Microbubble generation in a co-flow device operated in a new regime

Depósi o de in es igación de la Uni e sidad de Se illa h ps://idus.us.es/ "This documen is he Accep ed Manusc ip e sion o a Published Wo k ha appea ed in inal o m in La bon a Chip copy igh © Royal Socie y Chemis y a e pee e iew and echnical edi ing by he publishe . To access he inal edi ed and published wo k see 10.1039/c0lc00731e. ARTICLE TYPE www. sc.o g/xxxxxx |XXXXXXXX Mic obubble gene a ion in a co- low de ice ope a ed in a new egime Elena Cas o-He n´ andez,aWim an Hoe e,bDe le Lohse,band Jos´ e M. Go dillo∗a Recei ed X h XXXXXXXXXX 20XX, Accep ed X h XXXXXXXXX 20XX Fi s published on he web X h XXXXXXXXXX 200X DOI: 10.1039/b000000x A new egime o ope a ion o PDMS-based low- ocusing mic o luidic de ices is p esen ed. We show ha monodispe se mi- c obubbles wi h diame e s below one- en h o he channel wid h (he e w=50 µm) can be p oduced in low iscosi y liquids hanks o a s ong p essu e g adien in he en ance egion o he channel. In his new egime bubbles a e gene a ed a he ip o a long and s able gas ligamen whose diame e , which can be a ied by uning app op ia ely he gas and liquid low a es, is subs an ially smalle han he channel wid h. Th ough his p ocedu e he olume o he bubbles o med a he ip o he gas ligamen can be a ied by mo e han wo o de s o magni ude. The expe imen al esul s o he bubble diame e dbas unc ion o he con ol pa ame e s a e accoun ed o by a scaling heo y, which p edic s db/w∝(µg/µℓ)1/12 (Qg/Qℓ)5/12, whe e µgand µℓindica e, espec i ely, he gas and liquid iscosi ies and Qgand Qℓa e he gas and liquid low a es. As a pa icula ly im- po an applica ion o ou esul s we p oduce monodispe se bubbles wi h he app op ia e diame e o he apeu ical applica ions (db≃5µm) and a p oduc ion a e exceeding 105Hz. In oduc ion Mic obubble o ma ion is an a ea o g owing in e es due o i s coun less applica ions in ood p ocessing,1ma e ial science,2 pha macy and medicine.3In he las decades, mic obubbles ha e become he mos e ec i e ype o con as agen a ail- able o medical ul asound imaging4–6 o as ca ie s o a - ge ed d ug deli e y.7,8 In o de o ensu e ha mic obubbles can sa ely low h ough he smalles capilla ies, he diame e o he mic obubbles injec ed in o he pa ien ’s blood s eam needs o be be ween 1 and 10 µm; he p e e ed diame e is be ween 2 µm and 5 µm. La ge bubbles may p o oke edema and smalle ones possess a poo e lec i i y. Mic obubbles wi h sizes in he co ec ange o he apeu- ical pu poses can be easily p oduced by ei he sonica ion o by mechanical agi a ion.9–12 The gene a ion o bubbles wi h a size below 1µm can be achie ed h ough he injec ion o a gas using po ous memb anes, which equi es an ex emely high wo king p essu e ypically o he o de o 10 MPa.13 Howe e , all hese p ocedu es gene a e a polydispe se emulsion o bub- bles in he liquid, limi ing he po en ial use o mic obubbles in medicine. Indeed, i is o cu en in e es o he apeu ical applica ions o design a simple p ocedu e o he mass p o- duc ion o mic obubbles wi h con ollable diame e s anging om 2 o 5 µm and wi h a low polydispe si y index, ypically a´ A ea de Mec´ anica de Fluidos, Depa amen o de Ingenie ´ ıa Ae oespacial y Mec´ anica de Fluidos. Uni e sidad de Se illa. A da. de los Descub imien os s/n, 41092, Se illa, Spain. Fax: +34 954486041; Tel: +34 954481185; E-mail: jgo [email p o ec ed] bPhysics o Fluids, Facul y o Science and Technology, Uni e si y o Twen e, P.O. Box 217, 7500 AE Enschede, The Ne he lands. PDI=s/ b<5×10−2, wi h b he a e aged bubble adius and s he s anda d de ia ion.3When he alues o he PDI a e su - icien ly low (say, below 5%), he bubbles a e conside ed as monodispe se. Pe ec monodispe si y PDI=0 