Stability of Long Liquid Columns

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I. M a r t i n e z , J.M. P e r a l e s , J. M e s e g u e r Lanii-ETSLA, UPM, M a d r i d , S p a i n

A b s t r a c t

A description at this experiment, the data analysis performed and tlie results obtained a r e

presented. Three successful runs v/ere executed: the first one included a detailed oscillation test

around a low eigenlrequency of the liquid column, the second was a stretching at constant volume until breakage, and the third one included an unexplained instability of an unequal-discs liquid

column. The main diagnostic is the image analysis of the recorded videotape, and the most

important result is that a residual axial acceleration of less than 5 ]±g is deduced from this SL-D-2 experiment, in contrast to the 70 ,ug d e d u c e d from the SL-D1 experiment in 19S5.

K e y w o r d s : Capillarity, liquid bridge, inicrogravily, stability, g-jitter, ilocting zone, S p a c e l a b

I n t r o d u c t i o n

A liquid bridge is a liquid m a s s s p a n n i n g bctv/een two solid supports a n d held solely by capillary forces (surface tension a n d wetting constraint). It is e s t a b l i s h e d once in flight by feeding liquid from a syringe through a centre hole in one of the support discs (the lower one in Fig. 1), while s e p a r a t i n g the d i s c s (the feed-ing one is moved) proportionally, to avoid spillage. The liquid used is a silicone-oil 10 times more viscous t h a n water (5 times for the last run). The working length of the liquid column is 85 mm. The two solid supports a r e m a d e of a l u m i n u m of 30 mm in d i a m e t e r with a s h a r p c u t b a c k (30° e d g e ) to prevent liquid s p r e a d i n g over the e d g e s . This choice of g e -ometry allows a direct c o m p a r i s o n with other TEXUS experiments where discs of 30 mm in d i a m e t e r s e p a r a t e d 86 mm were u s e d to hold a cylindrical liquid column (35 m m discs were u s e d in SL-D1 a n d 40 mm discs on SL-1). R e s e a r c h on thus topic at this institution started in 1974 a s a n a n s w e r to a n ESA call tor i d e a s for S p a c e l a b e x p e r i m e n t a t i o n [1-5]. The ESA-AFPM, a multi-user facility similar to the Fluid Physics Module (FPM) u s e d in SL-1 a n d SL-D1, w a s u s e d in SL-D-2. D i a g n o s i s is

b a s e d on the o u t e r - s h a p e a n a l y s i s from i m a g e recording.

S c i e n t i f i c O b j e c t i v e

The aim of this experiment is to m e a s u r e the o u t e r s h a p e d e f o r m a t i o n of l o n g liquid b r i d g e s n e a r their stability limit under micro-gravity, c a u s e d by g-jitter a n d by some con-trolled m e c h a n i c a l d i s t u r b a n c e s ( c h a n g e of geometry, c h a n g e of volume, rotation a n d vi-bration). The liquid bridge configuration has, a s i d e of its own relevance in fluid-mechanics a n d interface science, a well-known applica-tion in materials processing, particularly in the floating zone technique of crystal growth in the semiconductor industry. As a spin-off of this research, this configuration h a s proved to be a u n i q u e weak-force t r a n s d u c e r at very low frequencies.

correspond-ing d i a m e t e r for instability at that length is D = I'/'l = 28 m m a n d , to b e in the safe side, a n o m i n a l d i a m e t e r of D = 30 mm w a s chosen. A lot of' stability d i a g r a m s for this geometry a n d different stimuli were computed to a s s e s the effect of a n a x i a l acceleration, a centrifu-g a l force field, a d e p a r t u r e from the cylindri-cal volume, different disc sizes a n d column s l e n d e r n e s s .

A known h a n d i c a p of p r e s e n t - d a y experimen-tation in s p a c e is the lack of repetitions of trials d u e to the scarcity of microgravity flights a n d crewtime, a n d the u n i q u e n e s s of S p a c e -l a b h a r d w a r e , s o that it w a s top priority of STACO to quickly verify the results of SL-D1, a n d b e c a u s e a n equivalent Bond number Bo = 0.007 w a s d e d u c e d from the SL-D1-FPM-F J Z experiment a n d there w a s no r e a s o n to expect a different behaviour, the SL-D-2-FPM-STACO experiment foresaw the use of un-e q u a l discs of 30 m m a n d 28 mm in a s un-e c o n d run to precisely c o u n t e r b a l a n c e the expected deformation a n d better quantify this effect.

The particular g o a l s of this SL-D-2 experi-ment [4] c a n then be g r o u p e d a s follows:

• S e n s e b a c k g r o u n d g-jitter a n d discern a g a i n s t the SL-D1 experiment results. • Force oscillations very n e a r a low

eigen-frequency (the s e c o n d one).

• M e a s u r e b r e a k i n g lengths of a stretching e q u a l - d i s c s column.

• M e a s u r e b r e a k i n g lengths of a stretching u n e q u a l - d i s c s column.

• M e a s u r e b r e a k i n g rotation rate of a n iso-rotating column.

Uncertainty a n a l y s i s is important to any ex-periment, but particularly crucial to STACO since we try to m e a s u r e the effect on a 60 cm liquid column of a p p l i e d forces in the r a n g e 1 0 -5N t o 10"7N.

E x p e r i m e n t D e s c r i p t i o n

The e q u i p m e n t used, the AFPM, is described elsewhere, but it s e e m s a p p r o p r i a t e here to look in detail to the uncertainties in the d a t a a n a l y s i s a s s o c i a t e d with the equipment, a s well a s with the working liquid.

