IOP PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING
J. Mic omech. Mic oeng. 20 (2010) 075035 (10pp) doi:10.1088/0960-1317/20/7/075035
Mic ome e glass nozzles o low ocusing
J M Mon ane o1,AMGa
˜
n´
an-Cal o2,AJAce o
1and E J Vega1
1Depa men o Mechanical, Ene ge ic and Ma e ial Enginee ing, Uni e si y o Ex emadu a,
A da. de El as s/n, E-06006 Badajoz, Spain
2Depa men o Ae ospace Enginee ing and Fluid Mechanics, Uni e si y o Se ille,
Camino de los Descub imien os s/n, E-41092 Se illa, Spain
E-mail: [email p o ec ed]
Recei ed 11 Feb ua y 2010, in inal o m 9 Ap il 2010
Published 17 June 2010
Online a s acks.iop.o g/JMM/20/075035
Abs ac
We discuss he use o lame-shaped glass mic o-nozzles o ul a- ine liquid a omiza ion by
low ocusing (DePon e e al 2008 J. Phys. D: Appl. Phys. 41 195505), which may ha e g ea
impo ance in e y a ied echnological ields, such as bio echnology, biomedicine and
analy ical chemis y. Some ad an ages o e ed by hese nozzles o e he o iginal pla e o i ice
con igu a ion (Ga˜
n´
an-Cal o 1998 Phys. Re . Le . 80 285) a e: (i) hey a e ex ao dina ily
smoo h e en a he mic ome e scale, (ii) one can eadily ob ain nozzles wi h neck diame e s in
he ange o a ew ens o mic ons, (iii) hey demand gas low a es signi ican ly smalle han
hose equi ed by he pla e o i ice con igu a ion and (i ) hey a e anspa en . Howe e , highly
demanding applica ions equi e a p ecise cha ac e iza ion o hei h ee-dimensional shape by
non-des uc i e means. This cha ac e iza ion canno be ob ained s aigh o wa dly om
op ical ansmission o elec on mic oscopy mainly due o op ical dis o ion. We p opose in
his pape a me hod o measu ing he shape and size o mic ome e nozzles o med inside
millime ic and submillime ic capilla ies made o anspa en ma e ials. The inside o he
capilla y is colo ed, and he capilla y is pu in a liquid ba h wi h almos he same e ac i e
index as ha o he capilla y o elimina e op ical dis o ion. The nozzle image, acqui ed wi h a
mic oscope using back-ligh illumina ion o ge a silhoue e e ec , is p ocessed o loca e he
con ou s o he nozzle wi h sub-pixel esolu ion. To de e mine he h ee-dimensional shape o
he nozzle, he capilla y is o a ed in on o he came a. The me hod p o ides p ecise esul s
o nozzle sizes down o a ew mic ons.
(Some igu es in his a icle a e in colou only in he elec onic e sion)
1. In oduc ion
The low ocusing (FF) me hod [1] is a con inuous d ople
p oduc ion echnique wo king in he so-called je ing mode
[2,3]. A gas cu en induces s eady- ip s eaming in a
liquid meniscus a ached o a eeding capilla y, and ‘ ocuses’
he mic oje emi ed om he meniscus ip ac oss an o i ice
( igu e 1). The mic oje b eaks up due o he g ow h
o axisymme ic pe u ba ions downs eam ( he Rayleigh
ins abili y [4,5]) leading o he o ma ion o d ops, which a e
commensu a e wi h he je diame e . FF has some ad an ages
o e o he echniques o p oduc ion o mic od ops: (i) i uses
pu ely hyd odynamic means o p oduce he d ops; (ii) i is,
he e o e, applicable o any liquid; (iii) i allows one o ob ain
d ops wi h diame e s om 500 nm o 500 μm; (i ) i p oduces
collec ions o d ops wi h a high deg ee o monodispe si y;
( ) i can each high p oduc ion a es (up o 106d ops s−1);
( i) i can be adap ed o a wo-dimensional opology [6,7].
