Tellus (1989), 418, 469473 Cotributios of film d jet drops to mrie erosols produed t the se surfe By JIN WU, AirSe Itertio Lbortory, College of Mrie Studies, Uiversity of Delwre, Lewes, Delwre 19958, USA (Musript reeived 17 November 1987; i fil form 5 My 1988) ABSTRACT Bubble popultios t the se surfe were dedued from oei mesuremets; drop produtios through the burstig of rtifiilly geerted bubbles were lso observed. Tkig these results together, otributios of film d jet drops to mrie erosols uder vrious wid veloities re estimted; they pper to osist of mily jet drops. 1. Itrodutio Air is etried ito the ersurfe oe by brekig wves. Subsequetly, ir bubbles beuse of their buoyy re retured to the se surfe d burst; those produed through frgmettio of the film p re film drops, d those, through the brekup of wter jet formed by the ollpse of the bubble vity, re jet drops (Kietzler et l., 1954; Blhrd, 1963; Dy, 1964). These drops re ssoited meteorologilly with the formtio of louds (Woodok, 195), oeogrphilly with evportio from the se (Wu, 1974), evirometlly with the erihmet of hevy metls d bteri (Due d Hoffm, 1976; Blhrd, 1978) d prtilly with dmge to ship turbies d light iterferee of guide systems (Ruski et l., 1981; Shher et l., 1981). Beuse vst umber of them be geerted by rtifiilly produed bubbles, film drops were ojetured to be the mjor otributor to mrie erosols (Ciprio d Blhrd, 1981). As poited out by Blhrd (1983), however, this lerly depeds o the size distributio of oei bubbles. Combiig reet omprehesive studies o erosols produed by ir bubbles burstig t the still wter surfe (Resh et l., 1986) d o size d oetrtio of bubbles i the ersurfe oe (Wu, 1988), we hve estimted reltive otributios of film d jet drops to the produtio of mrie erosols uder vrious wid veloities.. Summry d lysis of previous results.1. Size d oetrtio of bubbles t the se surfe Combiig reported omplemetry mesuremets of bubbles i the ersurfe oe (Kolovyev, 1976; Johso d Cooke 1979), geerl desriptio o oetrtios d sizes of bubbles t vrious depths uder wide rge of wid veloities ws proposed (Wu, 1988). From the ltter, the followig is bstrted..1.1. Size distributio. Size spetr of bubbles mesured by Kolovyev (1976) d Johso d Cooke (1979) were show to follow powerlw distributio f(d) D4, (1) where f(d) is the frequey of ourree of bubbles hvig dimeter D. The bove is pplible to bubbles s smll s 1 pm i dimeter, where the size distributio is peked..1.. Vertil distributio. The vertil distributio of bubble popultios ws first suggested (Wu, 1981) to follow expoetil expressio Nz)/No = exp(z/z,), ()
47 I. wu where N(z) is the bubble popultio t depth, No the popultio t the se surfe, d zb legth hrterizig the vertil etrimet of bubbles. The hrteristi legth zb ws suggested to follow zb =.4, zb=o.4+.1(u]7), Ulo < 7 m si, UIo>7m s1, (3) i whih zb is expressed i m, d Ulo i m sl is the wid veloity t 1 m bove the me se surfe..1.3. Wid depedey. Bubble popultios t the se surfe were dedued (Wu, 1981) from the dt of Kolovyev (1976) d Johso d Cooke (1979) over rrow rge of wid veloities; powerlw type vritio ws proposed by Wu (1981) to represet their dt. Subsequetly, vertil distributios of the ousti stterig ross setio of bubbles mesured by Thorpe (198) over wide rge of wid veloities were used to determie the surfe vlue (Wu, 1986). Cosiderig tht the bubble oetrtio d the ousti ross setio hve similr vritio with wid veloity, the followig ws suggested, No = 57 U::. (4) where No hs the dimesio of m3 d Ulo of gi m si..1.4. A geerl desriptio. Futiol vritios disussed bove were the ombied to obti geerl desriptio of bubble popultios s N(z, D) = 57 u:dexp(z/zb)f(d), f(d) D4, (5) i whih zb be obtied from q. (3)... Drop produtios through bubble burstig..1. Film drops. Usig hologrphi tehique, Resh et l. (1986) observed the burstig proess of rtifiilly produed sigle bubble t the still wter surfe. They obtied from both fresh wter d sewter the distributio i spe of