can ob iously ne e be achie able. No e ha he monodispe si y is essen- ial when mic obubbles a e used as ul asound con as agen s o imp o e he quali y o an echog aphical image. In he case ha mic obubbles a e used as d ug ca ie s, e y low alues o he PDI index a e also demanded in o de o p ecisely con ol he amoun o he d ug deli e ed in o he pa ien . In his manusc ip we will desc ibe and cha ac e ize in de- ail a no el p ocess o he p oduc ion o he ype o mic obub- bles needed o he apeu ical applica ions. Mo e speci ically, we p opose a no el me hod o he p oduc ion o ≃5µm bub- bles wi h a PDI o 5% and be e and a a p oduc ion a e ha exceeds 105Hz. P obably, he simples way o p oducing monodispe se bub- bles is o injec a small gas low a e h ough an unde wa e nozzle.14,15 Un o una ely, he bubbles eleased om a nee- dle wi h a diame e o 5 mic ons in o a s agnan ese oi o wa e is ∼50 µm,much la ge han he injec ion needle di- ame e . Clea ly, his me hod is no easible o he p oduc ion o monodispe se bubbles wi h po en ial he apeu ical applica- ions. Howe e , i is known om he ea ly wo ks o B agg and Nie16 –who modeled he dynamic s uc u e o c ys als h ough a we oam composed o monodispe se bubbles17– ha bubbles wi h sizes compa able o he needle diame e can be gene a ed when a small amoun o gas is injec ed wi hin a liquid c oss low16 o a liquid co low.18 Since hen, i has been shown ha mic on-sized bubbles can be p oduced i a su i- This jou nal is c The Royal Socie y o Chemis y [yea ] Lab on a Chip, 2010, [ ol], 1–8 |1 L a) Qg Qഢ/2 QഢQഢ/2 Gas supply channel Gas ligamen De achmen line Exi channel w 50 µm 25 µm b) glass liquid PDMS dg ai w c) h Fig. 1 (a) High speed pho og aph showing he o ma ion o mic obubbles using ou mic o luidic low- ocusing geome y, w=50 µm, L/w=30. The ou e liquid low o ces he inne gas low o o m a iny gas ligamen ha de aches om he channel wall and b eaks up in o mic obubbles. The size o he mic obubbles db=7.2µm is much smalle han he channel wid h. The gas and liquid p essu es a e pg=1555 mba and pℓ=1597 mba , espec i ely, and he liquid low a e is Uℓ=7.67 m s−1. (b) Mic obubbles immedia ely a e exi ing he channel. (c) Schema ic ep esen a ion o a c oss-sec ion o he mic o luidic channel downs eam he de achmen line. The gaseous ligamen dewe s he PDMS channel wall. cien ly small ube o channel h ough which a gas is injec ed, is placed in a s ong liquid co low14,19–25 o c oss low.26–33 Usually, he liquid is o ced o low hanks o an imposed p essu e g adien . Fa ook e al. and Pancholi e al.34–36 im- plemen ed he coaxial elec osp ay con igu a ion desc ibed by Losce ales e al.37 o gene a e 5 µm bubbles. In his pa icula case, he liquid co low is induced by he elec ical angen ial s esses. Howe e , his p oduc ion echnique does no esul in he o ma ion o mic obubbles wi h a su icien ly na ow size dis ibu ion. An al e na i e way o he p oduc ion o i ually monodis- pe se mic obubbles a high and con olled p oduc ion a es is o use a p ocedu e called low- ocusing.38–41 He e, a s ong co low o liquid is c ea ed when bo h he liquid and gas s eams a e o ced o low h ough a small cons ic ion. Plac- ing a cylind ical gas injec ion ube in on o an o i ice o smalle diame e , Ga˜ n´ an and Go dillo42 p oduced bubbles wi h db∼O(10)µm, which a e ypically smalle han he o i- ice diame e , by simply con olling he low a e a io. In- deed, he diame e dbo he bubbles ob ained in his way is gi en, app oxima ely, by db∝(Qg/Qℓ)β, wi h β≃0.38 ≃2/5, a) b) c) dgdb 50µm d) Fig. 2 The size o he mic obubbles p oduced can be accu a ely a ied by adap ing he gas and liquid low a es by con olling hei d i ing p essu es. In o de o Qg/Qℓ≪1, he gas p essu e in he supplying essel, pg, is