The FF p inciple [1] was o iginally applied using he pla e
o i ice (PO) con igu a ion ( igu e 1). In his con igu a ion, he
gas s eam co- lows wi h he liquid je ac oss an o i ice o
a pla e loca ed in on o he eeding capilla y. The wo
main geome ical pa ame e s o he luid con igu a ion a e
he capilla y- o-o i ice dis ance Hand he o i ice diame e D,
which essen ially de e mines he gas low pa e n. Vega e al
(2009) [8] ha e ecen ly s udied he undamen al impo ance
o he con e gence a e o he gas low a ound he ocused
liquid meniscus o ge he smalles possible d ops. This
con e gence a e is mainly de e mined by he dis ance H om
he eeding capilla y o he discha ge o i ice. They showed ha
he s abili y o bo h he ape ing meniscus and he emi ed je
can be c i ically and simul aneously me when H≃D/2, hus
0960-1317/10/075035+10$30.00 1© 2010 IOP Publishing L d P in ed in he UK & he USA
J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
Figu e 1. The s eady je ing egime in he o iginal FF con igu a ion.
ob aining he minimum je diame e o a gi en o i ice. The PO
geome y p esen s impo an d awbacks: (i) he sha p edges
o he o i ice cause s ong eci cula ion close o he o i ice
su ace [9], (ii) wi h con en ional echniques (mechanical,
lase , o elec ochemical d illing) i is p ac ically impossible o
achie e oughnesses smalle han he bounda y laye hickness
(∼1μm) a he o i ice su ace and (iii) he minimum sizes o
ound o i ices manu ac u ed wi h con en ional echniques a e
limi ed o ens o mic ons.
Nozzles a e used o p oduce je s, d ops, bubbles and
o he luid shapes in e y a ied p ac ical applica ions, such
as uel injec ion, ink-je p in ing and sp ays in indus ial
enginee ing [10,11], o p oduc ion o mic ocapsules [12],
emulsions [13] and bubbles [14,15] in chemical enginee ing
and bio echnology. Mic ome e nozzles ha e been used in
mic o luidics o e he las ew decades o ob ain je s and d ops
by simply injec ing liquids h ough hem wi h he app op ia e
low a e [16,17]. The diame e o he je s and d ops
p oduced in his way is simila o ha o he nozzle o i ice,
whose minimum alue is ine i ably limi ed o abou 10 μm
o g ea e by nozzle clogging. The nea ly liquid- ee su ace
smoo hness p o ided by lame-shaped glass nozzles educes
his isk because i makes deposi ions less p obable. Howe e ,
he p oblem emains a mic ome e scales, he sizes o g ea es
in e es in mos mode n applica ions.
DePon e and cowo ke s a A izona S a e Uni e si y ha e
ecen ly applied he FF p inciple [1] using a lame-polished
glass mic o-nozzle o p oduce je s o diame e s much smalle
han ha o he nozzle o i ice [18]. In his echnique, a capilla y
o hund eds o mic ons in diame e is in oduced in o a nozzle
h ough which a gas lows, d i en by a p essu e d op. Liquid
a a gi en low a e is injec ed h ough he capilla y. I he gas
p essu e d op and liquid low a e a e selec ed app op ia ely,
a s eady conical meniscus a aches o he end o he capilla y,
and i s ip emi s a s eady je o diame e much smalle han
ha o he nozzle o i ice. Figu e 2shows a mic oje p oduced
in ou labo a o y using his echnique. Ve y ecen ly [19], i
has been shown ha he ape ing liquid meniscus can also be
o med ou o he nozzle due o he ac ion o he co- lowing gas
s eam, which may en ail signi ican echnological ad an ages.
Figu e 2also shows a SEM mic og aph o a s eady liquid je
ob ained by his ou e ocusing echnique. Ou p elimina y
esul s indica e ha his p ocedu e equi es a p ecisely-shaped
nozzle exi .
In he p esen pape , we discuss he use o lame-shaped
glass mic o-nozzles o FF a omiza ion [18] by showing hei
signi ican ad an ages o e he o iginal PO con igu a ion. In
pa icula , we show ha ocusing wi h nozzles is much mo e
e icien han wi h hei equi alen PO con igu a ions. This
is because he ene gy (gas) consumed by he nozzle is much
smalle han ha used by he co esponding PO con igu a ion
o he same gas low pa e n.
The nozzle shape plays a undamen al ole in he s abili y
o he emi ed je s [18], and mus sa is y some equi emen s
o achie e ou e ocusing [19]. The e o e, he use o
mic o-nozzles in highly demanding FF applica ions equi es
measu ing hei h ee-dimensional (3D) shape p ecisely by
non-des uc i e means. This ac mo i a ed he second pa o
he p esen wo k, in which we p opose a me hod o cha ac e ize
he 3D shape o mic o-nozzles o med inside millime ic and
submillime ic capilla ies made o anspa en ma e ials. This
cha ac e iza ion is no i ial ask, mainly due o he op ical
dis o ion caused by he capilla y.
