THE REMOVAL OF ONE-COMPONENT BUBBLES FROM GLASS MELTS IN A ROTATING CYLINDER

Transcription

1 Orgnal papers THE REMOVAL OF ONE-COMPONENT BUBBLES FROM GLASS MELTS IN A ROTATING CYLINDER LUBOMÍR NÌMEC, VLADISLAVA TONAROVÁ Laboraory of Inorganc Maerals, Jon Workplace of he Insue of Chemcal Technology Prague and he Insue of Inorganc Chemsry AS CR Techncká 5, Prague, Czech Republc E-mal: Lubomr.Nemec@vsch.cz Submed May, 4; acceped July 15, 26 Keywords: Glass mel, Bubble, removal, Cenrfugal force The bubbles conanng pure oxygen or carbon doxde were nvesgaed n a roang cylnder conanng glass mel. The equaon of one componen bubble wh seady concenraon graden of gas on he bubble surface was appled, akng no accoun he effec of cenrfugal force. The mpac of he cylnder roaon velocy, he degree of s fllng by he mel, cylnder radus, emperaure, bubble sze and bubble nal poson n he cylnder on he bubble removal me from he mel was calculaed wh he am o fnd heorecal advanageous condons of he bubble removal process. Boh mechansm of bubble removal, namely bubble dssoluon and bubble separaon o he cylnder cenre, were found and evaluaed. The mechansm preference depended prmarly on he bubble nal composon. The dssoluon mechansm was crucal for n glass well soluble gas as s oxygen whereas less soluble carbon doxde exhbed only he mechansm of bubble separaon. Boh mechansms were parcularly acceleraed by ncreasng he cylnder roaon velocy. The applcaon of cenrfugal fnng needs he nvesgaon of mulcomponen bubbles wh composon correspondng o bubbles under real melng condons. INTRODUCTION In he las work, he equaons descrbng he behavor of small bubbles n a glass mel under effec of boh gravaonal and cenrfugal forces were derved [1]. The ncreasng effor of glass echnologss o accelerae and economze he ndusral glass melng process, as well as he ngong producon of hgh qualy glasses, evoke an address o non radonal ways of glass fnng. The novel conceps frequenly am a avodng he refnng agens owng o her conamnaon effec n boh glass and envronmen. The replacemen of he classcal refnng agen by an ner rapdly dffusng gas [2] or he applcaon of reduced pressure [3-5] are means how o ensure bubble growh and her acceleraed removal from glass by rsng. The applcaon of an addonal force feld nfluencng bubble behavor, such as supersonc energy [6] or cenrfugal force, s a furher way leadng o he physcal acceleraon of he fnng process. The applcaon of roang spaces conanng glass mel s a promsng concep, parcularly for specal glasses produced n a low or medum scale and preferably whou a connual producon. Ths work deals wh bubble removal from a model roang cylnder parally flled wh he glass for he producon of elevson bulbs as a model glass mel. Two represenave gases were chosen as a conen of one-componen bubbles n he glass mel: oxygen represenng a well soluble gas n he mel owng o s chemcal reacon wh oxdaon-reducon componens of glass, and carbon doxde, he mos usual gas n glass melng, mosly physcally soluble n glass mels. The nfluence of dfferen process parameers on he bubble removal process was calculaed by usng approprae bubble equaons. The examned parameers were he cylnder roaon velocy, he cylnder radus, he degree of cylnder fllng by he mel, emperaure, bubble sze and bubble nal poson n he cylnder. The bubble removal me from he mel by any removal mechansm was calculaed o reveal parameer sgnfcance and process feasbly. THEORETICAL The sngle one-componen bubble behavor A bubble conanng pure gas s consdered locaed n a roang vercal cylnder wh glass mel. The glass n he cylnder s quescen (dsconnual process). The posve drecons of movemen are owards he cylnder boom and o s perphery as s apparen from fgure 1a. The shapes of mel level a hgher angle veloces are presened n fgure 1b. Under he effec of he gravaonal feld only, he bubble wll move upwards. The bubble movemen n he smulaneous cenrfugal feld adds a radal componen of bubble n drecon of he cylnder cenre. For a sngle bubble con- 216 Ceramcs Slkáy 5 (4) (26)