chosen o be e y simila o ha o he liquid, pl. The ope a ing condi ions co esponding o each o he ou images a e: a) pℓ=1800 mba , pg=1757 mba , U=8.67 m s−1,db=4.33 µm, dg=2.60 µm; b) pℓ=1800 mba , pg=1763 mba , U=8.67 m s−1,db=5.73 µm, dg=2.92 µm; c) pℓ=1410 mba , pg=1383 mba , U=6.83 m s−1, Qg=0.0044 ml min−1,db=10.05 µm, dg=3.90 µm; d) pℓ=1410 mba , pg=1463 mba , U=6.83 m s−1, Qg=0.0134 ml min−1,db=15.58 µm, dg=5.84 µm. F om his igu e no e ha , as expec ed, o a ixed alue o Qℓ(o pℓ), db inc eases as pginc eases. Qg/Qℓ<1 and wi h Qgand Qℓindica ing he gas and liquid low a es, espec i ely.42,43 Howe e , due o he ac ha he alignmen o he injec ion ube wi h he exi o i ice is no an easy ask, he pa alleliza- ion o his ype o axisymme ic de ices o he mass p oduc- ion o mic obubbles is no s aigh o wa d. La e on, Anna e al.,44 Go dillo e al.45 and Ga s ecki e al.46 ci cum en ed his limi a ion o axisymme ic low ocusing bubble make s by implemen ing he same geome y in plana de ices. Plana mic o luidic de ices buil using so li hog aphy echniques and inco po a ing he low ocusing geome y, a e nowadays used by many esea ch g oups o p oduce monodispe se bub- bles wi h he apeu ical pu poses.47–50 We s ess ha , hough he low ocusing geome y in he plana e sion46 is e y simila o he axisymme ic one,42 he physical mechanism leading o bubble o ma ion is sub- 2|Lab on a Chip, 2010, [ ol], 1–8 This jou nal is c The Royal Socie y o Chemis y [yea ] s an ially di e en in bo h ypes o de ices. Fo he axisym- me ic case,42 liquid eloci ies a e such ha he dimension- less g oups We and Re sa is y We ≫1 and Re ≫1. No e ha he Webe numbe We quan i ies he ela i e impo ance o su ace ension s esses wi h espec o liquid ine ia and is de ined as We =ρU2w/σ, wi h ρ,Uand σindica ing he liq- uid densi y, he liquid mean eloci y and su ace ension co- e icien espec i ely and w he ans e sal dimension o he exi channel. On he o he hand, he dimensionless g oup ha compa es iscous s esses wi h espec o liquid ine ia is he Reynolds numbe , de ined as Re =ρUw/µℓ, wi h µℓ he liquid iscosi y. Due o he ac ha We ≫1 and Re ≫1, bubble o ma ion in he expe imen s epo ed by Ga˜ n´ an and Go dillo42 is con olled by liquid ine ia. Howe e , he yp- ical liquid low a es injec ed in he plana e sion o low ocusing a e so small (10−2 o 1 µLs−1), ha We ≪1 and Re .1 and, in addi ion, he capilla y numbe s (Ca =µℓU/σ) a e ypically such ha (Ca <10−2).46,51,52 The e o e, liquid ine ia is negligible when compa ed o iscous shea s esses and iscous shea is no s ong enough o o e come capilla y p essu e.31 Unde hese condi ions, bubbles block almos he whole c oss sec ion o he exi channel, o cing he ca ie luid o low h ough hin we ing ilms s addling a he walls o he de ice. This ac esul s in a signi ican inc ease o he liquid p essu e ups eam o he eme ging bubble, leading o he ’squeezing’ o he gas h ead.31 Excep in he inal s age o he collapse, in which gas ine ia accele a es he bubble pinch- o p ocess,53,54 he mechanism o bubble o ma ion is mainly con olled by he gas and liquid low a es and by he de ice geome y. A di ec consequence o he geome ically con olled mech- anism o bubble o ma ion is ha he polydispe si y index o he bubbles gene a ed h ough he ’squeezing’ mechanism is below 5%; mo eo e , Ga s ecki e al. ound ha he bubble size can be exp essed as a unc ion o he a io o gas and liquid low a es as db∝(Qg/Qℓ)1/3. No e ha he exponen 1/3, which di e s om he exponen ≃2/5 ha cha ac e - ize bubble size in he axisymme ic low ocusing de ices, al- eady e lec s he di e ences in he way bubbles a e o med in bo h ypes o geome ies. Bu he e is an e en mo e impo an di e ence be ween he wo ypes o implemen a ions: since bubbles block