1. Miscible and immiscible
liquid experiments on the
Rayleigh-Taylor instability
Michael Roberts, Matthew Mokler, Jeffrey Jacobs, William Cabot
University of Arizona, Tucson, AZ, 85721, USA

2. Weight and Pulley (WP) System
Drop Tower (3m)
Test Sled Weight/Pulley
System
Acceleration production
 Heavier mass falling transmits
force through 5:1 pulley system
 Produces 2g - 1g = 1g upwards
Backlight imaging
 (nD mismatch)
 200fps monochrome CCD
camera
 Red surface mount LED strobed
backlight
Accel. measurements
 ±5g
 ±100g
Release Mechanism


3. Forced Initial Perturbations
Parametric Excitation
 Constrained for vertical oscillation
 Utilizes resonance
 Utilizes voice coil / magnet
for forcing
 Produces small wavelength
Faraday wave initial perturbations
Adjustment Weight
Spring
Voice Coil
/ Magnet
Crossed
Roller Bearing
Plexiglass
Tank

4. LIM System
Backlight imaging (nD mismatch)
 Phantom 1200 fps CMOS untethered camera
 White surfacemount LED backlight
Acceleration ( 10g)
±100g accelerometer used with untethered
data logger
LIMs
Test Sled
Drop Tower (8m)
Permanent
Magnet Brakes


5. Fluid Combinations
Atwood Number
Forced Unforced
Miscible
Lithium Polytungstate salt
aqueous soln. / 90% Ethanol
– 10% Water mixture
Lithium Polytungstate salt
aqueous soln. / 90% Ethanol
– 10% Water mixture
Immiscible
Lithium Polytungstate salt
aqueous soln.
with AOT as surfactant / low
viscosity silicon oil
Lithium Polytungstate salt
aqueous soln.
with AOT as surfactant / low
viscosity silicon oil
480
ρρ
ρρ
12
12
.


 A

6. Immiscible Forced WP Exp.
 Denser liquid on bottom

 Acceleration 1g
 Forcing
 37.3 Hz, 0.23 mm disp.
 wavelength 2.5 mm
48.0A



7. Immiscible Forced WP Exp.

8. Immiscible Unforced WP Exp.

9. Miscible Forced WP Exp.

10. Miscible Unforced WP Exp.

11. WP Experimental Comparison
Miscible, UnforcedImmiscible, Unforced
Immiscible, Forced Miscible, Forced

12. Immiscible Unforced LIM Exp.

13. • Simulation performed to parallel unforced, miscible experiment
• 3D simulation performed using DNS capable code Miranda
• nm scale white noise initial perturbation
• 0.06 mm grid spacing
• 760 (x) × 760 (y) domain with periodic boundary conditions in x & y
• Integrated, RMS of Laplacian to mimic backlit imaging
•
• acceleration
Unforced WP Simulation
48.0A
g1

14. Unforced WP Simulation

15. 0
2
4
6
8
10
0 4 8 12 16 20 24
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Spike
Bubble
Forced Immiscible WP Results
time (s)
Agh
h
4
2

Agt
h
time (s)
Ensemble average
of 10 experiments 









26.1
0.047
059.0
Bubble
Spike
Bubble
Spike




Agh
h
4
α
2

 [Cabot and Cook]
0
0.05
0.1
0.15
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Spike
Bubble

16. 0
0.02
0.04
0.06
0.08
0.1
0 0.1 0.2 0.3 0.4 0.5
Bubble
Spike
WP DNS Results
time (s)
Agh
h
4
2

Agt
h
0
1
2
3
4
5
20 25 30 35
0.25 0.3 0.35 0.4 0.45
Bubble
Spike










26.1
0.023
029.0
Bubble
Spike
Bubble
Spike




time (s)
Experiment End

17. A 0.5
Forced Unforced
Misc
WP, 1g
Immis
WP, 1g
Comparison
αSpk αBub αRatio
WP, 1g 0.058 0.049 1.29
LIM, 10g 0.056 0.041 1.37
Youngs 0.069 0.053 1.3
Kucherenko 0.055
Dimonte 0.066 0.051 1.29
αSpk αBub αRatio
0.059 0.047 1.26

αSpk αBub αRatio
WP, 1g 0.046 0.029 1.59
C & C, DNS 0.02 0.017 1.2
WP, DNS 0.029 0.023 1.26
αSpk αBub αRatio
0.017 0.023 0.74

18. Conclusions
 Immiscible alpha values consistent with
those found from past experiments (rocket rig, LEM, etc.)
 Miscible exps. appears to produce smaller alpha values
closer to that of simulations
 Forcing does not appear to affect alpha much