2 The removal of one-componen bubbles from glass mels n a roang cylnder anng only one gas, he equaon provdng he rae of bubble dssoluon or growh rae s gven by he dervave of he Gay Lussac's equaon for he bubble volume [1]: da RT dm 2ω r ρ a 2g ρ a a dt = (1) 4πMpa 27η p 27ηp 3T where a s he bubble radus, τ s me, R s he unversal gas consan, T s emperaure n K, M s he molecular mass of he -h gas, p s he oal pressure nsde he bubble, m s he mass of gas n he bubble, ω s he cylnder angle velocy, r s he radal dsance, ρ and η are glass densy and dynamc vscosy. The oal pressure nsde he cylnder s [1]: 2 2 ρω r 2σ p (2) = pex + ρgh+ + 2 a where p ex s he exernal pressure, h s he bubble deph under glass level and σ s he surface enson of he mel. The bubble movng velocy nvolvng buoyancy and he cenrfugal componen s gven by: v = 2 ρ 2 a 2 g bub ( r ) 12 / ω (3) 9η The mass ransfer erm n equaon (1) s generally gven by: dm 2 = 4π ak( mb ma) (4) where m b s he bulk concenraon of gas n he mel, m a s s concenraon on he bubble boundary and k s he mass ransfer coeffcen of gas. The value of m a accordng o Henry's law s gven by: (5) where L s he gas physcal solubly n he mel and p s s paral pressure nsde bubble (for one-componen bubble, p = p ). Accordng o [7], he mass ransfer coeffcen beween movng bubble neracng wh he lqud s gven by: ShD 13 / k (6) = where Sh = 1+ ( 1+ Pe) ( 2a ) and Sh and Pe are he Sherwood and Pecle dmensonless crera and D s he dffuson coeffcen of gas. The Sh expresses he mass ransfer beween a movng bubble and he mel, whereas Pe demonsraes he rao beween he neral and he dffuson forces on he bubble surface. The Pecle number of a bubble n he quescen mel under he nfluence of he gravaonal and cenrfugal force s hen gven by: 2avbub 4 a Pe (7) D D g r = = ρ ( + ) 12 / ω 9η m a = Lp If Pe, as well as Pe 1/3» 1,.e. he bubble moves suffcenly fas (he case of movng n he cenrfugal feld), he bubble s no oo small or mass ransfer s slow, he mass ransfer coeffcen has a form: D k = / 3 1 / ρ ( g + r ) 16 / ω (8) 13 / η and he resulng equaon s obaned afer he subsuon of equaons (4, 5) and (8) no (1): da RTD ρ =. 2/ 3 1/ ( g +ω r ) 16 / ( mb m 13 / a )+ Mη p ω r ρ a 27η p 2g ρ a a dt ηp 3T (9) The frs, second and hrd erm on he rgh sde of equaon (9) express he mpac of mass ransfer, he gravaonal force and he cenrfugal force, respecvely, whle he las erm represens he nfluence of hermal expanson of gas. The level shape n he roang cylnder A hgher roaon veloces, he level has he shape shown n fgure 1b. The values of abscssa h u, h d, r u and r d for hs case are gven by followng equaons [1]: r u gho 2 V = + ro 2 ω πh 1a) 1b) (1) Fgure 1. a) The scheme of he cylnder wh posve radal and axal drecons; b) The shape of glass level n he roang cylnder a hgher roaon veloces. o 12 / Ceramcs Slkáy 5 (4) (26) 217