The me hod p oposed in his pape is based on he
conjunc ion o op ical imaging and ad anced image p ocessing
echniques. In op ical imaging, he image o a 3D objec is
magni ied wi h a mic oscope, and acqui ed and eco ded by a
monoch ome digi al came a. The silhoue e e ec is ob ained
using back-ligh illumina ion, so ha he objec appea s in he
image as an almos -black wo-dimensional shape on a g ay
backg ound. Ad anced image p ocessing echniques loca e
he con ou s delimi ing he objec wi h sub-pixel accu acy. The
conjunc ion o op ical imaging and ad anced image p ocessing
echniques has yielded e y p ecise esul s when analyzing
he shape and in e acial p ope ies o d ops [20–22], bubbles
[23,24], liquid b idges [25,26], liquid ilms [27,28] and
liquid lenses [29], among o he s. In he p esen wo k, we show
ha his me hodology, app op ia ely adap ed o measu ing he
3D shape o glass mic o-nozzles, p o ides p ecise esul s o
nozzle sizes down o a ew mic ons. Me hods capable o
measu ing accu a ely he 3D shape o nozzles o med inside
capilla ies a e o g ea in e es in se e al ields, including
biology o single cell manipula ion, cell so ing, e c.
The pape is o ganized as ollows. In sec ion 2,
we b ie ly desc ibe he p ocedu e o p oduce lame-shaped
glass mic o-nozzles o FF a omiza ion. In sec ion 3,we
discuss he ad an ages o using mic o-nozzles ins ead o he
classical PO con igu a ion. The me hod o nozzle geome ical
cha ac e iza ion is desc ibed in sec ion 4. The cha ac e iza ion
esul s a e gi en and discussed in sec ion 5. Some conclusions
a e p esen ed in sec ion 6.
2. On he ab ica ion o lame-shaped glass
mic o-nozzles
I is well known ha nozzles can be o med by applying
a lame o he ip o a clean-cu millime ic glass capilla y.
The glass mel s and begins o low d i en by he compe i ion
be ween su ace ension and iscosi y o ces, bo h exhibi ing
la ge g adien s in he hea ed egion. This low na ows he
inne duc o med in he capilla y. Be o e he glass inne ee-
su ace pinches, he hea sou ce is swi ly wi hd awn, and he
2
J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
Figu e 2. Le : digi al image o a s eady mic oje emi ed by a nozzle o med inside a capilla y. An ai s eam co- lows wi h he liquid
s e ching a meniscus inside he nozzle un il a mic oje ape s om he menicus ip. Righ : SEM mic og aph eco ded by DePon e and
collabo a o s a A izona S a e Uni e si y o a s eady ape ing liquid je [19]. The je was emi ed by a capilla y in oduced in o a con e gen
nozzle. The gas s eam co- lowing h ough he nozzle ocused he liquid meniscus o med a he capilla y end un il a mic oje was
pulled ou .
glass solidi ies in a a ie y o hou -glass shapes depending
on he lames in ensi y, ocus and loca ion. The cylind ical
geome y o he p ima y capilla y lea es he memo y o he
symme y axis o e he shaping p ocess as long as he hea
is applied symme ically. Due o he la ge cu a u es o he
capilla y inne ee su ace, he su ace ension s eng h o
glass ma e ials (a ound 0.2 N m−1), and he smallness o he
g a i y e ec s on he mel ed glass, he low keeps he nozzle
symme y down o neck sizes o a ew mic ome e s. As a
esul , almos oughness- ee, ound o i ices a e ob ained.
We ha e in es iga ed di e en lame con igu a ions and
capilla y-shaping p ocedu es (wi h a ied capilla y- o- lame
dis ances, lame applica ion imes, quenching speeds, e c.) o
p oduce nozzle shapes wi h a desi ed con e gence. Ou s udy
shows ha he nozzle con e gence inc eases as he empe a u e
g adien in he glass inc eases. In o de o p oduce nozzles
wi h a su icien ly high deg ee o con e gence, we applied
he ollowing p ocedu e. A lamina p opane lame was li
using a comme cial gas ligh e . The lame was placed so
ha i was jus ouching he capilla y end. In pa icula , he
capilla y end was a he ou e bo de o he yellow egion
o he lame, 4 mm abo e he ligh e nozzle. The glass
shaping p ocess was obse ed h ough a mic oscope. This
p ocess was quenched once he desi ed neck diame e had
been app oxima ely eached.
