(IASA-CR-1b2Uci't) PkiXSlCAL PtENOBEIA X Y N82-25466 C O l T A I Y BCLESS (:,ASS PSOChSSIIG Annual Technical Report (Clatkocn Ccll. of Techoology) 13 y LC A02/Mk A01 C S C i ZOD Unclas

G3/34 27922

NASA CCNTRACTOR REPORT

XASA CR- 162007

PHYS ICAL PHENOMENA IN CONTAINERLESS GLASS PROCESS ING

By R. Shankar Subramanian, Robert Cole. P . Annamalai, K . Jayaraj, P. Kondos, T . J . McNeil, and N . Shankar Departaent of Chemical Engineering Ciarkson College of Technology Potadam, New York 13676

January 1982

Annual Technical Report 'E

Prepared for

NASA-George C. Hershall Space Flight Center Warahall Space Flight Center, Alabama 35812

https://ntrs.nasa.gov/search.jsp?R=19820017590 2018-09-01T08:59:35+00:00Z

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I. RrCPOiti NO. j. RIQPl tMT ' I CAT- -1

NASA CR-162007 .1 , 4. TITLE AN0 8 U ) T I T U 8. RLCORT DATE

Physical Phenomena i n Container less Glass Janwry 1982 6. C I R m M I W Q OROAMIXATIOW COOL Processing

Department of Chemical Engineering Clarkson College o f Technology

1 Potsdam, New York 13676 1 1. COWTRACT OR -ANT NO.

1s. SUPPLEMENTARY NOTES

Contract Monitor: Robert A. Fal lon LA1 1 Marshall Space F l i q h t Center , AL 35812

1). USTRACT A Arrangements were made with the J e t Propulsion Laboratory t o obta in use of t h e i r 3-axis ambient temperature acous t ic l e v i t a t o r fo r some of t he model f l u i d experiments beginning with KC-135 f l i g h t s i n 1982 and continuing onto Shu t t l e f l i g h t s i n 1984-85.

12. rrcmsoalm AGENCY n*m AND ADWEIS

National Aeronautics and Space Administrat ion Washington, D.C. 20546

B. Arrangements were made with the Marshall Space F l igh t Center f o r our p a r t i c i p a t i o n i n the engineering t e s t of a high temperature acous t ic l e v i t a t i o n f a c i l i t y b u i l t by In te rsonics t o be conducted on a Shut t le f l i g h t i n l a t e 1982.

.-.

Contractor Report

14. S P O W S O R ~ ~ ~ C Y CODE

I C. F a p e r i v n t a l work was performed i n t he following areas : I I 1. Experiments were conducted on bubble migration i n r o t a t i n g l i q u i d bodies

contained i n a sphere. r 2. Experiments were i n i t i a t e d on the migration of a drop i n a s l i g h t l y less

dense continuous phase contained i n a r o t a t i n g sphere. The experiments w i l l be continued i n t o 1982.

3. A re f ined apparatus f o r t h e study of thermocapillar) flow i n a g l a s s melt w e s b u i l t , and d a t a were acquired co su r f ace v e l o c i t i e s i n the melt . Similar da t a a l s o were obtained from an ambient temperature f l u i d model. The da t a were analyzed and co r re l a t ed with the a i d of theory.

I 4. Data were obtained on flow v e l o c i t i e s i n a pendant drop heated from above. The motion i n t h i s system was dr iven p r inc ipa l ly by thermocapi l lar i ty . I

I 5 . A7 appara tw was designed fo r t h e study of v o l a t i l i z a t i o n from a g l aes melt. I 17 REV WORDS 18. 0ISTRtI)UTION STATEMENT I

Glass, Container less , Lev i t a t i on , Unclass i f ied - Unlimited Bubble, Thennocapillary , V o l a t i l i s a t i o n

Unclaasif i e d I Unc lass i f ied I 13 NTIS I Y I C * o m .)am ( Y v am

I lor rk by n.*ml T.sLld htormatks Irrvk., Ilplklunoa - fnb'

D. Theoret ical work was performe(1 in the following areas:

1. A computer model was construcled fo r p red ic t ing the ve loc i ty and temperature f i e l d s i n a c y l i n d r i c a l l i q u i d bridge. The r e s u l t s from the model were used f o r comparison with experiments, and f o r the co r r e l a t ion of experimental data.