3 Nìmec L., Tonarová V. r d h u = ω r = h d ( ro ru ) 2g ω u 2gh where V s he mel volume n he cylnder. RESULTS OF CALCULATIONSN ω ω 2 2 o ru = h 2g o 12 / (11) (12) (13) The oxygen solubly was calculaed from he chemcal equlbrum of oxygen wh anmony ons n he mel. The followng values were appled: ( C) m O2b (kg/m 3 ) The me developmens of he bubble radus and he bubble radal poson were followed. The quany τ max correspondng o he maxmum me needed o remove a bubble eher by dssoluon (denoed by asersks n pcures) or by separaon o he curved glass level (denoed by crcles) were used as a creron for he fnng effcency. Exen of calculaons and expermenal daa The followng calculaons were realzed a consan emperaure, only he nfluence of gas dffuson and he cenrfugal force on he bubble movemen and growh or dssoluon was consdered. Consequenly, he hrd and fourh members on he rgh sde of equaon (9) were omed. The mporan facors of he bubble removal were defned and arranged no a decreasng sequence correspondng o how easly her values can be adjused n he process: ω > V/V > R > > c > f (a ), r (r) (14) where f (a ) - he nal dsrbuon of bubble szes n he cylnder, r (r) - radal sarng bubble posons, c - he nal bubble composon, - emperaure ( C), R - he cylnder radus, V/V - fllng by glass, ω - angle velocy of he cylnder. The bubble sze dsrbuon and nal bubble posons n he mel are naural consequences of he melng process and are only hardly adjusable. The exen of calculaons nvolved he followng quany nervals: a (a ; m; a = ), r (r =.2;.225 and.25 m), ω (ω = 25, 5, 1, 2 s -1 ), ( = 13, 14, 15 C), V/V (V/V = 1;.75;.5), R (R =.25,.375,.5 m), h (h =.5 m), c (O 2 as a fas dffusng and well soluble gas, CO 2 as a slowly dffusng gas). TV panel glass and boh gases were characerzed by he followng values: ρ = T (kg/m 3 ), η = ρ exp [ /(T )] (Pa.s.) D O2 = exp( /t), D CO2 = exp( /T) (m 2 /s), m CO2 b =.98 (kg/m 3 ), L O2 = exp( /t), L CO2 = exp( /t) (kg/m 3 bar). Resuls In all he calculaons, he me developmens of he bubble radus and he bubble radal poson were followed, and he resulng value of τ max was asceraned by comparson of eher dssoluon mes or separaon mes of bubbles of dfferen nal rad under gven condons. The mos nal posons of bubbles n he cylnder were locaed on he cylnder perphery, he mpac of he nal bubble radal poson was examned by a seres of calculaons. As he sandard calculaon, he followng condons were chosen: ω = 5 s -1, V/V =.5, R = r =.25 m, = C, a m, m. The sandard gas was oxygen. The ypcal courses of he bubble wanderng n he form of radal dsance versus me are shown n fgure 2. Only bubbles of consdered mnmum and maxmum m, 13 C m, 14 C m, 15 C m, 15 C m, 14 C m, 13 C τ (s) Fgure 2. The ypcal courses of movemen of oxygen bubbles from he cylnder manel o s cenre under he effec of he cenrfugal force. The dependence beween he bubble radal dsance and me. Two grey bands correspond o he level exen for V/V =.5 and.75. R =.25 m. The nal bubble radus s a = m; m. 218 Ceramcs Slkáy 5 (4) (26)

4 The removal of one-componen bubbles from glass mels n a roang cylnder bubble szes are ploed n he fgure. The wo grey horzonal bands n he fgure correspond o he radal nerval of glass levels a V/V =.5 and V/V =.75 (see fgure 1b). The bubble s separaed from he mel when reachng s proper poson n he grey band, dependen on s nal deph under glass level. The asersks n he fgure denoe he bubble dssoluon. The slowng down of he bubble movemen owards he cylnder cenre s obvous durng laer sages. Ths s a consequence of a decreasng effec of he cenrfugal force. Therefore paral fllng of he cylnder by he mel appears o be only precondon for an effecve bubble separaon. Fgure 3 provdes he pcure of he same case n he form of bubble rad versus me. The almos lnear dssoluon of small oxygen bubbles s obvous whereas bgger bubbles grow due o a pressure decrease nsde hem. CO 2 bubbles exhb a parally dfferen behavor. The CO 2 gas has only a lmed solubly n he mel and he rae of s dffuson s smulaneously resrced by low values of s dffuson coeffcen n he mel. Tha s why all bubbles, ncludng small bubbles a = m, should be separaed by wanderng o he glass level, neverheless he separaon of small