Figu e 3shows wo nozzles ob ained wi h di e en
ela i e posi ions o he capilla y o he lame. When he
capilla y end was placed a he ou e bo de o he lame,
he empe a u e g adien in he glass was g ea e and he
esul ing nozzle was mo e con e gen . This ype o nozzle
p oduces low pa e ns simila o hose o he op imum PO
con igu a ion, i.e. wi h H≃D/2 (see he in oduc ion).
As will be shown in sec ion 3, hese nozzles cons i u e a
mo e e icien al e na i e o he classical PO con igu a ion
o gene a e he hinnes capilla y je s by FF. In his way,
we no only imp o e he o iginal PO con igu a ion, bu
also in oduce an op imiza ion p ocedu e o he new FF
embodimen concei ed and de eloped by DePon e e al [18]
a A izona S a e Uni e si y.
Figu e 3. Nozzle shapes ob ained wi h he indica ed posi ion o he
capilla y ela i e o he lame.
3. Mic o-nozzles e sus he pla e o i ice
con igu a ion
Mic o-nozzles o e ou majo ad an ages o e he o iginal
PO con igu a ion: (i) hey a e smoo h e en a he mic ome e
scale, (ii) one can eadily ob ain nozzles wi h neck diame e s
in he ange o ens o mic ons, (iii) hey demand gas low
a es signi ican ly smalle han hose equi ed by he PO
con igu a ion and (i ) hey a e anspa en . The i s h ee
ad an ages a e commen ed on in he nex h ee subsec ions.
3.1. Nozzle smoo hness
Singula i ies and i egula i ies o he solid su aces ha e a
nega i e in luence on he s abili y o je s p oduced by a
FF de ice. The sha p edges o he o i ice ine i ably cause
s ong eci cula ion close o he o i ice su ace [9], while he
su ace oughness may p oduce signi ican low pe u ba ions.
These pe u ba ions a e damped by iscous o ces i he
su ace oughness is subme ged in o he bounda y laye which
de elops on he solid su ace. O he wise, he pe u ba ions
g ow downs eam owing o he dominance o ine ia o e he
iscous o ce in he gas s eam.
The gas low induced by he p essu e di e ences equi ed
by ul a- ine FF nebuliza ion [1,18] has cha ac e is ic speeds
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J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
in he ange om abou 200 o 400 m s−1. The bounda y laye
de eloped on he nozzle su ace has a cha ac e is ic hickness
δ∼μgL
ρgUg1/2
,(1)
whe e μg,ρgand Uga e he cha ac e is ic gas iscosi y,
densi y and eloci y a he nozzle neck, espec i ely, and L
is he cha ac e is ic nozzle leng h. He e, we conside he
diame e a he nozzle neck as he cha ac e is ic leng h. I
one conside s he ai p ope ies and a cha ac e is ic leng h
L∼20 μm (see, e.g., igu es 14 and 15), hen δ≃1μm.
No manu ac u ing means o he han lame polishing o
iso opic chemical e ching on ela i ely simple ma e ials (e.g.,
amo phous silicon) would yield oughnesses smalle han he
bounda y laye hickness.
I is well known ha one o he main obs acles in
p oducing mic oje s and d ops is he clogging o he emi ing
o i ice. Clogging is caused by he deposi ion, on he o i ice
su ace, o impu i ies anspo ed by he liquid which canno
be swep away by he low. The oughness o he solid su aces
plays a key ole in he blockage o he emi ing de ice because
i makes he impu i ies a ach o hose su aces. The e o e, he
smoo hness o he lame-shaped glass mic o-nozzles en ails
an impo an addi ional ad an age: i a o s he emo al o
impu i ies and hus p e en s he nozzle om clogging.
3.2. O i ice and nozzle neck diame e s
FF equi es a conical s eady liquid meniscus o ejec a mic oje
which ul ima ely b eaks in o d ople s. The es ablishmen o
ha meniscus is he esul o a delica e balance be ween he
s esses exe ed on he ee su ace, which becomes c i ical
close o he meniscus ip. Tangen ial iscous s esses τsplay a
undamen al ole in ha balance because hey a e essen ial o
d aw he liquid su ace in he di ec ion o he gas s eam [30].
