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

Spacelab-D2, Experiment “STACO”, Run 2

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. 220-231, 1995. Martínez, I., http://webserver.dmt.upm.es/~isidoro/lc1/SL/ST2_118_13_30_41stretch_xvid.avi

Automated image edging

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

Experimental values (length, volume, stability)

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

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

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

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

Necking dynamics

Stability margin

Linear inviscid stable and unstable response

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

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).