film drops immeditely fter the rupture of the iterfil film p. Histogrms of the umber of film drops i terms of the drop dimeter were reported for bubbles of four dimeters, D = 4, 6, 8 d 1 mm. The umber of film drops obtied by Resh et l. from se wter is replotted o logrithmi sles, isted of loglier sles s i the origi l, i Fig. l versus the dimeter of their pret bubbles. A systemti vritio ow ppers to emerge i this type of presettio; the lie fitted to the dt be pproximted by power lw whee f, is the umber of film drops produed by bubble hvig the dimeter D (mm); the subsript is tthed to idite tht these re the results obtied with rtifiil bubbles. From histogrms reported by Resh et l., we lso obtied the verge drop dimeter (df) for eh size of bubble, see Fig. lb. The film drops re see to hve overll verge dimeter of 95 pm, but irese with the dimeter of their pret bubble. The rtio betwee the filmdrop d bubble dimeter ws lso lulted d is preseted i Fig. lb; it flls i the rge of 1 1.8% d dereses s the size of bubble ireses.... Jet drops. Muh of our kowledge of jet drops ws provided by Kietzler et l. (1954), while ll the results were iely reviewed d summrized by Blhrd (1963, 1983). The dimeter of jet drops d, ws foud to rge betwee.1.15 times tht of their pret bubble, d the umber produed by sigle bubble ever exeeded 1, d deresed s the bubble dimeter iresed, s: J = 7 exp(d/3), (7) where J is the umber of jet drops produed by bubble hvig the dimeter D (mm); eq. (7) is lso illustrted i Fig. l. 3. Reltive ompositios of film d jet drops The bubble popultio t the se surfe be obtied from eq. (5) for z = s: No(D) = 57 U:b5D4, (8) where gi No(D) is expressed i m3, Ulo i m sl, d D i mm. The umber of film d jet drops produed the be foud from fno(d) d,,n( D), respetively. As for the reltive ompositios of film d jet drops, we estimte them by simply ombiig eqs. (I), (6) d (7) to obti,,,.65 Dl,8s (9) Jo 7 exp( D/3) D4,
I CONTRIBUTIONS OF FILM AND JT DROPS TO MARIN AROSOLS 47 1 g 3 L 1 5 B ;r 11 r 5 z 5 1 o ' I, D 15 1 i 9. I; 6 W 1 m 4 (b) 8.5 3 5 df d,/d 5 1 15 x. g? D L W g 15 ; P 3 m. 1. LL p Bubble Dimeter, D (mm) Fig. 1. Numbers d dimeters of film drops produed by bubbles of vrious sizes. The results were dedued from tht dt obtied by Resh et l. (1986). where the subsript is tthed to idite tht the size distributio of oei bubbles hs bee iorported. The results re illustrted i Fig., whih re pplible to ll wid veloities by multiplyig the umber i the digrm with 57 Ufd s show i eq. (8), to obti the bubble popultio. As show i Figs. l,, dividig dimeter of bubbles is estblished t.15 mm; below this dimeter, more jet drops re tully produed by bubbles, while more film drops re produed bove this dimeter. Note tht this dividig dimeter is ot ffeted by the size distributio of oei bubbles; the ltter oly hge the slope of urves show i Fig.. As for the totl reltive umbers of film d jet drops produed, we itegrte eq. (9) d ompre two itegrls; suh itegrtios were performed from lower limits of vrious bubble dimeters (,) to upper limit of 1 mm. Reltive otributios of film d jet drops to the produtio of mrie erosols obtied with differet lower itegrtio limits re preseted i Tble 1. It is lerly illustrted i Tble 1 tht mrie erosols produed t the se surfe osist mily of jet drops. Although more film drops re produed by lrge bubbles, D >.15 mm, there re just too my smll bubbles whih produe my more jet drops. As disussed erlier, the size distributio, o whih the preset estimte is bsed, exteds oly to bubbles s smll s 1 pm i dimeter, orrespodig to the smllest D, i Tble I. Oly the vlues ssoited with D, = 1 pm show i Tble 1 should be outed, with the others beig listed s referees. The lk of estblished size distributio for smll bubbles (D < 1 pm) does ot ffet the olusio of the preset results; s disussed erlier, the produtio of jet drops outumbered tht of film drops from smll bubbles with D<.15 mm. Note tht due to optil limittios, droplets