2 . A t heo re t i ca l so lu t ion f o r the migration of a bubble i n a r o t a t i n g l iqu id body i n the low Taylor number regime was obtained f o r comparison with experiments.

3. Work was conducted on the descr ip t ion of thermocapillary motion i n drops of a r b i t r a r y a x i a l l y symmetric shapes.

4. The problem of the quas i - s t a t i c motion of a bubble eccen t r i ca l ly placed i n a drop was solved f o r the axisymmetric case. Computer programs were developed f o r p l o t t i n g s t reamlines and isotherms d i r e c t i y .

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ORIGINAL FAOE IS OF POOR QUALITY

Table of Contents --- - Page

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abst rac t 1

. . . . . . . . . . . . . . . . . . . . . . . . . I n t r o d u c t i o n . . . . . 3

The Migra t ion of a Bubble/Droplet i n a R o t a t i n g Liquid: P. Anfiamalai . . 7

Thermocapil lary Convection i n Drops: K. J a y a r a j . . . . . . . . . . . . . 7

Vo1at:lization i n Glass Melts: P. Kondos . . . . . . . . . . . . . . . . 8

Thennocapi l lary Convection i n Model F l u i d s and Glass Melts: T.J. McNeil. 9

Therrnocapillary Motion o f Bubbles I n s i d e Drops: N. Shankar . . . . . . . 10

Appendix A: P u b l i c a t i o n s i n J o u r n a l s i n 1981

A- 1 "Slow Migrat ion of a Gas Bubble i n a Thermal Gradient R. S. Subraalanian ( r e p r i n t )

A- 2 "Asym-itotic Expansions f o r the Desc r ip t ion o f Gas Bubble D i s s o l u t i o n and Growth," R.S. Subramanian and M.C. Weinberg ( r e p r i n t )

A- 3 "The D i s s o l u t i o n of a S t a t i o n a r y Bubble Enhanced by Chemical React ion," Michael C. Weinberg and R. S. Subramanian ( r e p r i n t )

A- 4 "Thermocapil.lary Migrat ion of a Bubble Normal t o a Plane Sur face , " M. Meyyappan, Will iam R. Wilcox, and R.S. Sub ramanian ( r e p r i n t j

A- 5 "Thermocapil lary Migrat ion of a F lu id Drople t I n s i d e a Drop I n a Space Laboratory ," N . Shankar, Robert Cole and R.S. Subramanian ( r e p r i n t )

Appendix B : Some P e r t i n e n t Proceedings Papers

B- 1 "Bubble Motion I n A Rota t ing Liquid Body," P. Annamalai, K.S. Subramanian, and R. Cole ( r e p r i n t )

B- 2 "Thennocapil lary Convection i n a Pendant Drop," K . J a y a r a j , Robert Cole, and R.S. Subramanian

B- 3 "Surface Tension Driven Flow I n Glass ' Melts and Model F l u i d s , " Thomas J . McNeil , Robert Cole and R. S. Subramanian

B-4 "Thermocapil lary Motion of Bubbles I n s i d e Drops ," N. Shankar, Robert Cole and R. S. Subramanian

iii

ORIGINAL PAGE IS OF POOR QUALrrY

I n t h i s r e p o r t , che progrebs of resea rch i n t h i s p r o j e c t dur ing t h e pe r iod January 1, 1981 t o December 31, 1981 is desc r ibed . Since Lhe r e p o r t covers a one-year pe r iod , i t r e p l a c e s t h e two semi-annual r e p o r t s t h a t normally would have been prepared t o cover thn same per iod.

The o v e r a l l o b j e c t i v e of t h i s p r o j e c t is t o s tudy f l u i d motion and bubble behavior i n a reduced g r a v i t y environment i n model f l u i d s and g l a s s mel t s when such motion is t h e r e s u l t of

( i ) i n t e r f a c i a l t e n s i o n g r a d i e n t s

( i i ) r o t a t i o n , o s c i l l a t i o n , e t c .

The r e s u l t s of t h i s r esea rch a r e expected t o be of use i n r e f i n i n g space- processed g l a s s e s , and i n improving our unders tanding of t h e p rocesses involved i r the formation of hollow g l a s s s h e l l s used i n l a s e r fus ion . C

D e t a i l s on t h e above o b j e c t i v e s and t h e a p p l i c a t i o n s of t h i s work may be found i n e a r l i e r r e p o r t s .