The AFPM is a high-precision a p p a r a t u s but, being a multi-user facility, its wide operating

r a n g e s h a v e forced some tolerances that im-p a c t on the STACO exim-periment. For instance, a precision for a n axial oscillation of 0.01 Hz from 0.1 Hz to 5 Hz is very g o o d for a multipledegreesoffreedom m e c h a n i s m , but it h a p -p e n s that the first eigenf requency of the liquid b r i d g e u n d e r study is just below 0.1 Hz, a n d a 0.01 Hz resolution lor the second eigenire-quency at 0.4 Hz is not very much.

Most other AFPM tolerances were judged ir-relevant for STACO. For instance, for disc s e p a r a t i o n L a n d volume injection V, the A F P M a c c u r a c i e s a r e Alinin = 0.1 mm, di/dfmin = 0.04 mm/s, AdI/dt = + 0.02 mm/s

3 3

a n d AVrrT1in= 0.5 cm , dV7dtmin= ± 0.5 cm is. AdV/df = 0.05 cm Is, so that for s p e e d v a l u e s for c y l i n d r i c a l i n j e c t i o n s e t to d l / d t = 0.72 mm/s a n d dV/dl = 0.50 cm3/s, t h e y a r e d i g i t a l l y c o n t r o l l e d to dL/dt = 0.72 ± 0 . 0 2 m m / s a n d dV/dt = 0.50

n

± 0.05 cm /s (or worst, a s in the first cylindrical injection, set todV/df = 0.50 cm / s a n d having a value of dWdf = 0.40 + 0.05 em3/s d e d u c e d from the AFPM d c t c ) .

However in s o m e c a s e s a more detailed a n a -lysis after flight cast s o m e doubts on the irre-levance of AFPM tolerances, a s for the three fixed-frequency trials in Run 1, that were in-t e n d e d in-to b e e q u i s p a c e d n e a r in-the s e c o n d eigenfrequency (at 0.40 Hz, 0.41 Hz a n d 0.42 Hz), w h a t s e e m s inconsistent with the AFPM a c c u r a c y of Afmin = 0.0! Hz (related AFPM a c c u r a c i e s a r e df/d'min = 1/30 Hz/s a n d Aamin = 0.1 mm).

A reservoir with 1 litre of Dow Corning silicone oil of viscosity v=10" m /s (10 cSt) w a s u s e d for STACO a n d U C O R experiments. To b e a b l e to visualise the internal motion, the liq-uid w a s s e e d e d with 0.2 gram/litre of tracers ( F x c o s p h e r e s from Emerson a n d Cummings, silver-coated in the ULB-MRC, with density of 360-1000 k g / m3 a n d diameter of 100+20 urn). The n o m i n a l illumination however w a s such that the c o l u m n e d g e visualisation w a s en-h a n c e d a n d ten-he tracers were invisible.

-[• iront iced

ubralmg rear disc *v;:

liquid coiumn •—%:•-'

m„%:&

w^~

Fig. 1: C o m p a r i s o n b e t w e e n the ideal s c e n e inside the AFPM test-chamber a n d the real one (in flight). Thi liquid column a n d the raster a p p e a r a t dL'ferent s c a l e s b e c a u s e of the conical perspective.

with 27 mm stem a n d a plastic o n e (PMMA) a l s o cf 30 mm. There were three front discs (all of them with a 10 mm hole for liquid feeding): a metallic 30 mm 0 , protruding 6 mm with 27 mm 0 , a n o t h e r metallic disc of 28 mm 0 , protruding 6 m m with 25 mm 0 a n d a plastic one (PMMA) of 30 mm 0 .

The working surface of the metallic discs w a s black a n o d i s e d a l u m i n u m (AlMgSi 0,8) with a r o u g h n e s s of 0.3 urn CLA (ISO 468-1382), a n d the s i d e s were a n f i s p r e a d treated by bak-ing a coatbak-ing of 1.2 |.irn thickness of teflon (PTFE), plus brushing a coating of 3M-FC-723.

The interior of the AFPM l e s t - c h a m b e r a s s e e n by the v i d e o e a m e r a is p r e s e n t e d in Fig. 1 in two versions, the i d e a l s c e n e i m a g i n e d by the experimenter a n d the real o n e observed in flight. It m a y b e a r g u e d that e v e r y t h i n g should have b e e n known a n d a c c o u n t e d for, particularly for a n e x p e r i e n c e d FPM investi-gator, but there a r e so m a n y details a n d so little interaction (the flight e q u i p m e n t is inac-cessible before flight, the e n g i n e e r i n g unit nearly the s a m e , a n d the last details so d e -cisive: working disc protrusion, raster d e s i g n a n d fitting, etc.) that one cannot realistically be p r e p a r e d for so m a n y things. For instance, d u e to a late c h a n g e in v i d e o e a m e r a orientation, the i m a g e on SLD2 a p p e a r s u p s i d e -down with respect to previous flights a n d to the c r e w m a n sight, so that now the front disc with the feeding hole is at the bottom (that is the disc.that travels up a n d down), a n d the rear (oscillating) disc is at the top.

Diffuse b a c k g r o u n d illumination by a n a r r a y of 9x8 LEDs a n d a o p a l i n e g l a s s diffuser w a s

used to e n h a n c e the visualisation of the outer s h a p e of the liquid column, although a meri-d i a n light sheet coulmeri-d be usemeri-d if meri-desiremeri-d to visualise tracer motion inside. This AFPM il-lumination h a s g o n e a q u a n t u m step forward in optical quality (brightness a n d uniformity) c o m p a r e d to the crude performances of the o l d F P M i n S L - 1 a n d SL-D1.