J. WU I I Tble 1. Reltive ompositios offilm d jet drops obtied from the itegrtio of eq. (9) from D, to D=lOmm Lower itegrtio Reltive ompositios of drops (%) limit, D, (mm) film drops jet drops.1. 99.8..8 99..3. 97.8.4 4.3 95.7.5 7. 9.8 11 5 1 5 Bubble Dimeter. D (mm) Fig. Numbers of film d jet drops produed by oei bubbles. The umbers, orrespodig to those show i eq. (9), re rbitrry. ply the most importt role i irse exhges. This view ws subsequetly hlleged by Ciprio d Blhrd (1981) o the bsis of their mesured bubble spetr produed by wter jet, d ssumed reltioship betwee film drops d pret bubbles. Suh estimte is gretly upgrded here by usig the size distributio of oei bubbles d the experimetlly determied umber of film drops produed by bubbles. Although muh still eeds to be lered bout other relevt ftors used i this kid of estimte, suh s the bubble surfe lifetime d the bubble flux spetrum, the olusio tht iitilly produed mrie erosols osist mily of jet drops is likely to be true, s the domie of jet drops is just too overwhelmig. smller th 8 pm i dimeter were ot mesured by Resh et l. (1986); the dividig dimeter my therefore shift somewht to lower vlue with more refied mesuremets. 4. Coludig remrks Beuse of their lrger sizes, it ws suggested by Blhrd d Woodok (1957) tht jet drops 5. Akowledgmets The uthor is very grteful for the sposorship of his reserh provided by the Fluid Dymis Progrm (Cotrt N1483K316) d the Oe/Atmospheri/Polr viromets Progrm (Cotrt N1487K557). Offie of Nvl Reserh. RFRNCS Blhrd, D. C. 1963. The eletrifitio of the tmosphere by prtiles from bubbles i the se. Prog. Oeogr. I, 711. Blhrd, D. C. 1978. Jet drop erihmet of bteri, virus, d dissolved orgi mteril. Pure d Appl. Geophys. 116, 338. Blhrd, D. C. 1983. The produtio, distributio d bteril erihmet of the seslt erosol. I AirSe xhge of Gses d Prtiles (eds. P. S. Liss d W. G. N. Sli). Dordreht: D. Reidel, 47454. Blhrd, D. C. d Woodok, A. H. 1957. Bubble formtio d modifitio i the se d its meteorologil sigifie. Tellus 9, 145 158. Ciprio, R. J. d Blhrd, D. C. 1981. Bubble d erosol spetr produed by lbortory brekig wve. J. Geophys. Res. 86, 88589. Tellus 41B (19891, 4
CONTRIBUTIONS OF FILM AND JT DROPS TO MARIN AROSOLS 413 Dy, J. A. 1964. Produtio of droplets d slt uleii by the burstig of ir bubble films. Qurt. J. Roy. Meteorol. So. 9, 778. Due, R. A. d Hoffm,. J. 1976. Chemil frtiotio t the irlse iterfe. A. Rev. rth Plet. Si. 4, 1878. Johso, 9. D. d Cooke, R. C. 1979. Bubble popultios d spetr i ostl wters: photogrphi pproh. J. Geophys. Res. 84, 37613766. Kietzler, C. F., Aros, A. B., Blhrd, D. C. d Woodok, A. H. 1954. Ivestigtio of the projetio of droplets by bubbles burstig t wter surfe. Tellus 6, 17. Kolovyev, P. A. 1976. Ivestigtio of the oetrtio d sttistil size distributio of widprodued bubbles i the ersurfe oe lyer. Oeology (gl. Trsl.) IS, 659461. Resh, F. J., Drrozes, S. J. d Afeti, G. M. 1986. Mrie liquid erosol produtio from burstig of ir bubbles. J. Geophys. Res. 91, 131919. Ruski, R.., Lepple, F. K. d Jek, K. K. 1981. Slt erosol survey t gs turbie ilet bord USS Sprue. Memo. Rep. 4419, Nvl Reserh Lbortory, Wshigto, D.C. Shher, G.., Dvidso, K. L., Firll, C. W. d Spiel, D.. 1981. Clultioofoptil extitio from erosol spetrl dt. Appl. Optis, 395 13957. Thorpe, S. A. 198. O the louds of bubbles formed by brekig widwves i deep wter, d their role i irse gs trsfer. Phil. Trs. Roy. So. Ld. A34, 1551. Woodok, A. H. 195. Atmospheri slt prtiles d ridrops. J. Meteorol. 9, 1. Wu, J. 1974. vportio due to spry. J. Geophys. Res. 79, 417419. Wu, J. 1981. Bubble popultios d spetr i ersurfe oe: Summry d review of field mesuremets. J. Geophys. Res. 86, 457463. Wu, J. 1986. Whiteps, bubbles d spry. I: Oei whiteps d their role i irse exhge proesses (eds.. C. Moh d G. MNioill). Dordreht: D. Reidel Pub. Co., 11314. Wu, J. 1988. Bubbles i the ersurfe oe geerl desriptio. J. Geophys. Res. 93, 58759. Tellus 419 (1989), 4