During t h e r e p o r t i n g p e r i o d , t h e r e were f i v e graduate s t u d e n t s a c t i v e l y a s s o c i a t e d wi th t h e p r o j e c t . Four a r e d o c t o r a l s t u d e n t s , and t h e f i f t h , Mr. P. Kondos, a t t h i s time, is an M.S. s t u d e n t . S ince s e v e r a l o f t h e d o c t o r a l s t u d e n t s (Messrs. J a y a r a j , McNeil, and Annamalai) a r e expected t o complete t h e i r t h e s e s i n 1982, ano ther s t u d e n t , M s . Radha Sen, was r e c r u i t e d i n t h e F a l l of 1981. M s . Sen a l r e a d y has an M.S. degree , and w i l l t ake h e r Ph.D. q u a l i f y i n g examination b e f o r e Summer 1982. She w i l l work i n t h e genera l a r e a of i n t e r f a c i a l t e n s i o n g r a d i e n t d r i v e n flows caused by composit ion g r a d i e n t s .

The bu lk of t h e work i n 1981 was performed on ground-based-research. Th is was due t o a l a c k of a v a i l a b i l i t y o f s u i t a b l e f l i g h t hardware. However, d i s c u s s i o n s w i t h I n t e r s o n i c s were i n i t i a t e d i n t h e F a l l o f 1981 concerning t h e p o s s i b i l i t y of b u i l d i n g a p p r o p r i a t e hardware f o r t h e reduced g r a v i t y model f l u i d experiments on t h e r m o c a p i l l a r i t y . Also, arrangements were made f o r t h e p a r t i c i p a t i o n of Clarkson personne l i n a forthcoming KC-135 f l i g h t of t h e JPL (room-temperature) 3-axis a c o u s t i c l e v i t a t o r t o g a i n exper ience w i t h t h i s equipment. This f l i g h t is scheduled t o occur i n A p r i l 1982. Our c u r r e n t p l a n i s t o conduct a p o r t i o n of t h e model f l u i d experiments on bubble migra t ion i n drops i n t h i s appara tus , beginning w i t h KC-135 f l i g h t s i n l a t e 1982, and con t inu ing on t o s h u t t l e f l i g h t s i n 1984-85.

I n 1981, d i s c u s s i o n s a l s o were he ld wi th t h e Marshal l Space F l i g h t Center . ,

concerning our p a r t i c i p a t i o n i n a n eng ineer ing test f l i g h t o f a h igh temperature a c o u s t i c l e v i t a t o r t o be b u i l t bv I n t e r s o n i c s . The MEA f l i g h t o f t h i s appara tus is t e n t a t i v e l y scheduled f o r l a t e 9982, and w e !:ave agreed t o provide 114" diameter g l a s s spheres f o r t h e purpose of tests i n t h i s hardware. I t is expected t h a t t h e re tu rned sample(s) from f l i g h t w i l l provide some in format ion on t h e behavior of a g l a s s melt under reduced g r a v i t y c o n d i t i o n s . However, due t o p o s s i b l e uncon t ro l l ed sample r o t a t i o n t h a t might occur i n t h i s experiment, t h e r e s u l t s probably w i l l be more u s e f u l i n des ign ing f u t u r e exper iments , than be of immediate s c i e n t i f i c va lue .

ORIGINAL PAGE IS OF POOR QUALITY

. . The fo l lowing papers based on resea rch supported by the MPS program were

publ ished, accepted f o r p u b l i c a t i o n , o r submit ted d u r i n g the r e p o r t i n g per iod . Copies of a l l t h e publi.shed a r t i c l e s a r c a t t a c h e d a s .Ippc*ndfx A .

Published D_uring Reporting Per iod

1. Subramanian, R.S., "The Slow Migrat ion of a Gas Bubble i n a Thermal Gradient," AIChE J l . , 27, NO. 4 , 646-654 (1981).

2 . 'subramanian, R. S. , and M. C. Weinberg, "Asymptotic Expansions f o r t h e Descr ip t ion of Gas Bubble D i s s o l u t i o n and Growth," AIChE J l . , 27, No. 5 , 739-748 (1981).