he exi channel in he plana e sion o low ocusing, he diame e s o he bubbles o med in his way a e necessa ily la ge han he wid h o he exi channel. Con a - ily, in he axisymme ic e sion o low ocusing de ices, db is smalle han he exi o i ice diame e as poin ed ou abo e. This ac has an impo an consequence when bubbles a e p oduced using he plana low ocusing geome y, namely, bubbles wi h sizes o he o de o 5 µm ob iously equi e he use o iny mic ochannels o wid hs w≈5µm (see e.g. He - ia achchi e al.47). We implemen ed he low ocusing geom- e y inco po a ing exi channels o wid hs o 5 µm and expe i- enced ha hese iny channels end o clog e y easily due o he accumula ion o impu i ies. Thus, we decided o ind a di - e en way o he p oduc ion o 5 mic on bubbles ha di e s om he me hods al eady exis ing in he li e a u e.46–51,53 He e we desc ibe a new me hod o he con olled p oduc- ion o ∼5µm bubbles wi h a polydispe si y index below 5 % a high p oduc ion a es (>105bubbles/s) by means o a pla- na low ocusing de ice. The essen ial geome ical di e ence o ou de ice wi h espec o all p e ious implemen a ions is ha he leng h o he exi channel Lis much la ge han i s wid h, namely, L/w≫1, as depic ed in igu e 1. This, o- ge he wi h he ac ha he imposed liquid and gas low a es a e such ha Re &102,We ≫1 and Qg/Qℓ≪1, enables he p oduc ion o bubbles in wa e wi h sizes one o de o mag- ni ude smalle han he channel wid h. In his way, we a e able o p oduce, in a single s ep, bubbles wi h sizes wi hin he ange needed o he apeu ical applica ions a oiding clogging p oblems. The inal esul , which we p esen in de ail in he “Resul s” sec ion and de i e in he “Discussion” sec ion, is ha bubble size can be p edic ed based on he gas o liquid low a e a io and he luid p ope ies as db/w≃2.75(µg/µℓ)1/12(Qg/Qℓ)5/12 .(1) Equa ion (1) is applicable i he gas and liquid low a es sa - is y he condi ions Qg/Qℓ≪1 and Qℓ Q0 >3(Qg Q0)−1/7 ,(2) whe e he e e ence low a e Q0is gi en by Q0=(σw3 ρ)1/2 .(3) No e ha he exponen 5/12 in equa ion (1), which di e s om he exponen s 1/3 and 2/5 o calcula e bubble diame- e as a unc ion o he a io Qg/Ql epo ed in p e ious pub- lica ions42,46, e eals ha ou me hod is di e en om hose al eady published. The di e ences can be isually app ecia ed in igu e 2: in ou de ice, bubbles a e o med a e he o ma- ion o a long gas je , whose diame e is much smalle han he channel wid h, and bubbles b eakup up om i s ip. The gas je , which has a diame e o only a ew mic ons, is o med a he en ance o he exi channel, whe e he liquid p essu e g a- dien eaches i s maximum alue. To ou knowledge, his is he i s ime ha he exis ence o such iny and s able gas je s wi hin a mic ochannel is desc ibed. No e, howe e , ha Anna e al44 epo expe imen al e idence o he o ma ion o e y hin liquid h eads, simila o hose app ecia ed in igu e 2, bu in he case o he ocused luid is a liquid ins ead o a gas. Mo eo e , his is he i s ime ha bubbles wi h a size o one- en h he channel wid h a e p oduced in a low iscosi y liquid This jou nal is c The Royal Socie y o Chemis y [yea ] Lab on a Chip, 2010, [ ol], 1–8 |3 such as wa e . Since a long gas je is c ea ed be o e bubbles a e emi ed om i s ip, bubbles a e no o med in he way desc ibed in Re .42. Clea ly, since bubbles do no block he exi channel, hey a e no p oduced in he ’squeezing’ egime desc ibed by Ga s ecki e al.31,46,51 ei he . Le us poin ou ha he ad an age o mic obubble o ma ion in he way p e- sen ed in his pape as compa ed o he squeezing egime is ha bubbles wi h sizes in he ange o in e es o medical ap- plica ions (db.5µm) a equencies ha exceed 105Hz a e o med om a squa e mic ochannel o 50 ×50 µm2c oss sec- ional a ea. This one o de o magni ude educ ion in bubble size wi h espec o channel wid h, a oids he clogging o he exi channel and eno mously dec eases he p essu es a which bo h he gas and he liquid need o be injec ed in o he mi- c o luidic de ice. Ou p ocedu e also allows o easily a y he bubble olume o e mo e han wo o de s o magni ude by simply a ying he gas and liquid low a es. The pape is o ganized as ollows: in sec ion ’Ma e ials and me hods’, we desc ibe in de ail he expe imen al p ocedu e ollowed o gene a e mic on-sized bubbles. In sec ion ’Re- sul s’ we epo he bubble o ma ion equencies as well as hei associa ed PDI as a unc ion o bubble diame e . In ad- di ion, we indica e he anges o bo h he gas and liquid low a es needed o c ea e bubbles o less han 10 mic ons. Fo hose eade s in e es ed in echnical de ails, equa ions (1) and condi ions (2)-(3) a e deduced in sec ion ’Discussion’. The i- nal sec ion o he pape is dedica ed o p esen he conclusions o ou s udy. Ma e ials and me hods The bubble gene a o s we e p oduced by so li hog aphy echniques. A mold was c ea ed om a nega i e pho osen- si i e ma e ial (SU-8 GM 1060, Ge s el ec SARL) and spin- coa ed on a silicon oxide subs a e, o imp in a e iculable polyme PDMS (Polydime hylsiloxane), Sylga d 184, Dow Co ning) which was i e e sibly bounded o a glass co e pla e in a plasma cleane . We placed he mic obubble-gene a ing de ices in an o en a 65◦du ing one hou and hey we e used only a e 24 hou s o ensu e he hyd ophobici y o he PDMS. No e ha , con a ily o mos mic o luidic applica ions, we im- pose he hyd ophobici y o he PDMS52 since, in ou case, he gas ligamen should emain a ached o he PDMS su - ace o s abili y pu poses. The heigh o he mic obubble make is uni o m and equal o h=50 µm and he wid h and leng h o he exi channel a e, espec i ely, w=50 µm and L=1500 µm (see Fig. 1). No e ha he main geome ical di - e ence be ween ou bubble gene a o and hose used in p e i- ous s udies46,47,51,53 is ha , in o de o bubbles o be o med a he en ance egion o he exi channel, ou de ices sa is y he condi ion L/w≫1. To a oid luc ua ions in he gas low a e, ai was injec ed h ough a ube wi h 0.5 m in leng h and 50 µm o inne diame e . The ai p essu e, pg, was con olled h ough a p essu e egula o (Bosch Rex o h) and was mea- su ed using a digi al manome e (Digi on 2000P). The con in- uous phase was dis illed wa e wi h a 2%(w/ )o Tween 80 (Sigma Ald ich) added. The addi ion o he su ac an lowe ed he wa e -ai in e acial ension coe icien o σ≃40 mN/m and he con ac angles wi h he PDMS and glass subs a es we e, espec i ely, θPDMS =89◦and θglass =39.5◦. Since he liquid was supplied om a p essu ized essel ins ead o om a sy inge pump, he liquid injec ion p essu e, pℓ, was con olled and measu ed in he same way as he gas. The liquid low a e Qℓwas de e mined by measu ing he olume o liquid col- lec ed a he exi o he de ice du ing se e al minu es. The se up was placed unde an in e ed mic oscope (3000B Leica) which was connec ed o ei he a high-speed came a (Phan- om V 7.3, wi h a esolu ion o 80 ×16 pixels and a ield o iew o 163 ×33 µm2when ope a ed a an acquisi ion a e o 2×105 ps) o o an In ensi ied Re iga Fas came a ( esolu ion o 1280 ×800 pixels, wi h a ield o iew o 415 ×260 µm2). We checked he pe ec ep oducibili y o he expe imen s. To ake da a, expe imen s we e epea ed wice o each couple o alues pℓ,pg: Fi s , he bubbling equency ωwas de e mined using he high-speed came a. Second, in an independen ex- pe imen o he same pa ame e s he bubble diame e dbwas measu ed om he high- esolu ion images aken wi h he in- ensi ied came a. Knowing ωand db, he olume ic gas low a e was de e mined as Qg=πd3 bω/6. We checked ha he alues o Qgcalcula ed in his way we e p ac ically