1. Universidad Politécnica de Madrid, Spain
Experimental analysis of the breakage of a liquid bridge under microgravity conditions
I. Martínez, J.M. Perales
Universidad Politécnica de Madrid, Spain
COSPAR 2010
Thursday, 22nd July 2010

2. Spacelab-D2, Experiment “STACO”, Run 2

3. Experiment description
Experiment performed on board Spacelab D-2 (1993) with AFPM.
Fluid used: silicone oil of n=10 cSt, r=920 kg/m3, s=0.020 N/m.
Supports: two 30 mm in diameter circular coaxial disks made of aluminium black-anodized, with a 30º dove-tail cut back.
Nominal shape: cylindrical liquid column with L=85 mm length.
Diffuse white background illumination (9·8 leds).
Ref.:
Martínez, I., Perales, J.M., Meseguer, J., Stability of long liquid columns (SL-D2-FPM-STACO), in Scientific Results of the German Spacelab Mission D-2, Ed. Sahm, P.R., Keller, M.H., Schiewe, B, WPF, pp , 1995.
Martínez, I.,

4. Automated image edging

5. Stability diagram for unloaded liquid bridges Stretching evolution at constant volume from A to B

6. Experimental values (length, volume, stability)

7. Non-dimensionalization
Unit length
Unit time
Slenderness
Reduced slenderness
Excess liquid volume

8. Column shapes and their stability (nondimensional)
Equilibrium shapes with v<<1 (linearized) and L~π
Dynamic shapes (first eigenfunction)
Stability limit

9. Fitting the liquid shape with 1-, 2-, 3-terms

11. Evolution of the first sine term (a) and cosine term (b)

12. Necking dynamics

13. Stability margin

14. Linear inviscid stable and unstable response

15. Diverging amplitude (amphora-type deformation)
𝑚 d 2 𝑎 d 𝑡 2 +𝑚𝐶 d𝑎 d𝑡 + 𝑣 2 −𝜆 𝑎− 3 4 𝑎 3 =0, with 𝑎 𝑡 0 = 𝑎 0 𝑎 𝑡 0 = 𝑎 0

16. Conclusions
Non-linear dynamic simulation of the breaking process has yield a perfect matching with experimental results, which linear theories did not achieve.
Many small details in the experimental results are still unexplained (e.g. the lack of decay in the small free oscillations; g-jitter?).
Automated image analysis has progressed a lot, but small problems remain (full image analysis helps a lot, but details of the discs are not visible).
Digital imaging nowadays would solve many of the old video problems.
Actual liquid column in space appear always oscillating (microgravity):
Around an equilibrium shape that is unexpected (a residual load shows up)
With a small but non-decaying amplitude (0.3 mm peak-to-peak)
With a frequency very close to the first natural frequency (axial, and lateral).
Useful experimental time in space is always very scarce (e.g. a couple of minutes in half an hour, here).
Unique experiments may have some unknown boundary conditions (repetition is a must, but these experiments have not been reproduced yet).