Concerning the p r o p o s e d a n d the executed e x p e r i m e n t timeline there a r e a l s o major c h a n g e s b e c a u s e the matching of crew avai-lability, a u d i o a n d video links to ground, a n d so m a n y n e e d e d resources in a stressed oper-a t i o n oper-a l environment oper-a s Spoper-acc'.oper-ab, h oper-a s oper- al-w a y s proved to be a n impossible fitting.

Unfortunately, due to the time shift, Run 1 was executed in the blind (not TV link) and the experimenters only gathered a short verbal report saying that the three frequency trials

run nominally, and the middle one (at 0,41 Hz) seemed to be precisely the second eigenire-quency. Without further information before the second run was due to start, the

investiga-G M T cidd/hh:nun:ss RUN-1 118/11:13:47 118/11:14:00 118/11:15:50 118/11:15:50 118/11:25:10 118/11:25:10 118/11:30:54 118/11:31:27 118/11:33:12 118/11:33:35 118/11:36:05 118/11:36:28 118/11:37:55 118/11:37:55 118/11:40:35 RUN-2 118/13:19:15 118/13:20:55 118/13:20:55 118/13:22:18 118/13:22:32 118/13:26:08 118/13:28:04 118/13:28:17 118/13:28:18 118/13:31:15 RUN-3 125/14:04:52 125/14:07:07 125/14:12:18 125/14:12:18 125/14:13:07 125/14:13:07 125/14:13:27 125/14:13:27 125/14:14:27 125/14:14:27 125/14:15:10 125/14:15:10 125/14:15:25 125/14:15:25 125/14:18:15 MET d/hh:nnn:ss 1/20:23:47 1/20:24:00 1/20:25:50 1/20:25:50 1/20:35:10 1/20:35:10 1/20:40:54 1/20:41:27 1/20:43:12 1/20:43:35 1/20:46:05 1/20:46:28 1/20:47:55 1/20:47:55 1/20:50:35 1/22:29:15 1/22:30:55 1/22:30:55 1/22:32:18 1/22:32:32 1/22:36:08 1/22:38:04 1/22:38:17 1/22:38:18 1/22:41:15 8/23:14:52 8/23:17:07 8/23:22:18 8/23:22:18 8/23:23:07 8/23:23:07 8/23:23:27 8/23:23:27 8/23:24:27 8/23:24:27 8/23:25:10 8/23:25:10 8/23:25:25 8/23:25:25 8/23:28:15 Count s 55960 55973 560S3 56083 56643 56643 56987 57020 57125 57148 57298 57321 57408 57408 57568 6348S 63588 635SS 63671 63685 63901 64017 64030 64031 64208 671025 671160 671471 671471 671520 671520 671540 671540 671600 671600 671643 671643 671658 671658 671828 L mm 15 17.2 85 85 85 85 85 85 85 85 85 85 85 85 85 15 85 85 85 85 85 85 85 85 94 15 15 15 15 52 52 52 52 80 80 80 80 84 84 S4 V cm3 10.5 16.9 59.5 59.5 59.5 59.5 59.5 59.5 59.5 59.5 59.5 59.5 59,5 59.5 59,5 10 64 64 60 60 60 60 60 60 60 10 10 10 35 35 35 35 59 59 59 62 62 66 66 Zoom" 3,26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3.26 3,26 3.22 3,22 3,56 3.56 3.17 3.17 3.17 3.17 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 3.06 Slant % 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.3 1.3 2.3 2,3 1.7 1.7 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 Notes

Start stretching: Run la (120 s) Good lime origin

End stretching

End stretching: Run lb (600 s) Start vibration

Start vibration: Run 1c (300 s) End vibration

Start vibration: Run Id (100 s) End vibration

Start vibration: Run lc (150 s) End vibration

Start vibration: Run 11(100 s) End vibration

End vibration: Run l g (150 s) Start recover

Start stretching: Run 2a End stretching

Start camera quiet: Run 2b (90 s) End camera quiet

Start cam.quiet: Run 2c (200 s) End camera quiet

Start camera quiet: Run 2d (13 s) End camera quiet

Start cam.quiet: Run 2e (ISO s) Bicakinp

Discs at 15 mm

Bridge formed: Run 3a (300 S) Start stretching

Start stretching: Run 3b (50 S) End stretching at 50 mm End stretching: Run 3c (20 S) Start stretching

Stan stretching: Run 3d (60 S) End stretching to 80 mm End stretching: Run 3c (30 S) Start stretching

Start stretching: R u n 3 f ( 1 0 S) End stretching

End stretching: Run 3g (ISO s) Breaking

Table 1: SL-D-2-FPM-STACO timeline a s flown.

tor chose to c o m e bock to the last e x e c u t e d step in the previous run a n d follow on with the s a m e working discs.