3. 'weinberg, M . C . , and R.S. Subramanian, "The D i s s o l u t i o n of a S t a t i o n a r y Bubble Enhanced by Chemical Reaction," Chem. Engng. Sc i . 36, No. 12, - 1955-1965 (1981).

* 4. Meyyappan, M . , W.R. Wilcox, and R.S. Subramanian, "Thermocapillary

Migration of a Bubble Normal t o a Plane Surface ," J. Col lo id I n t e r f a c e Science - 83, No. 1, 199-208 (1981).

5. Stlanknr. N . , K. Cole, and R. S. Subramanian, "Thermocapil lary Migrat ion of a Fluid Droplet I n s i d e a Drop i n a Space Laboratory, ' ' I n t . J . Multiphase Flow .- 7, No. 6 , 581-594 (1981).

Accepted -- f o r P u b l i c a t i o n During Report ing Per iod

1. J a y a r a j , K. , R. Cole, and R. S. Subramanian, "Combined Thermocapil lary and Buoyant Flow i n a Drop i n a Space Laboratory," J. Col lo id I n t e r f a c e Science, i n p r e s s , 1982.

2 . Jucha, R.B., D. Powers,ZJ.McNeil, R.S. Subramanian, and R. Cole, "Rubble Rise i n Glass Melts," J. Amer. Ceram. Soc., i n p r e s s , 1982.

Submitted f o r P u b l i c a t i o n During Reporting Per iod

1. Annamalai, P. , R. S. Subramanian, and R. Cole, "Bubble Migrat ion i n a Rotat ing L iqu id-F i l l ed Sphere," Phys. of F l u i d s , Submitted f o r p u b l i c a t i o n , June 1981.

2. Shankar, N., and R.S. Subramanian, "The Slow Axisymmetric Thermocapil lary Migration of an E c c e n t r i c a l l y Placed Bubble I n s i d e a Drop i n a Space Laboratory," J. F lu id Mechanics, submit ted f o r p u b l i c a t i o n , October 1981.

t Research performed w h i l e R.S. Subramanian was on s a b b a t i c a l l eave at J e t Propuls ion Laboratory.

* Related resea rch supported by t h e MPS program through a s u b c o n t r a c t from Westinghouse R 6 D Center.

The fol lowing papers were preseqted a t va r ious meetings dur ing t h e r e p o r t i n g L

per iod. Several o f the, paller:, wtsre . )r \ i 1 l be included i n t h e proceedings of t h e va r ious symposia where they were presented. These a r e marked by a dagger.

w 1. Subramanian, R. S . , "The 'I 'he~moc.lpillay Mip,ration of a Bubble i n a Large Body of Liquid," European Mechanics Colloquium 138, Kar lsruhe, Weet Germany, March 1981.

2. Shankar, N . , M. Meyyappan, R.Cole, W.R. Wilcox, and R.S. Subramanian, "Some I n t e r a c t i o n E f f e c t s i n Thermocapil lary Bubble Migration," European

,\ w . Mechanics Colloquium 138, Kar lsruhe, West Germany, March 1981 ( P o s t e r P resen ta t ion) .

3. McNeil, T. J . , R. Cole, X.R. Wilcox, and R.S. Subramanian, "An I n v e s t i g a t i o n of Surf, e Tension Driven Flows i n Glassmel ts ," American Ceramic S o c i e t y 83rd Annual Meeting, Washington, D.C., May 1981.

b

4 . t h n a m a l a i , P . , N. Shankar, R. Cole, and R.S. Subramanian, "Bubble Migration I n s i d e a Liquid Drop i n a Space Laboratory ," Symposium on Mechanics and Physics of Bubbles i n L iqu ids , i ' a l i f o r n i a I n s t i t u t e of Technology, C a l i f o r n i a , June 1981 (Proceedings t o be publ ished i n Applied S c i e n t i f i c Research, 1982) . "r

5. Subramanian, R.S., and R. Cole, "Transport Phenomena i n Space Process ing," Soc ie ty cf Engineer ing Science 18th Annual Y l e t ing , Brown Univers i ty , Rhode I s l a n d , September 1981.

6. tMcNeil, T.J. , R. Cole, W.R. Wilcox, and R.S. Subramanian, "Thermocapillary w Convection i n a C y l i n d r i c a l Zone," I n t e r n a t i o n a l Chemical Engineering ,

Congress, Montreal , Canada, October 1981.