bubbles s sgnfcanly slow as s shown n he correspondng fgure 4, provdng he bubble radal dsance as a funcon of me. The very slow ncrease of rad of small bubbles a = m s presened n fgure 5. The nal radal poson of he bubble n he cylnder plays a role n he bubble removal as boh pressure nsde a bubble and he gas concenraon graden on s m, 15 C m, 14 C m, 13 C m, 15 C m, 14 C m, 13 C m, 15 C m, 13 C m, 14 C τ (s) Fgure 3. The ypcal dependences beween he bubble radus and he me for bubbles wanderng accordng o he fgure 2. The nal bubble radus s a = m; m m, 15 C m, 13 C m, 14 C τ (s) Fgure 5. The ypcal dependences beween rad of CO 2 bubbles and he me correspondng o bubbles n fgure m, 15 C m, 14 C m, 13 C m, 14 C m, 15 C m, 13 C τ (s) Fgure 4. The courses of he separaon of CO 2 bubbles n he roang cylnder. The dependence beween he bubble radal dsance and me. V/V =.5, R =.25 m ω = 25 ω = 5 ω = 1 ω = Fgure 6. The dependence beween he dssoluon mes of small oxygen bubbles and her nal radal posons n he roang glass layer. Oxygen bubbles a 13 C, R =.25 m, V/V =.5. Ceramcs Slkáy 5 (4) (26) 219

5 Nìmec L., Tonarová V. surface are affeced. Fgures 6 and 7 show, ha he effec of he nal bubble poson s dependen on he mechansm of bubble removal. The small dssolvng bubbles need hgh nernal pressure. Consequenly, bubbles close o he cylnder perphery dssolve slghly faser han ohers n he cylnder wh R =.25 m (he ypcal case s shown n fgure 6). On he conrary, he bgger bubbles removed by he separaon mechansm are separaed faser f her nal dsance from he cylnder cenre s small. Ths s obvous from he fgure 7. Only he mechansm of bubble separaon s relevan for bubbles conanng CO 2 ; he characer of he dependence beween he bubble separaon me and s nal radal dsance s depced n fgure 7. Temperaure always plays an mporan role n bubble behavor, parcularly under condons of chemcal solubly of gas n glass mel. The maxmum bubble removal mes were obaned from calculaons of he bubble behavor a dfferen emperaures and he resuls for he case of sandard cylnder (R =.25 m) and for nal bubble posons a he cylnder perphery are ploed for boh gases n fgure 8. The bubble removal mes of CO 2 always decrease wh emperaure ncreasng due o decreasng glass vscosy. The removal mes of oxygen, however, show maxma or mnma a 14 C and a lower roaon veloces. The maxmum removal mes were obaned for bubbles exhbng he combned removal mechansm: he bubble of he med ω = 25, CO 2 ω = 25 ω = 5 ω = 1 ω = Fgure 7. The dependence beween he bubble separaon me (regardless of he nal bubble sze) o he glass level and s nal radal poson n he roang cylnder. Oxygen bubbles a 15 C, V/V =.5, R =.25 m ω = 1 s -1 ω = 2 s -1 ω = 5 s Fgure 9. The dependence beween he bubble removal me (regardless of he nal bubble radus) and emperaure for dfferen rad of he cylnder. Oxygen bubbles, V/V =.5, r =.25 m ω = 5, CO 2 CO 2 O 2 ω = 25, O ω = 5, O 2 ω = 1 ω = Fgure 8. The dependence beween he bubble removal me (regardless of he nal bubble radus) and emperaure. Oxygen and CO 2 bubbles, V/V =.5, R =.25 m, r =.25 m. The dssoluon mes are denoed by asersks, he separaon mes by crcles. 2 ω = 5 s -1 ω = 1 s -1 ω = 2 s Fgure 1. The dependence beween he maxmum bubble removal me (regardless of emperaure and he nal bubble radus) and radus of he cylnder. Oxygen bubbles, V/V = Ceramcs Slkáy 5 (4) (26)