The liquid column w a s r e s t a b l i s h e d , what wc mark a s Run 2, a l t h o u g h d u e to the time con-straint, one air b u b b l e of 8 rum in d i a m e t e r w a s ingested in the working oil. Then the investigators on g r o u n d h a d for a first time a view of the liquid column (real-time TV), but noticed that the e d g e s of the column were out of s c i e e n a n d instructed the c r e w m a n to zoom-out a little bit, what h a p p e n e d to be a time-wasting interaction since it w a s the out-put video-signal from the frame g r a b b e r a n d not the original signal that w a s clipped. Be-c a u s e experienBe-ce h a d shown that b r e a k i n g a liquid column by isorotation is more d a n -g e r o u s (to loose control of the liquid m a s s ) t h a n b r e a k i n g by disc s e p a r a t i o n , the investi-g a t o r a s k e d the c r e w m a n to e x c h a n investi-g e the order of trials. Unfortunately, in spite that in SL-D1 there were five column b r e a k a g e s a n d the liquid a l w a y s r e m a i n e d well-anchored a n d could b e m e r g e d easily, in SL-D-2 this first b r e a k a g e a n d all the rest h a p p e n e d to b e catastrophic (waste of liquid control by over-s p r e a d i n g to the back-over-side of the r e a r diover-sc) a n d the experiment h a d to b e terminated pre-maturely to allow sufficient time to c l e a n - u p before the next experiment.

The D-2 t e a m m a n a g e d to a l l o c a t e a n extra run for STACO, but p r o b l e m s with the AFPM power-up s e q u e n c e prevented even to start. Fortunately the AFPM w a s recovered a n d the extra a m for STACO (Run 3) w a s finally ex-ecuted a week after. For still unknown rea-sons, the 84 mm long liquid column between u n e q u a l discs of 30 mm a n d 28 mm w a s trembling for more than three minutes without a p p a r e n t stimuli until it broke, in a n unre-coverable m a n n e r a s before.

D a t a A n a l y s i s

Three sets of d a t a were foreseen: the first a n d m a i n o n e w a s the video recording (either real-time link or stored a b o a r d ) , the s e c o n d w a s the AFPM h o u s e k e e p i n g d a t a of disc position, v o l u m e injected, a n d v a l u e s of a p p l i e d stimuli, a n d the third one w a s a 35-mm photo-c a m e r a 36-exposure film to b e u s e d only a s high resolution s a m p l e s .

It must be s a i d from the b e g i n n i n g that thp quality of the SL-D-2 video link w a s much better than e x p e c t e d from p a s t experience on S p a c c l a b a n d TEXUS, a n d a l s o that i he AFPM h o u s e - k e e p i n g d a t a presentation in real-time w a s a n a c h i e v e m e n t in comparison with the old s t a t u s s c r e e n for SL-i a n d SL-DI Even the p h o t o c a m e r a , that w a s premature!-,-a b premature!-,-a n d o n e d for lpremature!-,-ack of confidence premature!-,-a s ex-p l a i n e d a b o v e , did ex-perforin flawlessly a n d furnished the best a v a i l a b l e pictures of a l a r g e liquid column in s p a c e .

Problems with house-keeping d a t a from the AFPM a r e minor: a s s a i d before, s o m e of the tolerances enter into the working r a n g e (f.i. for low frequencies), s o m e l a g g i n g h a s b e e n dis-covered in the start of disc s e p a r a t i o n , a n d the fact that non-operating c h a n n e l s were full of noise instead of calm.

Problems with the video d a t a , on the contrary, a r e important a n d plentiful, a s c a n be grasD from the following list:

• Real i m a g e s were s e e n only during the a c t u a l flight (plus one d e m o simulation of very little quality).

• The c h a n g e s in video s i g n a l s t a n d a r d (NTSC to PAL) greatly impoverishes the quality of the video s i g n a l .

• Videotape recording (a VHS copy) h a s b e e n u s e d for all the a n a l y s i s , the anal-o g u e videanal-o s i g n a l making difficult the repetition of time s e q u e n c e s .

• C o n i c a l p e r s p e c t i v e i n t r o d u c e s s c a l e s a n d p a r a l l a x deformations.

• C a m e r a zoom a n d p a n (and the a s s o c i a t e rotation d u e to a n e c c e n t r i c pivoting) make video a n a l y s i s too c u m b e r s o m e .

• M i s a l i g n m e n t t h r o u g h the optical axis (three intermediate mirrors) introduces a slant deformation.

• Frame g r a b b e r clipping w a s a big handi-c a p during flight o p e r a t i o n s a n d for later analysis.

• Defocusing of the grid introduces large uncertainties.

Fortunately, lime a n d s p a c e references en-a r en-a v e d on e en-a c h videofren-ame h en-a v e h e l p e d en-a lot in correlating s e q u e n c e s .

An a c c o u n t of the uncertainties related to i m a g e a n a l y s i s follows. It is important to k e e p in mind that b e c a u s e of the conical p e r s p e c -tive a n d the n o n - s q u a r e pixel used, four dif-ferent length s c a l e s c a n be used in a n i m a g e : m i l l i m e t r e s a t t h e b a c k g r o u n d r a s t e r (mm ras), millimetres at the object p l a n e or meridian cut of the liquid column (mm_obj), pixels a l o n g the horizontal direction of the frame g r a b b e r (px_hor) a n d pixels a l o n g the v e r t i c a l d i r e c t i o n of t h e f r a m e g r a b b e r (px_ver).

The d i s t a n c e from the liquid column axis to the v i d e o c a m e r a is taken a s 800+5 mm (the uncertainty d u e to the several dioptrics inter-posed). The d i s t a n c e from the liquid column axis to the b a c k g r o u n d raster is taken a s 80±1 mm (uncertainty d u e to the dioptrics in-terposed). With those n u m b e r s (see Fig. 2) some a p p a r e n t sizes a r e :

• The l e n g t h of 85 m m _ o b j is s e e n a s 85-(800 + 80)/800 = 93.5+0.6 m m j r a s .