iden ical – albei mo e accu a e – o hose ob ained assuming Poiseuille low along he gas injec ion pipe. Resul s Figu e 1 shows a global iew o he mic ochannel en ance e- gion, which is whe e he mic obubbles a e o med. The igu e e eals ha – hanks o ou choice Qg/Qℓ<0.03 – he gas ilamen con ac s om he wid h o he gas supply channel (400 µm) o a s eady ligamen whose diame e is subs an ially smalle han w. Due o he ac ha he heigh (h) o he de- ice is equal o he wid h o he exi channel (h=w≫db), he gas h ead sepa a es om he lowe glass su ace a he egion indica ed as de achmen line in Fig. 1. Indeed, since he PDMS subs a e is less hyd ophilic han he glass one (θPDMS ≃90◦and θglass =39.5◦), he na ow gas ligamen , o diame e dg≪w, is a ached o he uppe PDMS su ace, as ske ched in Fig. 1c. Once he s eady gas ligamen is o med, i b eaks in o uni o mly sized bubbles wi h diame e s db∼dg, as depic ed in Fig. 2. In igu es 3a-b we plo , as a unc ion o db, he bubbling equencies ex ac ed om he analysis o he high speed ideos and hei co esponding alues o he PDI calcula ed om he image analysis o he high esolu ion pic- u es. Clea ly, igu es 3a-b e eal ha ou p ocedu e enables 4|Lab on a Chip, 2010, [ ol], 1–8 This jou nal is c The Royal Socie y o Chemis y [yea ] a) b) 2.5 2 1.5 1.0 0.5 0 5 10 15 20 25 db (µm) b (×105 Hz) 5 10 15 db (µm) 20 PDI (%) 7.5 5 2.5 0 10 12.5 15 Fig. 3 (a) Bubble o ma ion equencies as a unc ion o bubble diame e . No e ha all bubbles wi h diame e s below 10 µm a e p oduced a equencies ha exceed 105Hz. (b) PDI index, in %, as a unc ion o bubble diame e . No e ha o many expe imen al condi ions bubbles wi h diame e s db≃5µm can be p oduced wi h alues o he PDI index below 5%. The eason o which he (appa en ) PDI index is la ge o some expe imen s is a ibu able o he ac ha some images a e ou o he ocus plane and a e a bi blu ed. he p oduc ion o bubbles wi h diame e s ≃5µm and e y low polydispe si y index a equencies ha exceed 105Hz. We will now indica e he ange o alues o Qℓand Qg o which bubbles wi h sizes subs an ially smalle han he chan- nel wid h, a e p oduced. No e i s ha he mean liquid eloc- i y along he exi channel, U=Qℓ/(w2), needs o be abo e a ce ain h eshold. Indeed, he liquid p essu e dec eases by an amoun o ∆pℓ≃ρU2 om he de achmen line o he inle o he exi channel. Since he liquid p essu e d op is much la ge han he gas p essu e a ia ion in he same egion, namely, ∆pg∼µgQg/w3, he no mal s ess condi ion a he gas-liquid in e ace, when e alua ed a he channel inle can be exp essed as ρU2≃2σ/dg, implying Wej=ρU2dg/σ>Wemin ≃2.5. I dgis exp essed as a unc ion o he a io Qg/Qℓby means o equa ion (5) – deduced in he beginning o he nex sec ion – i is s aigh o wa d o show ha he condi ion Wej>2.5 is equi alen o he one gi en by equa ion (2), which exp esses ha he liquid low a e has o be abo e a ce ain h eshold 0.03−1 Qg/Qo 3 Qg/Qo−1/7 12.5 10 7.5 5 2.5 0 10−3 100 Qഢ / Qo Qg / Qo 10−2 10−1 Fig. 4 Values o he liquid and gas low a es conside ed in his s udy. Liquid eloci ies we e a ied be ween 6 m s−1and 8.5 m s−1, whe eas he gas low a e a ied be ween 4×10−4ml min−1and 4×10−2ml min−1. Red diamonds indica e he ope a ing condi ions o which db<10 µm whe eas black do s indica e db>10 µm. No e ha he liquid and gas low a es conside ed he e sa is y he condi ion Qg/Qℓ≪1 as well as he condi ion Qℓ/Q0>3(Qg/Qℓ)−1/7gi en in equa ion (2). This la e condi ion is deduced om he ac ha , in o de o he gas ligamen o be o med, he Webe numbe based on he gas ligamen diame e namely, Wej=ρU2dg/σ(see igu e 2 o a de ini ion o dg), needs o be abo e a ce ain cons an o o de uni y. ha depends on he gas low a e. Mo eo e , in o de o gen- e a e bubbles wi h sizes subs an ially smalle