6 The removal of one-componen bubbles from glass mels n a roang cylnder um radus progressed farly o he cylnder cenre durng earler sages and consequenly only slowly dssolved n he mel, he dssoluon beng he removal mechansm. If, on he conrary, he separaon mechansm domnaed and bubble parally dssolved durng earler sages, he subsequen separaon mechansm s slow and he separaon me s hgh as s demonsraed by he curve for and R =.25 m n fgures 8 and 9. Fgure 9 summarzes he emperaure mpac on τ max for cylnders havng R =.25,.375 and.5 m. Boh fgures 8 and 9 also show ha emperaure almos sops o be an mporan facor a hgher roaon veloces, characerzed by low values of bubble removal mes. Fgure 9 also demonsraes he expeced benefcal nfluence of a greaer cylnder radus on he rae of he bubble removal by boh mechansms. The dependence of τ max on he cylnder radus a all emperaures and nal bubble rad, and a gven value of ω, s gven by fgure 1. The fgure reveals ha a greaer cylnder radus s benefcal a lower roaon veloces, bu he endency s fla for rapd roaons. The mpac of he degree of he cylnder fllng by mel s obvous from fgure 11. The lower fllng ses up a hnner glass layer on he cylnder manle and decreases he bubble separaon mes ω = 5 s -1 4 O 2 CO 2 5 ω = 1 s -1 ω = 2 s Fgure 11. The dependence beween he maxmum bubble removal me (regardless of emperaure and he nal bubble radus) and he degree of cylnder fllng by mel. Oxygen bubbles, R =.25 m, r =.25 m Fgure 13. The dependence beween he maxmum bubble removal me (regardless of emperaure and nal bubble radus) and he cylnder roaon velocy. Oxygen and CO 2 bubbles, V/V =.5, R =.25 m, r =.25 m. 1 8 R =.25 m m m 6 R =.5 m m m R =.375 m Fgure 12. The dependence beween he maxmum bubble removal me (regardless of emperaure and nal bubble radus) and he cylnder roaon velocy. Oxygen bubbles, V/V = m Fgure 14. The dssoluon and growh raes of oxygen bubbles n he roang cylnder wh glass mel as a funcon of he cylnder roaon velocy. Temperaure 13 C, V/V =.5, R =.25 m, r =.25 m. Ceramcs Slkáy 5 (4) (26) 221

7 Nìmec L., Tonarová V. The mos sgnfcan facor of he process appeared o be he cylnder roaon velocy affecng boh mporan phenomena durng he bubble removal: he rae of bubble dssolvng or growh and bubble movemen. Fgure 12 demonsraes hs fac for oxygen bubbles and for hree cylnder rad. The dssoluon mechansm of smaller bubbles appeared o be he crcal one n mos cases. The ncrease of he roaon velocy from ω = = 25 s -1 o ω = 5 s -1 was generally decsve for a subsanal decrease of maxmum bubble removal mes. The dfferen preference of he removal mechansm for oxygen and CO 2 gas n he sandard cylnder R =.25 m s obvous from fgure 13. The only feasble mechansm for bubbles conanng CO 2 was he separaon o he m m m m m Fgure 15. The dssoluon and growh raes of oxygen bubbles n he roang cylnder wh glass mel as a funcon of he cylnder roaon velocy. Temperaure 15 C, V/V =.5, R =.25 m, r =.25 m ω = 2 s -1 ω = 1 s ω = 5 s Fgure 16. The dependence beween he maxmum bubble removal me and he nal bubble radus. Oxygen bubble, emperaure 13 C, V/V =.5, R =.25 m, r =.25 m. glass level, hs mechansm beng slow a lower roaon veloces. Tha s why only he roaon velocy ω = = 1 s -1 decreased he maxmum bubble separaon mes of CO 2 bubbles o he value sandard for oxygen bubbles. DISCUSSION The prmve mechansm of he parcle separaon from a lqud n roang cylnders s her wanderng o he perphery or he cenre of he cylnder due o densy dfferences beween parcles and lqud, bubbles swmmng o he cylnder cenre. In addon, he gaseous parcles may ncrease her szes due o he pressure drop from he cylnder perphery o s cenre, and hey may dssolve or grow f he gas nsde a bubble has a remarkable solubly n he mel, e.g. due o a chemcal reacon. The bubbles n glass mel exhb all he menoned effecs accordng o bubble and glass properes, and wh respec o he parameers of cenrfugng. As a resul of ha, bubbles may dsappear from he mel eher by he complee dssoluon or by he separaon o he curved glass level n he cylnder. The