• The d i a m e t e r of 30 mm_obj is s e e n a s 30-(800 + 80)/800 = 33±0.2 mm_ras.

• The disc p a r a l l a x at 50 mm off-axis gives a 50-30/800-(800 + 80)/800 = 2.0 m m _ r a s a p p a r e n t size (minor axis of the ellipse).

The video-digitiser u s e d (a D a t a Translation DT 2862 plug-in b o a r d ) t a k e s n o n - s q u a r e pixels of a clipped video frame, resulting in a

1 px_hor/mm = 0.685±0.00i px_ver/mm ratio or a 1.460±O.Q02 px_ver/'mm = 1 px_hor/mm ratio, according to a high precision test per-formed in-house.

Zooming c h a n g e s the px-to-mm ratio a n d the origin for liquid s h a p e s , a s well a s for p a n

-ning, what, a d d e d to the in-the flight m o d e of v i d e o d i g i t i s a t i o n , r e n d e r s t h e s e s c e n e s ( c h a n g i n g zoom or p a n ) u s e l e s s for a c c u r a t e a n a l y s i s , so that the classification of useful s c e n e s p r e s e n t e d in Table 1 w a s b a s e d on that.

With the e q u i p m e n t used, only odd or even videolines c a n b e s c a n n e d on the s a m e frame clue to synch problems, what have contributed the most to the uncertainty to accurately de-tect disc e d g e s . The disc cutback of 0.9 mm only gives a 2 or 3 pixels trace (it should h a d b e e n built to 5 mm, d e c r e a s i n g the d i a m e t e r of the stem accordingly, at least locally).

W h e n a n i m a g e (as in Fig. 1) is digitised a n d a n a l y s e d , the grey-levels at every pixel show profiles of the kind p r e s e n t e d in Fig. 3, where the raster-print c a n be discerned. Looking in detail at such grey-level profiles one c a n find the following results.

The e d g e detection algorithm u s e d defines the e d g e position a s the location of the ex-treme of the first derivative (position of the p e a k s at the bottom of Fig. 3a), fitting the discrete v a l u e s to a p a r a b o l a , what a s s u r e s a typical uncertainty of O.i pixels for the kind of profiles o b t a i n e d in SL-D-2.

It is a m a z i n g to note that the levelling of the field of view, that w a s left to the c r e w m a n sight, a p p e a r s to be a l w a y s tilted clockwise, a c c o r d i n g to the figures of slant given in Table 1 (a 1.4% slant for Run 2b m e a n s that the c o r r e s p o n d i n g horizontal reference line, 100 m m _ r a s to the right, is (1.4/100)* 100= 1.4 m m j r a s below (3 px_ver) a s c a n be appreci-a t e d f.i. appreci-at the bottom of Fig. l b .

For the zoom corresponding to Run 2b, the 1 m m j a s reference line thickness gives 4.1+0.1 px_hor a n d 5.8+0.1 px ver width, instead of the 3.22 p x j i o r a n d 3.22* 1.43 = 4.7 px_ver a c

"Y'\

i \

M 500 li'O IO0 r-f/1 X0 160 •U'l} -00

!

• 1

i

'"^1" (

n

'I

\

0 !*) 100 1M ^ B :^'3 3.U XH *OT *-iJ a/)

Fig. 3: a) Grey-levels of a mid-heights horizontal line of a n i m a g e of Run 2b showing from left to right the three reference lines, the left b o r d e r of the liquid column, the a x i a l reference line, tire right border a n d the other three reference lines. The a b s o l u t e v a l u e of tire first derivative is a l s o plotted a t tire bottom, b) Grey-levels of a n e a r - a x i a l vertical line of the s a m e i m a g e were the reference tick m a r k s of the raster centre-line c a n b e a p p r e c i a t e d . White b a c k g r o u n d should h a v e a 2.56 grey-level. Black raster lines, b e c a u s e of defacusing, h a v e mid grey-levels.

cording to Table 1, so the res; is d u e to defo-cusing. On the other h a n d , the 1 0 m m _ r a s l i n e s p a c i n g of the s q u a r e reference b o x e s gives 32.3+0.1 px_hor a n d 47.4+0.2 p x j i o r , practi-c a l l y e q u a l to t h e 3 2 . 2 p x _ v e r a n d 3.22-1.46 = 47.0 px_ver estimations with per-fect focusing. By the way, the horizontal-to-vertical pixel size ratio o b t a i n e d from the raster is (47.4+0.2)/(32.3±0.1)= 1.47+0.01, in a c -c o r d a n -c e to the -calibration (1.46+0.005).

The 27 mm_obj width of the disc stem (that m a k e s the disc protruding from the AFPM base-plate), gives 35.5+0.1 px hor width, per-fectly matching the 27-3.22-880/800 = 9S.6±0.2 px_hor). Similarly, the 30 mm_obj width of a cylindrical liquid column (or at least n e a r the discs), gives s o m e 105.5±0.1 px hor width, a l s o m a t c h i n g the 30-3.22-880/800= 106+0.2 px_hor).