The diame e Dis p obably he geome ical pa ame e ha
a ec s he balance mos be ween he ee su ace s esses close
o he meniscus ip. He e, Dis he o i ice diame e in he PO
con igu a ion and he nozzle neck diame e when ocusing wi h
mic o-nozzles. To analyze he e ec s o bo h he angen ial
iscous s esses τsand he diame e Din he balance men ioned
abo e, one can in oduce he wo dimensionless pa ame e s
τsD/σ and D/dj, whe e σis he su ace ension and dj
is he je diame e a he exi . A la ge expe imen al eco d
acc ued o e mo e han a decade wi h he PO con igu a ion
[30,31] indica es ha τsD/σ 0.3 and D/dj60 in
he FF ealiza ions ( igu e 4). This las esul shows ha
submic ome e je s and d ople s can be p oduced wi h FF only
i Dis smalle han a ew ens o mic ons. This equi emen
can be eadily sa is ied in lame-shaped glass mic o-nozzles
(see e.g., igu e 9), while i becomes a se ious obs acle in pla e
o i ices manu ac u ed wi h con en ional echniques, such as
mechanical, lase and elec ochemical d illing.
One o he main di icul ies in using nebulize s wi h e y
small o i ices is ela ed o he s a ing s age. In he i s ins an s
o he injec ion, he liquid sp eads, we s he solid su aces
and accumula es in he o i ice blocking i s exi . One has o
emo e his o p ope ly es ablish a s eady je ing egime. In
Figu e 4. The ‘ ocusing s ess’ pa ame e τsD/σ as a unc ion o
he a io D/d.
Figu e 5. The op imum PO con igu a ion and an equi alen nozzle.
FF wi h nozzles, his ope a ion can be eadily done by simply
inc easing he p essu e d op applied o he gas s eam in he
s a ing s age. Due o he smoo hness o he nozzle su ace, he
gas cu en easily sweeps away he deposi ed liquid and opens
he discha ge o i ice. Then he p essu e d op is dec eased un il
he alue co esponding o he s eady egime is eached.
3.3. E iciency
The gas low in he PO con igu a ion exhibi s a s eamline
geome y essen ially de e mined by he o i ice diame e . This
low pa e n can be gene a ed app oxima ely by a amily
o nozzle shapes wi h di e en neck diame e s. Figu e 5
illus a es his idea. The igu e depic s he op imum (H=
D/2) PO con igu a ion [8] and an almos equi alen nozzle.
The hin-dashed do ed lines a e he gas s eamlines while
he con inuous lines indica e he liquid- ee su ace loca ion.
The dashed lines ep esen he mic o-nozzle which p oduces
almos he same gas (and hence liquid) low pa e n abo e he
neck. No e ha he con ou o he con e ging pa o he nozzle
p ac ically coincides wi h a s eam ube due o he negligible
hickness (abou 1 μm) o he gas bounda y laye s in ha pa
o he nozzle.
The main conclusion d awn om igu e 5is ha he gas
(ene gy) consumed by he nozzle is much less han ha used
by he equi alen PO con igu a ion because he nozzle neck
diame e is much smalle han he o i ice diame e . In o he
4
J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
Figu e 6. The nozzle analyzed in igu e 14 and he co esponding
PO con igu a ion.
wo ds, he nozzle is much mo e ene ge ically e icien han he
equi alen PO con igu a ion, which may become impo an o
massi e a omiza ion in, o ins ance, indus ial and ag icul u al
applica ions.
In p inciple, one could eplace a gi en PO con igu a ion
by a nozzle nebulize wi h he same ocusing p ope ies and
he desi ed gas consump ion. Fo his pu pose, he s eps o
ake migh be he ollowing. Fi s , he gas s eam ubes
o a gi en PO con igu a ion a e ob ained om nume ical
simula ion [9]. Second, one calcula es he diame e Do
he nozzle discha ge o i ice co esponding o he desi ed gas
consump ion. Finally, one ab ica es a nozzle such ha he
con ou o i s con e ging pa app oxima ely coincides wi h
he gas s eam ube o diame e Da a dis ance H om he
capilla y. Figu e 6illus a es his p ocedu e wi h one o he
nozzles cha ac e ized in sec ion 5. The powe consumed by
he nozzle is N=p (Qg+Ql)≃p Qg∼p UgD2,
while ha consumed by he equi alen PO con igu a ion is
N∼p UgD2. He e, Qgand Ql(QlQg) a e he gas and
liquid low a es, espec i ely, p is he p essu e d op applied
o he gas s eam and ene gy dissipa ion in he gas and liquid
injec ion sys ems has been neglec ed.
In con as o wha happens wi h he classical PO
con igu a ion, he p oduc ion o app op ia e mic o-nozzles o
FF a omiza ion equi es a p ecise me hod o cha ac e izing
hei in e nal shape. In he nex sec ion, we p opose a non-
des uc i e echnique o ob ain he 3D shape o mic o-nozzles
o med inside capilla ies made o anspa en ma e ials.