7. t Jucha , R .B . , D. Powers, TJ. McNeil, R.S. Subramanian, and R. Cole, "Bubble Rise i n Glassmelts," I n t e r n a t i o n a l Chemical Engineering Congress, Montreal, Canada, October 1981. *

8. t J a y a r a j , K . , R. Cole, andR.S. Subramanian, "Thermocapil lary Convection i n Pendant Drops," I n t e r n a t i o n a l Chemical Engineering Congress, Montreal , Canada, October 1981 ( P o s t e r Sess ion) .

9. tMeyyappan, M., W.R. Wilcox, and R.S. Subramanian, "The Migrat ion of Gas Bubbles i n a Thermal Gradient -- I n t e r a c t i o n E f f e c t s , " I n t e r n a t i o n a l Chemical Engineering Congress, Montreal , Canada, October 1981 ( P o s t e r Sess ion) .

10. t shankar , N. , R. Cole, and R. S. Subramanian, "Thermocapil lary Migrat ion of a Gas Bubble I n s i d e a Liquid Drop i n a Space Laboratory," I n t e r n a t i o n a l

'CI, Chemical Engineering Congress, Montreal , Canada, October 1981 ( P o s t e r Sess ion) .

-

c t Publ ished, o r t o be pub l i shed , i n Conference Proceedings

11. t h n a m a l a i , P . , R.S. S ~ h r a m ~ ~ n i i i n , lnd K. Cole, "Bubble Migrat ion i n a Rota t ing , L iqu id-F i l l ed Sphere: Appl ica t ion t o t h e Formation of Hollow Glass Laser Fusion Targe t s , " I n t e r n a t i o ~ ~ a l Chemical Engineer ing Congress, Montreal, Canada, October 1981 (Pou tel- S e s s i o n ) .

12. Shankar, N . , R. Cole, and R.S. Subramanian, "Thermocapil lary Migration of a Gas Bubble E c c e n t r i c a l l y Located I n s i d e a Liquid Drop," AIChE 74th Annual Meeting, New Orleans , Louis iana, November 1981.

13. Jucha, R.B., D. Powers, T.J. McNeil, R.S. Subramanian, and R. Cole, "Bubble Rise i n Glass Melte ,'I AIChE 74th Annual Meeting, Nev Or leans , Louis iana, November 1981.

14. t shankar , N . , Y . Annamalai, R. Cole and R.S. Subramanian, "The Motion of Bubbles I n s i d e Drops i n C o n t a i n e r l e s s Process ing," I n t e r n a t i o n a l Colloquium on Drops and Bubbles, Monterey, C a l i f o r n i a , November 1981 ( P o s t e r Sess ion) .

15. tMeyyappan, M., W.R. Wilcox, and R.S. Subrantanian, " I n t e r a c t i o n E f f e c t s i n Thermocapil lary Bubble Migrat ion," I n t e r n a t i o n a l Colloquium on Drops and Bubbles, Monterey, C a l i f o r n i a , November 1981.

16. t.McNeil,~.J., R. Cole , and R.S. Subramanian, "Surface-Tepsion Driven Flow i n Glassmel ts and Model F lu ids , " M a t e r i a l s Research Soc ie ty Annual Meeting, Boston, Massachusetts , November 1981.

17. tAnnamalai, P . , R.S. Subramanian, and R. Cole, "Bubble Motion i n a Rota t ing Liquid Body," M a t e r i a l s Research Soc ie ty Annual Meeting, Boston, Massachusetts , November 1981.

18. tMeyyappsn, M. , R.S. Subramanian, W. R. Wilcox, and H. D. Smith, "Bubble Behavior i n Molten Glass i n a Temperature Gradient ," M a t e r i a l s Research Socie ty Annual Meeting, Boston, Massachusetts , November 1981.

19. t shankar , N . , R. Cole, and R.S. Subramanian, "Thermocapil lary Motion of Bubbles I n s i d e Drops," Materials Research S o c i e t y Annual Meeting, Boston, Massachusetts , November 1981.