The Q.9 mm_obj vertical projection of the cut-b a c k of t h e d i s c s o n l y a l l o w s for 0.9-3.22-1.46 = 4.2 px_ver, that is only two! o d d pixels, m e a n i n g that the uncertainty in the column length a s m e a s u r e d from the i m a g e

is 0.5 px_vor or 0.1 mm_obj, w h e r e a s column radii ( a s s u m i n g a circular cross-section) is m e a s u r e d with a n uncertainty of 0.1 px hor (0.03 mm obj). However, when only relative v e r t i c a l p o s i t i o n w a s n e e d e d , t h e

(30-21)j2-~ 1.5 mm obj horizontal projection of the

cutback of one disc could be tracked to an uncertainty of 0.2 px ver. Using this trick, the; a m p l i t u d e p e a k - t o - p e a k oi the a p p l i e d axial vibrations in Run 1 w a s m e a s u r e d to be 100.2 px_ver, c o r r e s p o n d i n g to 10/(3.26-1.46) = 2.1+0.05 m m _ o b j , perfectly m a t c h i n g the 2.0±0.1 mm setting at the AFPM.

C o n s i d e r i n g now the behaviour of the liquid b r i d g e , let u s b e g i n by the vibration trials in Piun 1. Figure 4 p r e s e n t s successive '/•, period i m a g e s for a full period of 0.25 s correspond-ing to the forccorrespond-ing frequency of 0.40 Hz in Run lc. Note that /=0.40 Hz w a s the nominal fre-q u e n c y seiting, but the AFPM d a t a gives /

= 0.39+0.01 Hz, a l t h o u g h the i m a g e analysis gives the value / =0.40+0.005 Hz from the FFT spectrum of either the disc motion or the main r e s p o n s e of tire liquid s h a p e , p r e s e n t e d in Fig. 5, where the time s t a g e s corresponding to the i m a g e s in Fig. 4 have b e e n marked. Similar pictures c a n b e obtained for Run Id, Run l e a n d Run 11 , a n d the following points a r e found:

The centres of the liquid column slices a! ''/•„

xh a n d 3/i of its length (starting at the vibrating disc), oscillate with a period of 4.5+0.1 s (first l a t e r a l e i g e n f r e q u e n c y ) a s s e e n from the video c a m e r a (it is not yet clear if this motion is a s i n u s o i d a l vibration in the meridian plane or just the projection of a uniform circular motion, a s a skipping rope); their ordinate shift is d u e to the tilting of the i m a g e in the field of view. To discern between these two options, the motion of the big b u b b l e in Run 2 a n d the difference in a p p a r e n t optical posi-tion of the tic-marks b e h i n d the liquid dioptric have b e e n tried, but without conclusive re-sults.

The radii of the liquid column slices at '/t, 'l'i

oscillations a r e clearly asymmetric, with the radius at '/i oscillating in p h a s e with the disc, the r a d i u s at V2 in c o u n t e r p h a s e a n d with a larger a m p l i t u d e (demonstrating that it is very n e a r the s e c o n d eigenfrequency), a n d the radius at 3A oscillating in a bizarre fashion

with s i n u s o i d a l hills but flat valleys a n d with the smallest a m p l i t u d e , a s c a n b e expected horn its iar position from the source.

The main p e a k in the respective spectrums a r e / =0.40+0.005 Hz for Run lc, / =0.41+0.01 Hz lor Run Id, / =0.42+0.005 Hz for Run l e a n d / =0.42+0.01 Hz for Run If. Note that in order to have a given a c c u r a c y A/ a r o u n d a given frequency / w i t h a known s a m p l i n g rate of fc the n u m b e r of d a t a points n e e d e d is iVp = /.j/A/tfor i n s t a n c e , to m e a s u r e / = 0.40+0.01 Hz, sampling at the video frequency of ls =25 Hz, one n e e d s a s e q u e n c e of jVp = 2S/0.0i =2500 d a t a points). Also, to h a v e at least three points inside the spectral interval A/ to minimise the l e a k a g e effect (to better define the p e a k in the FTT), one h a s to transform three s a m p l e s of

Np, rVp + AiVpS a n d Np + 2ANp3, were AJVp3 is

the n u m b e r of d a t a points in a third of a period, that is, ANp3 = U(3-[); f.i. AWp3 = 25/(3-0.4) = 21 points.

it is very interesting a l s o to a n a l y s e the d e c a y of a perturbation. At the b e g i n n i n g of Run l b , just after the s u d d e n stop of the cylindrical injection, the liquid b r i d g e oscillates in the first m o d e with a period of 14+0.5 s (the first e i g e n f r e q u e n c y ) a n d h a s a h a l f - d a m p i n g time of s o m e 40+5 s (time to d e c r e a s e the a m p l i t u d e to o n e half). At the e n d of the oscil-lation runs, it c a n b e s e e n that the first a x i a l mode h a s a l s o a half-damping time of s o m e 40+5 s, but the s e c o n d a x i a l m o d e (the o n e purposely excited) h a s a half-damping time of just 7+0.5 s. T h e s e results m a y b e used to check the validity of theoretical d e v e l o p m e n t s of viscous effects [7, 3 a n d 10].

The s e c o n d run (Run 2) w a s the first seen on the g r o u n d control centre, a n d there w a s a 8 mm in d i a m e t e r air b u b b l e inside. For un-known r e a s o n s , the cylindrical filling w a s overdone in volume, with a n AFPM r e a d i n g of 64 cm i n s t e a d of the n o m i n a l GO cm , but the crewman noticed it a n d removed the excess of liquid in two 2 cm s t e p s (Run 2b). The first axial e i g e n f r e q u e n c y h a d a period of 12+0.5 s at this volume of 64 c mJ (Run 2b) instead of

r r

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J«5W --!;,-.•

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1 '

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230

220

210

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4 5 6 time [s]