dssoluon mechansm s obvously sgnfcan for small bubbles under oherwse equal condons (see fgure 3). The wanderng of small bubbles n he radal drecon s slow (fgure 4), he pressure nsde a bubble supporng bubble dssoluon s herefore hgh for a long me. As oxygen chemcal solubly ncreases wh decreasng emperaure and he dffuson coeffcen grows, he emperaure dependence of bubble dssoluon me s less sgnfcan. The average dssoluon and growh raes of oxygen bubbles a 13 C and 15 C are presened n fgures 14 and 15 as a funcon of he cylnder roaon velocy. Small bubbles (a = m) exhb a slgh ncrease of her absolue values wh growng ω. The dssoluon s parly characersc also for bubbles wh a = m a lower emperaures. The bubbles of greaer szes grow under dencal condons, even f he gas dffused ou of bubbles. The rapd nal radal bubble wanderng, resuls n a pressure drop nsde bubbles, whch s responsble for a consderable bubble growh. Ths fac s clear as well from fgures 14 and 15 for bubble szes greaer han abou m. The pressure drop n bubbles, compensaed by he growh of bubble sze, sgnfcanly ncreases he bubble radal velocy and he bubble quckly reaches he curved glass boundary. The pressure drop decreases owards he cylnder cenre and he effec of he cenrfugal force s herefore more sgnfcan for cylnders havng a low fllng by glass. The problem occurs wh medum bubble szes, here abou a = m, exhbng boh mechansms n a comparable nensy. The dssoluon mechansm s consderably slowed down f a bubble wandered o he glass boundary before (he 222 Ceramcs Slkáy 5 (4) (26)

8 The removal of one-componen bubbles from glass mels n a roang cylnder C 13 C 15 C Fgure 17. The nal radus of he bubble, characerzed by he maxmum removal me, as a funcon of he cylnder roaon velocy. Oxygen bubble, V/V =.5, R =.25 m, r =.25 m. case of bubble a = m, a 13 C). The separaon mechansm s slowed down by bubble`s prevous paral dssolvng n he mel. In order o fnd he mos dsadvanageous condons for he bubble removal, he values of bubble removal mes were ploed as a funcon of he nal bubble radus. The example s provded by fgure 16 for he case of R = r =.25 m, V/V =.5 and emperaure 13 C. The bubble dssoluon mes (asersks) n hs fgure grow lnearly wh he nal bubble radus whereas he bubble separaon mes (crcles) progressvely ncrease wh decreasng nal bubble radus. If boh dependences are exrapolaed o her nersecon, he maxmum bubble removal me s found, correspondng o he case when boh mechansms are of equal value. As s apparen from fgure 16, he value of he bubble radus, correspondng o he maxmal bubble removal me, a max, decreases wh growng cylnder roaon velocy, whch was also obvous fac a hgher emperaures. The dependences beween values of a max and he cylnder roaonal velocy are presened by fgure 17 showng ha he value of a max a hgh roaon veloces s almos ndependen of emperaure. Noce ha he value of τ max a 15 C and s absen n fgure 17 as only he mechansm of he bubble separaon s presen under hese condons. Despe he fac ha wo equally realzed mechansms lead o maxmal bubble removal mes, he bubble removal mes are always defne and he accepable bubble removal condons for bubbles conanng soluble gas may always be found. The bubble conanng gas almos nsoluble n he mel exhbs only he separaon mechansm. The mechansm s fas, only slghly dependen on emperaure, and s sgnfcanly acceleraed by he ncreasng cylnder roaon velocy. However, he problem of he separaon of very small bubbles arses as he bubble separaon me ends o nfny for he zero bubble sze. The dependence beween he separaon me of he CO 2 bubble and s nal sze ploed n a logarhmcal form n fgure 18 ndcaes ha he problem of he bubble separaon may occur for bubbles havng he sze less han abou.1 mm log τ (s) ω = 5 s ω = 2 s -1 ω = 1 s Fgure 18. The dependence beween he maxmum bubble separaon me (regardless of emperaure) and he nal bubble radus. CO 2 bubbles, emperaure 15 C, V/V =.5, R =.25 m, r =.25 m Fgure 19. The orgnal bubble radus (a pressure 1 bar) as a funcon of he cylnder roaon velocy, correspondng o he value of he maxmum bubble separaon me 1 s (regardless of emperaure), CO 2 bubbles, V/V =.5, R =.25 m, r =.25 m. Ceramcs Slkáy 5 (4) (26) 223