20. +Smith, H.D. , D.M. Mattox, W.R. Wilcox, R.S. Subramanian and H. b y y a p p a n , "Experimental Observat ion of t h e Thermocapil lary Driven Motion o f Bubbles i n a Molten Glass under Zero Gravi ty Condit ions, ' ' M a t e r i a l s Research Soc ie ty Annual Meeting, Boston, Massachusetts , November 1981.

The resea rch conducted by t h e f o u r d o c t o r a l s t u d e n t s , Hessrs . P. Annamalai, K. J ayaxa j , 7 3 . McNeil, and N. Shankar, and the M.S. s t u d e n t , Mr. Kondos, on t h e i r ongoing t h e s i s p r o j e c t s d u r i n g t h e r e p o r t i n g per iod is suranrarized belaw. M s . Sen h a s been spending h e r ti= p r i n c i p a l l y i n becoming f a m i l i a r w i t h t h e p e r t i n e n t l i t e r a t u r e on h e r t h e s i s t o p i c : "Flove Driven by I n t e r f a c i a l Composition Gradients . "

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THE M I G g X E V 01' A BIJB1%LE/DROPLE1' I N A KOTATING L I Q U I D

P. Annamalai

The ob jec t ive of t h i s p ro j ec t i s t o s tudy, both experimentally and t h e o r e t i c a l l y , the motion of a bubble/droplet i n a r o t a t i n g l i q u i d body.

A t h e o r e t i c a l model of bubble migration i n a r o t a t i n g l i q u i d was con- s t ruc t ed and the equat ions solved i n the l i m i t of low values of the Taylor nun;her. Su i t ab l e experiments on the motion of bubbles i n s i l i c o n e o i l s contained i n r o t a t i n g spheres were performed t o v e r i f y the p r inc ipa l p red ic t ions of t he theory. A prel iminary comparison of t h e o r e t i c a l r r a j e c t o r i e s and asymptotic bubble l c c a t i o n s wi th those observed i n t he c-l.xperiments was made. De ta i l s may be found i n Appendix B-1 which contains a copy of t he paper by Annamalai e t a l . on t h i s sub j ec t which ..-as presented a t t h e Boston meeting of t he Mater ia l s Research Society he ld i n November 1981.

An experimental study of drop migrat ion i n a r o t a t i n g l i q u i d system yielded the s u r p r i s i n g observat ion t h a t , under c e r t a i n condi t ions , t he heavier ( w ~ t e r ) drop a c t u a l l y migrated toward the r o t a t i o n a x i s , and reached a s t a b l e pos i t i on near t he a x i s a t low r o t a t i o n r a t e s . A t h igher r a t e s , the drop was found t o leave t h i s p o s i t i o n , and migrate toward the boundary. The observat ions were found t o be reproducible , and were confirmed with o the r combinations of a heavy drop i n a l i g h t e r continuous medium. More q u a n t i t a t i v e experiments on t h i s new phenomenon a r e now underway.

THEWCAPILLARY CONVECTION I N DROPS

K. Jayara j

The ob jec t ive of t h i s research is to study thexmocapillary motion i n drops both experimentally and t h e o r e t i c a l l y .

The t u l k of t he e f f o r t during the year was spent on r e f in ing the experimental apparatus, and acqui r ing da ta . The apparatus was described i n the l a s t semi- annual repor t . I t c o n s i s t s of a thermocouple junct ion from which a pendant drop of a s u i t a b l e f l u i d is suspended. The drop is heated from above by conducting heat through the thermocouple lead wires, and i l luminated i n a meridian s ec t ion by means of a 50pm shee t of l a s e r l i g h t . Lycopodium p a r t i c l e s se rve a s t r a c e r mater ia l . Provis ions a r e a v a i l a b l e t o make video o r motion p i c t u r e records of w the drop during t h e experiment through a microscope. The da ta a r e analyzed using an X-Y i nd i ca to r o r a motionanalyzer connected t o a microprocessor.

The i n i t i a l e f f o r t s a t measuring v e l o c i t i e s were confined t o the use of a stopwatch and a c a l i b r a t e d r e t i c l e i n the microscope eyepiece. These r e s u l t s were reported i n a paper presented i n October i n Montreal a t the Second World Congress on Chemical Engineering. The paper by Jaya ra j e t a l . , iacluded i n the proceedings of t h a t meeting, i e a t tached a s Appendix B-2, and may be consulted f o r add i t i ona l d e t a i l s .

