiscible liquids at Reynolds number of order ~ 105. The
images show a complex internal fine structure in the bubbles and spikes. While the large
bubbles and spikes define the boundaries of the DMZ, their small-scale internal structures
increase the mix entropy, which eventually (for miscible fluids) leads to molecular mix. This
study shows that: (i) the measured ab is consistent with recent experiments[15]; and (ii) the
internal structure is responsible for the large amount of contact area between the mixing fluids.
2. Experimental configuration
The present experiments use the Linear Electric Motor (LEM) [20] at Lawrence Livermore
National Laboratory to accelerate a container for 50 ms at a downward constant g (~ 73go
where go = earth's gravity). The fluid cavity is 73mm wide, 88 mm high, and 73mm deep. For
LIF, a laser sheet parallel to the acceleration illuminates the central plane of the cavity from
below. Images of the fluorescence are recorded on 35mm film.0More information - Email: schneider5@llnl.gov
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Schneider, M. B.; Dimonte, G. & Remington, B. A. Structure of Mix in a Rayleigh-Taylor Unstable Fluid Cell, article, September 2, 1997; California. (https://digital.library.unt.edu/ark:/67531/metadc691849/m1/3/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.