10

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FigS: Evolution of tliree equispaced slices oi the liquid column during Run 1c. The forcing is by up-and-down oscillations of the upper disc with an amplitude of 2 mm peak-io-peak (10 vertical pixels in the image) and a frequency oi 0.40 Hz. The liquid column responds with radial oscillations in the second axial mode at the forcing frequency (the radius nearest to the forcing disc is HIM and bulges when the disc pushes), and lateral oscillations in the first lateral eigenfrequency (all in horizontal pixels). The five dot-lines correspond to the pictuies in Fig. -1.

the 13+0.5 s tor the cylindrical volume at of 60 cm (Run 2c). The a c c u r a c y in liquid vol-u m e metering, or the effect oi the b vol-u b b l e , may explain the difference b e t w e e n the 13±0.5 s in Run 2c a n d the 14+0.5 s in Run 1 for a p p a r -ently the s a m e settings. Similarly, the first l a t e r a l e i g e n f r e q u e n c y h a d a p e r i o d of 4.8±0.2 s at the 64 c m3 volume a n d 4.5±0.2 s at the 60 cm of the cylindrical volume.

The extra run (Run 3) is plenty of u n k n o w n s a n d h a s yield Utile d a t a , u p to now, to check the extensive work on the b e h a v i o u r of liquid columns b e t w e e n u n e q u a l discs [11-13]. It w a s p e r f o r m e d o n e w e e k after the other STACO runs, just after a n extra run oi the LICOR experiment. A s m a l l 15 mm long liquid bridge w a s left idle for more t h a n 5 minutes d u e to drop-outs in the voice link. A rosary of steps in length a n d volume (L= 15,52,79,80

a n d 84 m m a n d V= 10,36,43,53,62 a n d 66 cni ) w a s followed, instead oi the direct step from L = 1 5 m m t o L = 85 mm a n d V= 1 0 c mJ to V=5B

3

cm oi the n o m i n a l p r o c e d u r e . A residual r e a d i n g from the AFPM d a t a of the frequency threshold (0.1 Hz) a n d the a m p l i t u d e thre-shold (0.1 mm), just n e a r the first axial eigen-frequency, throws no light.

95

e

E 90

85 -20

~--'~^

x~::r:::....

I i

-10 10

lime [s]

20 30 "40

r i g . 6: Breaking evolution in Run 2e c a u s e d by disc s e p a r a t i o n at constant liquid volume. The initial liquid column s h a p e w a s almost cylindrical, 85 mm long, 30 mm in d i a m e t e r a n d 60 cm in volume, a n d separation started at time 0, a s s e e n in the position of the lower disc d e d u c e d from the video i m a g e s (unfortunately the disc g o e s out of sight at 92 mm, before the 94 mm stop. Lateral oscillations of tire center Line (Cs) a n d radial evolution (fis) a r e shown at three initially e q u i s p a c e d column sections (but the s a m e 'video-lines a r e s c a n n e d during trie stretching).

liquid c o l u m n o s c i l l a t e s l a t e r a l l y with a period of 4.5±0.2 s a n d a maximum a m p l i t u d e of 12 px_hor peak-to-peak, a n d in the first axial m o d e with a period of 12+0.5 s a n d a m a x i m u m a m p l i t u d e of 4 px_hor p e a k t o -p e a k until at a certain s t a g e a n d without - pre-vious notice the b u l g e of liquid, that h a d b e e n ail the time (oscillating) in the u p p e r part, moved to the lower half a n d in the s u b s e q u e n t swing s u r p a s s e d the stability limit a n d the column broke (see Fig. 7), unrecoverable/ a s in the former c a s e s .

With respect to the r e s i d u a l axial a c c e l e r a -tion, or more precisely with the s t e a d y aver-a g e d deformaver-ation of the liquid outer s h aver-a p e , the extrapolation (accounting for only the difference in disc size) from the SLD1 m e a s u r e -ment of 70 ug [3], predicted for SL-D-2 a steady r a d i a l deformation from the

cylindri-cal s h a p e of 3 px_hor bulging in the feeding disc side CR3/4) a n d of 3 px_hor necking in the rear disc side CR1/4). The findings however d o not support this extrapolation. Instead oi this d i f f e r e n c e of H3/4- J?i/-i = 6 pixels, STACO yields 0.6 pixels for Run l b , 0.2 pixels for Run 2b a n d Run 2c, a n d 0.3 pixels tor Run 2e. For Run 3, b e c a u s e of the difference in disc size, the correlation is much more involved a n d h a s not yet b e e n worked out.

10 1 — | i l | I ~ T

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s

20 60 80 100

a)

120 140 160

65

60

f •

M

\

tf

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80 100 time [s]

Fig. 7: Evolution during Run 3g. A liquid column 84 mm-long s p a n n i n g b e t w e e n discs of 28 m m (bottom disc) a n d 30 m m in d i a m e t e r (top disc), with 66 cm of liquid, oscillating laterally (a) a n d axially (b), without known a p p l i e d stimuli, for nearly 150 s until it unexpectedly b r e a k s . Nomenclature is a s in Figs. 5-6.

R e s u l t s a n d C o n c l u s i o n s

The STACO experiment b e l o n g s to a s e r i e s of microgravity e x p e r i m e n t s o n the m e c h a n i c a l deformation of long liquid columns that, al-though performed over a 10-year period, only-a m o u n t to only-a few severonly-al-minutes trionly-als per-formed in a hurried a n d s t r e s s e d o p e r a t i n g environment.

The main a c h i e v e m e n t of STACO is the high a c c u r a c y r e a c h e d in a u t o m a t i c i m a g e a n a -lysis, of the o r d e r of 30 urn in object size (0.1 pixels in the 512x512 imago), what is a g r e a t improvement if c o m p a r e d lo the m a n u a l l y digitised hard-prints in SL-D1-FPM-FLIZ.