Subsequent t o the above work, motion p i c tu re records were made using a Bolex movie camera, These d a t a a r e s t i l l being analyzed. Also, video recordings of t he motion i n the drop have been made, and w i l l be analyzed i n 1982.

The t h e o r e t i c a l w r k on the motion i n a sphericcil drop due t~ the comhined ac t ion of buoyancy and thermocapi l lar i ty discussed i n the l a s t r epo r t wae sub- mit ted f o r publ ica t ion in the Journal o f c:olloLd and In t e r f ace Science. It was accepted, and is scheduled t o appear i n 1982.

E f f o r t s spent on extending the theory t o a r b i t r a r y axisynmetric shapes v i a co l loca t ion methods have not been successfu l so f a r . The p r inc ip l e source of d i f f i c u l t y appears t o be i n the use of poorly converging s e r i e s i n kgendre Polynomials i n the co l loca t ion procedure. In 1982, the d i f f i c u l t i t s w l l l e i t h e r be resolved o r a l t e r n a t i v e methods of so lu t ion such a s complete numerical i n t eg ra t ion of the f i e l d equat ions w i l l 5e pursued.

VOLATILIZATION IN GLASS MELTS

P. Kondos

The objec t ive of t h i s research i s t o s tudy experimentally the k i n e t i c s of v o l a t i l i z a t i o n from g l a s s melts.

i I n the f i r s t phase of t h i s work, a de t a i l ed search of t h e pe r t i nen t litera- tu re was made. The l i t e r a t u r e search revealed the following,

(1) The process of v o l a t i l i z a t i o n i n even a "simple" binary g l a s s is not completely understood. Detai led information on the na ture of t he spec ies evaporating from a binary melt such as sodium bora te a t var ious temperatures and compositions is not ava i l ab l e .

( 2 ) Information on equi l ibr ium p a r t i a l pressure versus temperature f o r the various spec ies i n multicomponent g l a s s melts is not genera l ly ava i l ab l e . Some da t a on pure component vapor pressures e x i s t . However, the solutions formed i n multicomponent melts a r e probably nonideal.

( 3 ) No attempt has been made i n t he experiments conducted by o the r s s o f a r t o cont,rol the f l u i d mechanical condi t ions i n the surrounding gas phase o r i n the g l a s s melt. Thus, empir ical parameters a r e introduced i n t o "models" t o account fo* buoyant convective t r anspor t i n the gas phase. Buoyar~t motion i n the a ~ l t is usua l ly ignored. Such parameters obscure t h e i n t e r p r e t a t i o n of experiments .

( 4 ) Typical experiments i n t he pas t have Involved the weighing of c ruc ib l e s containing g l a s s samples exposed t o a spec i f i ed furnace temperature f o r var ious periods. This procedure can introduce mixing i n the melt when it is d is turbed , a process ignored i n the "diffusion" models used t o i n t e r p r e t the data.

In view of the above, a conceptual experiment was designed in our labora- t o ry fur t,he study of v o l a t i l i z a t i o n wherein some of t h e above shortcomings of previous inves t iga t ions could be overcome. The essence of t h e experimental idea is t o suspend a drop of g l a s s melt i n a cont ro l led forced-convection environment ins ide a t ransparent furnace, and t o monitor both i t s s i z e and its mass a s funct ions of time. Fram t h i s da t a , important information on the kin- e t i c s of v o l a t i l i z a t i o n can be ex t r ac t ed with the use of s u i t a b l e t ranspor t models.

A l l of our e f f o r t i n 1981 in t h i s p ro j ec t w a s spent i n cons t ruc t ing a eu i t ab l e apparatus f o r the above experiment. Experimental problems sti l l t e r n i n

i n t he a r ea o i long-term s t a b i l i t y i n the mlcrobalmce w e d f o r t he measurement of the weight of t he drop a e a funct ion of time, and i n t he rneaaurement of the drop s i z e using microscope techniques.

Out plans f o r 1982 a t t i l ie time a r e f o r completing t h e i n i t i a l phase of t h e experimental etudy of v o l a t i l i e a t i o n phenomena using sodium borate a s a candidate mater ial .

TtlERMOCAPILLA&Y CONVECTION I N MODEL FLUIDS AND GLASS MELTS

The objec t ive of t h i s research is t o s tudy thermocapillary motioir i n p l a s s melts a s w e l l as In model f l u i d syetems.