han he channel wid h, we also choose o impose he condi ion Qg/Qℓ≤0.03 i.e, he liquid low a e has o be subs an ially la ge han he gas one. Clea ly, as depic ed in igu e 4, he di e en expe imen s conside ed in his s udy sa is y he condi ions Qg/Qℓ≪1 and ha gi en in equa ion (2). The da a poin s ep esen ed wi h ed diamonds indica e hose expe imen al condi ions o which bubbles wi h diame e s below 10 µm a e p oduced, which a e o pa icula in e es o hei use as ul- asound con as agen s. Discussion o he esul s Scaling o he gas ligamen diame e No e i s ha , o he ange o liquid eloci ies in es iga ed he e, Re =Udb/νℓ∼O(102)wi h νℓ≃10−6m2s−1 he kine- ma ic iscosi y o wa e . This es ima e indica es ha he low in he exi channel is lamina . Mo eo e , o he ange o This jou nal is c The Royal Socie y o Chemis y [yea ] Lab on a Chip, 2010, [ ol], 1–8 |5 Reynolds numbe s conside ed he e, he en ance leng h is such ha Le≃0.1Qℓ/νℓ≃1.5L. The e o e, since he gas ligamen b eaks a a dis ance o ∼h≪Le om he duc inle (see Fig. 2), bubbles a e p oduced wi hin he en ance egion o he mic ochannel. In his en ance egion, he liquid eloci y p o ile is app oxima ely uni o m excep a he hin bounda y laye s o ypical wid h δ≪wnea he walls.55 Mo eo e , since he gas Reynolds numbe is such ha Reg=Qg/(νgdb)∼O(1), being νg he kinema ic iscosi y o ai , he low a e along he gas ligamen can be calcula ed as Qg=−Kd4 g µg dpg dx,(4) whe e µgis he gas iscosi y, Kis a cons an and dpg/dxin- dica es he p essu e g adien along he gas je . Due o he ac ha he c oss-sec ion o he ligamen ha dly a ies down- s eam (c . Fig. 2), −dpg/dxapp oxima ely coincides wi h he liquid p essu e g adien e alua ed a he channel inle , −dpℓ/dx=CµℓU/w2, wi h µℓ he liquid iscosi y and Cis a cons an ha depends on he geome y o he channel and on he wid h δo he liquid bounda y laye s a he channel walls. No e ha he smalle δ, he la ge Cand he e o e he liquid p essu e g adien is maximal a he duc en ance.55 Fo ins ance, in he pa icula case o a ci cula channel wi h a ully de eloped Poiseuille low, o which δ≃w, he p essu e g adien is gi en by −d pg/d x =32µℓU/w2. Consequen ly, since δ≪w, he cons an Csa is ies C≫32.55 Now, as ex- p essed by equa ion (4), dgdec eases o a ixed alue o Qg when −d pg/d x =−d pℓ/d x =CµℓU/w2inc eases. We con- clude ha , hanks o he la ge alues o C– i.e., hanks o he ac ha bubbles a e p oduced a he duc en ance – dgcan be educed down o only a ew mic ons, as depic ed in igu e 2. Wi h −d pg/d x =CµℓU/w2equa ion (4) yields he ollowing exp ession o dg: dg w∝(µg µℓ)1/4 λ1/4,(5) whe e λ=Qg/Qℓ. Fig. 5 shows ha he bes i o he expe - imen al da a ollows e y closely he p edic ion dg∝ λ1/4o equa ion 5, alida ing ou physical easoning. Bubble size We now mus only ind he size o he bubbles as a unc ion o dg,U, and Qg. Fi s , no e om Fig. 2 ha he gas ligamen b eaks only sligh ly downs eam he channel inle . A his lo- ca ion, he liquid p essu e g adien is smalle han CµℓU/w2 and hus, acco ding o equa ion (4), dgmus inc ease in o - de o keep Qgcons an . Indeed, his is seen in Fig. 2. The inc ease in he je diame e igge s he bubble o ma ion p o- cess and also induces a ia ions in he gas p essu e g adien o λ db/W 0.05 0.1 0.2 0.5 0.2 0.1 0.05 λ dg/W a) b) db/W = 1.97λ5/12 dg/W = 0.3568λ0.2582 10-4 10-3 0.01 0.1 10-4 10-3 0.01 0.1 Fig. 5 (a) Op ically measu ed (minimal) wid h dgo he gas ligamen as unc ion o he gas low a io λ. In spi e o he la ge e o ba s associa ed o he ac ha dgis o he o de o only a ew mic ons, he bes i o he expe imen al da a (s aigh line) closely ollows he p edic ion ∝ λ1/4gi en by equa ion 4. (b) Op ically measu ed mic obubble diame e dbas unc ion o he gas low a io, oge he wi h he scaling law db/w∝ λ5/12 ollowing om he p esen ed scaling heo y. He e he e o ba s a e smalle as he bubbles a e sphe ical and la ge han he minimal wid h o he gas ligamen . 