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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
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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. E.d.C. and J.M.G. hank he inancial sup-
po by bo h he Spanish Minis y o Educa ion unde p ojec
DPI2008-06624-C03-01 and he Jun a de Andaluc´
ıa unde
p ojec P08-TEP-03997.
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