9 Nìmec L., Tonarová V. CONCLUSION The man physco-chemcal problem bound wh he applcaon of he cenrfugal force for he bubble removal s he separaon of very small bubbles conanng slowly dffusng and n mel slghly soluble gas. Only he mechansm of he bubble separaon o he cylnder cenre s relevan because he bubble dssoluon s a oo slow process here. The problem wh very small bubbles s gven by he fac ha, τ max for a for a oally nsoluble gas. Ths fac should be aken no accoun as well he fac ha he orgnal bubble sze decreased due o a pressure ncrease jus afer he bubble enered he roang cylnder. Fgure 19 shows he dependence beween he orgnal bubble sze (a pressure 1 bar) and he cylnder roaon velocy for he bubble removal me τ max = 1 s and CO 2 bubbles. The bubbles wh he orgnal sze smaller han abou.15 mm already have relavely hgh separaon mes even a he roaon velocy of 2 s -1. Bubbles n he real melng process always conan a mxure of gases boh soluble and almos nsoluble n he mel. The problem of a proper nal bubble composon hen becomes sgnfcan and s soluon calls for an examnaon of he behavor of mul componen bubbles n he cenrfugal feld. Acknowledgemen Ths work was suppored by he research program MSM , Preparaon and research of funconal maerals and maeral echnologes usng mcroand nanoscopc mehods. References 1. Nìmec L., Tonarová V.: Ceramcs-Slkáy 49, 162 (25). 2. Beerkens R.: Proc. 7 h Inernaonal Conference on Advances n Vson and Processng of Glass III, Orcheser NY, July 27-31, Ross C.P.: Am.Ceram.Soc.Bull. 83, 18 (24). 4. Kunkle G. E., Welon W. M., Schwennger R. L.: US Pa. 4,738,938 (1988). 5. Kloužek J., Nìmec L., Ullrch J.: Glasechn. Ber. Glass Sc. Technol. 73, 329 (2). 6. US Pa. 4,316, Clf R., Grace J. R., Weber M. E.: Bubbles, drops and parcles, Academc Press, New York, London ODSTRAÒOVÁNÍ JEDNOSLOŽKOVÝCH BUBLIN ZE SKELNÉ TAVENINY V ROTUJÍCÍM VÁLCI LUBOMÍR NÌMEC, VLADISLAVA TONAROVÁ Laboraoø anorganckých maerálù, spoleèné pracovšì Vysoké školy chemcko-echnologcké v Praze a Úsavu anorgancké cheme AVÈR Techncká 5, Praha V éo prác jsme zkoumal chování bubln obsahujících èsý kyslík nebo oxd uhlèý nacházejících se v roujícím válc se skelnou avennou. Pro výpoèy chování byla použa rovnce popsující chování bublny za podmínek usáleného koncenraèního gradenu plynu na povrchu bublny a za pùsobení odsøedvé síly. Vyšeøoval jsme vlv úhlové rychlos roace, supnì naplnìní válce avennou, polomìru válce, eploy, poèáeèní velkos bubln a jejch poèáeèní polohy ve válc na dobu poøebou k odsranìní bublny z avenny s cílem naléz opmální podmínky pro eno proces. Pø odsraòování se uplanl jak mechansmus úplného rozpušìní nìkerých bubln, ak mechansmus jejch odsøedìní ke søedu válce. Pùsobící mechansmus byl závslý pøedevším na poèáeèním složení bubln. Rozpoušìcí mechansmus byl vedle mechansmu odsøedìní významný pro bublny obsahující ve skelné avennì dobøe rozpusný plyn, kerým byl kyslík, zaímco málo rozpusný oxd uhlèý byl odsraòován pouze odsøedìním. Oba mechansmy urychlovala zvyšující se rychlos roace. Aplkace odsøedvé síly pø výrobì skla vyžaduje zkouma rovnìž chování vícesložkových bubln, jejchž složení odpovídá reálným podmínkám. 224 Ceramcs Slkáy 5 (4) (26)