6|Lab on a Chip, 2010, [ ol], 1–8 This jou nal is c The Royal Socie y o Chemis y [yea ] he o de o ∆(dpg/dx)∼σ/(dgw).∗Thus, since C≫32,55 he ela i e a ia ion o he gas low a e is gi en by ∆Qg Qg =∆(dpg/dx) dpg/dx∼1 C σ µℓU w dg ≪1.(6) The condi ion exp essed by equa ion (6) means ha bubbles a e o med unde cons an low a e condi ions21 and, conse- quen ly, he bubbling equency is gi en by ω ∝ U/dg.14,21,42 The e o e, he bubble diame e can be easily calcula ed om he mass balance as πd3 b 6∝Qg dg U→db w∝(µg µℓ)1/12 λ5/12.(7) Figu e 5b shows ha once he p opo ionali y cons an is ixed o 2.75, equa ion (7) p edic s he size o he bubbles o med wi h a maximum ela i e e o o ±10%. This maximum el- a i e e o co esponds o he minimum alue o λ. We a - ibu e his small disc epancy be ween expe imen s and heo y o he ac ha , o he smalles alues o dg, he gas ligamen is embedded wi hin he liquid bounda y laye , esul ing in o a smalle local liquid eloci y and hus an unde es ima ion o λ. Conclusions and Ou look To conclude, we succeeded o p oduce monodispe se mi- c obubbles in a con ollable and ep oducible way wi h mi- c ochannels wi h dimensions o ens o mic ons, a oiding clogging p oblems, and easily being able o adjus he mi- c obubble size by a ying he liquid and gas low a es. We ha e p o ided he ope a ing condi ions in e ms o he gas and liquid low a es o which mic obubbles wi h db<10 µm and, hus, in he size ange equi ed o medical applica ions, can be p oduced wi h e y low alues o he PDI index a equen- cies ha exceed 105Hz. F om he poin o iew o applica- ions, ou me hod is able o p oduce ∼1010 i ually monodis- pe se mic obubbles wi h db≃5µm wi h a o al ene gy con- sump ion o only ∼200 J. Mo eo e , we could heo e ically accoun o his new egime o ope a ion o he co low de ice: The cen al issues a e an ex emely low gas low a e (as compa ed o he liquid low a e) and a s ong p essu e g adien in he en ance e- gion o he channel whe e he mic obubbles o m. The heo y allows o de i e he co ec scaling laws o he mic obubble size as unc ion o he con ol pa ame e s. The nex s ep will be o s abilize he o med bubbles by phospholipids o su ac an s o p e en ha he bubbles dis- sol e o coalesce in he pool whe e hey a e apped. I one succeeds, he new de ice allows o an al e na i e way o ∗In his es ima e i has been aken in o accoun ha he leng h o he gas liga- men is ≃w(c . Fig. 2) p oduce ul asound con as agen s, wi h p esumably a much sha pe dis ibu ion o bubble sizes, i.e., monodispe se bub- bles. Fo comme cial applica ions one ob iously has o go beyond PDMS de ices (e.g., silicon), o gua an ee s able long ime beha io . Ano he issue is he mass p oduc ion o eal applica ions, bu he ac ha ou de ices inco po a e he low ocusing egion in a plana geome y, acili a es he mul iplex- a ion o hese ypes o de ices.56 Anyway, ypically, he num- be o bubbles injec ed in o a pa ien ’s blood s eam is ∼1010 bubbles. Since his is he amoun o bubbles gene a ed by jus one de ice du ing one day, one hund ed o hese de ices wo k- ing in pa allel would c ea e 100 doses a day wi h a powe con- sump ion o only ∼1W. Acknowledgmen s We would like o hank Lingling Shui, Hao Gu, and Da id Fe nandez Ri as o echnical assis ance in he ab ica ion o he mic o luidic de ices. We kindly acknowledge Michel Ve sluis and Benjamin Dolle o discussions. The UTwen e pa o he p esen wo k was inancially suppo ed by he Mi- c oNed echnology p og am o he Du ch Minis y o Eco- nomic A ai s h ough i s agency Sen e No em unde g an Bsik-03029.5. 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