The r e s p o n s e of the 85 mm-long cylindrical liquid column to a forced a x i a l vibration of

o n e of the supporting d i s c s is in very good a g r e e m e n t with the theory, a n d c o m p l e m e n t s other m e a s u r e m e n t s performed in the s a m e (light (see LICOR report) with shorter col-u m n s .

Many unnoticed characteristics of the equip-ment, the optical set-up a n d the d a t a acquisi-tion system have b e e n discovered that should b e improved in future trials.

contrary, there w e r e live b r e a k i n g s a n d merg-ings without liquid loss.

The m o r e p u z z l i n g q u e s t i o n left a l t e r the STACO trials is the lack oi reproducibility of the s t e a d y a v e r a g e d deformation m e a s u r e ment, p e r h a p s b e c a u s e it is not a c h a r a c teristic of the configuration a n d m a y b e d e -p e n d e n t on d e t a i l s of h a r d w a r e (f.i. m a t e r i a l s u s e d , r o u n d i n g of wetted corners, etc.) that e s c a p e to the control of the e x p e r i m e n t e r a n d a r e different in e a c h c a m p a i g n . As u s u a l , more e x p e r i m e n t s a r e n e e d e d to e l u c i d a t e the u n e x p e c t e d results oi this o n e , but a c l e a r p r o g r e s s in the overall e x p e r i m e n t p l a n n i n g is evident.

A c k n o w l e d g e m e n t

Tire i n v a l u a b l e h e l p of o u r s t u d e n t ].E. M o r e n o in p r o g r a m m i n g t h e v i d e o frame g r a b b e r , the a s s i s t a n c e of the ESTEC a n d SLD2 t e a m s (particularly to the c r e w m e m -b e r s H. S c h l e g e l a n d U. Walter), a n d the fi-n a fi-n t i a l s u p p o r t of the S p a fi-n i s h G r a fi-n t from the CICYT ESP92-0001-CR is a c k n o w l e d g e d .

R e f e r e n c e s

[1] Martinez, 1., Liquid column stability. .Experiment

l-ES-331, in Materials Science under

Micro-gravity, ESA SP-222, pp. 31-36, 1985. [21 Martinez, I. & M e s e g u e r , )., Floating liquid

zones in microgravity, in: Scientific Results oi

the Gam-tan Spacelab Mission Dl, Sahm, PR.,

/arisen, R., Keller. M.H. (Eds.), DFVLR, Koln.

FRG.pp. 105-112, 1987.

[3] Martinez, 1. & Sanz, A., Experiments with long liquid b r i d g e s u n d e r microgravity, in

Ma-terials Science under Microgravity. ESA SP-295. pp. 413-419, 1930.

[4] Martinez, 1., Meseguer. J. & P e r a l e s . J.M., 1991, Stability ol Long Liquid Columns, in

"Re-searchprogram of the German Spacelab Mission D-2\ Sahm, P.R.. Keller, MJ-L,

Schievve. B. (Eds.l. Wissenchaltliche

Projekt-luhrung Spacelab Mission D-2, pp 221-222.

[51 Bezdenejnykh, N.A., M e s e g u e r , ]. & Perale3, J.M,, 1992, Experimental Analysis of Stability Limits of Capillary Liquid Bridges, Physics ol

fluids A Vol. 4. pp. 677-680.

(6) M e s e g u e r , J., Sanz, A. & P e r a l e s , J.M.. 1990, Axi-symmetric Long Liquid Bridges Stability a n d R e s o n a n c e s , Appl. Microgrcrvhv Tech.. Vol. 2, p p . 186-192.

[7] P e r a l e s , J.M. & M e s e g u e r , J.. 1992, Theoretical a n d Experimental Study of the Vibration of Ax-isymmetric Viscous Liquid Bridges, Phvsics ol

Fluids A Vol. 4. pp. 1110-1130.

[8] Nicolas, J.A., 1991, Frequency R e s p o n s e of Axi-symmetric Liquid Bridges to a n Oscillatory Microgravity Field, Microgravity Science a n d Technology, VbJ. 4. pp. 188-190.

[9] M e s e g u e r , J. & Perales, J.M.. 1991, Viscosity Ef-fects on the Dynamics oi Long Axrsymmetric Liquid Bridges, Microgrcrviry Science a n d

Technology. Vol. 4, pp. 139-142.

[101 M e s e g u e r , J. & P e r a l e s , J.M., 1992, Non-steady P h e n o m e n a in the Vibration of Viscous Cylind-rical Long Liquid Bridges, MicrograWry

Science and Technology. Vol. 5, pp. 69-72.

[1 Ij P e r a l e s , J.M., Meseguer, J. & Martinez, I., 1991, Minimum Volume of Axisymmetric Liq-uid Bridges between U n e q u a l Disks in a n Axial Microgravity Field, Journal ol Crystal Growth, Vol. i 10, pp. 855-86J.

[12] Martinez, L, P e r a l e s , J.M. a n d Gomez, M.. 1992, Effects of Axial a n d Centrifugal Forces on trie Stability of Liquid Bridges, ESA SP-333,

pp. 123-130.

[13] Bezdenejnykh, N.A. & M e s e g u e r , J., 1991, Sta-bility Limits of Minimum Volume a n d Breaking of Axisymmetric Liquid Bridges b e t w e e n Un-e q u a l Disks, Microgravity SciUn-encUn-e and TUn-ech-