The experimental s y s t e m used f o r t h e study a r e small c y l i n d r i c a l l i q u i d br idges he ld between v e r t i c a l rods. The apparatus and procedure have a l ready been de t a i l ed i n the l a s t semi-annual r epo r t .

- Considerable e f f o r t was spent during the year 1981 i n r e f i n i n g the a p p a r a t u s , f o r the g l a s s melt e tud ie s which employed a t ransparent furnace. After s eve ra l a t tempts t o e l imina te problems assoc ia ted with undesirable bubble nucleat ion i n the m e l t , the so lu t ion was found. Graphite end rods were used with a sodium borate melt , and the probl m w a s eliminated. Surface v e l o c i t i e s i n the melt were measured using diamond dust as a t r a c e r . A stopwatch and a ca l ib ra t ed r e t s c l e i n the microscope eyepiece were used f o r the ve loc i ty measurements. The Reynolds and Marangoni numbers were varied over a s wide a range a s possible . Sui tab le model f l u i d experiments a l e o were performed using Dow-Corning DC-200 s i l i c o n e o i l s .

A t h e o r e t i c a l model of the system was constructed. The governing conser- va t ion equat ions along with the asaociated boundary condit ions were solved using the method of f i n i t e d i f ferences.

Some of the r e s u l t s from the theory and the experiments were presented a t the Mater ia l s Rssearch Society meeting i n Boston held i n November. A paper prepared f o r inc lus ion i n the proceedings of t h a t meeting is at tached (Appendix B-3h and may be consul ted f o r d e t a i l s .

X doc to ra l t h e s i s based on t h i s repearch was prepared i n l a t e 1981. It w i l l be defended shor t ly .

The above research focused on the development of an apparatus f o r the study of thermocapillary flow i n a high temperature melt. Many important and in te ree- t i n g experiments on the a c t u a l flow s t i l l remain t o be performed. These include the study of t he inf luence of composition i n binary and multlcomponent melts ,

* and the study of melts exh ib i t i ng a pos i t i ve c o e f f i c i e n t of sur face tension with tenperature, Aleo, the range of Harangoni numbers can he extended by t h e use of video o r motion p i c tu re techniques f o r recording motion i n the system. It is expected t h a t in 1982 o r '83, a new graduate s tudent w i l l be r ec ru i t ed t o coutlnue t h i r e f f o r t .

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OF PO09 Q U A m

THERMOCAPlLLARY MOTION I N BUBBLES INSIDE DROPS

N. SHANKAR

The o b j e c t i v e of t h i s work is t o develop t h e o r e t i c a l models t o d e s c r i b e bubble motion i n s i d e a drop when a known temperature f i e l d is p r e s c r i b e d on t h e drop s u r f a c e .

The year 1981 was s p e n t completing t h e t h e o r e t i c a l c a l c u l a t i o n s f o r t h e axisymmetric motion of a bubble e c c e n t r i c a l l y l o c a t e d i n s i d e a drop. Computer programs were developed f o r c a l c u l a t i n g t h e r e s u l t s f o r t h e temperature and t h e s t reamfunct ion f i e l d s a s w e l l a s Lhe bubble m i g r a t i o n v e l o c i t y as a f u n c t i o n of system parameters. Graphics r o u t i n e s were developed s o t h a t s t r e a m l i n e s and isotherms could be p l o t t e d d i r e c t l y on a p l o t t e r connected t o t h e Col lege computer. A manuscript based on t h i s work was submit ted f o r and is under review a t t h i s time. Some d e t a i l s a r e g iven i n Appendix B-4 which is a copy of t h e paper p resen ted a t t h e Boston meeting of t h e M a t e r i a l s Reeearch Soc ie ty .

E f f o r t s were begun on extending t h e tneory t o account f o r t h e deformat ion of t h e shape of t h e drop. l 'h is t o p i c w i l l be pursued a c t i v e l y i n 1982.

APPENDIX A

Publications i n Journals in 1981

APPENDIX B

Some Pertinent Proceedings Papers

Copies of the publications and proceedings l i s t e d under Appendix A and Appendix B in the Table of Contents may be obtained from:

Dr. R . Shankar Subramanian Department of Chemical Engineering Clarkson College of Technology Potsdam, New York 13676