4. Me hod o geome ical cha ac e iza ion
4.1. Appa a us
Figu e 7shows he main componen s o he appa a us used o
cha ac e ize he nozzles. The nozzle o med inside a capilla y
(A) made o bo osilica e (haema oc i glass capilla y wi h
OD =1.55 mm and ID =1.15 mm) was pu in a cubic glyce in
(wi h e ac i e index n=1.474) ba h (B), which had almos
he same e ac i e index as ha o bo osilica e (n om 1.47 o
1.5). The capilla y was held on o a p ecision o a ion pla o m
(C) o o a e he capilla y a ound a e ical axis. Digi al images
o he capilla y consis ing o 1292 ×964 pixels we e acqui ed
Figu e 7. Expe imen al appa a us: nozzle (A), glyce in ba h (B),
p ecision o a ion pla o m (C), came a (D), op ical lenses (E),
iaxial ansla ion s age (F), back-ligh ing (G) and op ical able (H).
wi h an AVT STINGRAY F-125B CCD came a (D) equipped wi h
op ical lenses (a MITUTOYO 10×magni ica ion zoom-objec i e
and an OPTEM 70XL se o lenses wi h a iable magni ica ion
om 0.75× o 5.25×) (E) p o iding a a iable ame co e ing
an a ea om 672 ×502 μmdown o97.7×72.9μm. The
esul ing magni ica ion could be selec ed wi hin an in e al o
app oxima ely be ween 520 and 75.6 nm/pixel. The came a
could be displaced by means o a high-p ecision iaxial
ansla ion s age (F) o ocus he capilla y. The capilla y was
illumina ed using back-ligh illumina ion (G) o ge a silhoue e
e ec , so ha he inne con ou o he capilla y ( he nozzle)
appea ed in he image as a black wo-dimensional objec on a
g ay backg ound. All he componen s o he appa a us we e
moun ed on an op ical able wi h a pneuma ic an i- ib a ion
isola ion sys em (H) o damp he ib a ions coming om he
building.
4.2. P ocedu e
Be o e cha ac e izing he nozzles, he image acquisi ion
sys em was calib a ed. Fo his pu pose, digi al images o
calib a ion ods wi h di e en diame e s we e acqui ed and
analyzed o calcula e he magni ica ions used subsequen ly.
We also acqui ed and p ocessed images o a calib a ion
g id using lenses wi h less magni ica ion o e i y ha
he pixel aspec a io was p ac ically uni y. The op ical
dis o ion associa ed wi h he op ical lenses was assumed o
be negligible as compa ed o ha caused by he bo osilica e
capilla y/glyce in ba h se .
The p ocedu e o cha ac e ize a nozzle consis ed o he
ollowing s eps.
(i) The inne wall o he capilla y ( he nozzle) was colo ed
by injec ing ink and d ied wi h an in a ed lamp.
(ii) The capilla y was pu in he glyce in ba h o pa ially
emo e he op ical dis o ion caused by he capilla y.
Figu e 8shows an image o he nozzle be o e (a) and
a e (b) colo ing and pu ing i in he glyce in. The wo
images we e acqui ed wi h he same op ical sys em, and
hus hey co espond o almos he same ield o iew.
The capilla y dis o ed he appa en shape o he nozzle
in such a way ha he nozzle looked a con e ging duc
while ac ually i had a di e ging pa .
5

J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
(a)(b)
Figu e 8. Digi al image o he nozzle be o e (a)anda e (b)
colo ing and dipping in glyce in. The wo images we e acqui ed
wi h he same op ical sys em, and hus hey co espond o he same
ield o iew.
(iii) Fo a gi en posi ion o he o a ion pla o m, a digi al
image o he capilla y in he glyce in ba h was acqui ed
and eco ded.
(i ) The capilla y was o a ed 9◦a ound a e ical axis using
he p ecision o a ion pla o m.
S eps (iii) and (i ) we e epea ed 180/9=20 imes o ge
images o he 20 me idional planes used o compose he 3D
shape o he nozzle.
I mus be no ed ha he capilla ies could be easily cleaned
o e-use hem a e cha ac e izing he shape o he nozzles.
When he size o he nozzle was su icien ly small (say less
han 100 μm), i was no necessa y o colo he inne wall o
he capilla y o ge he silhoue e e ec (see igu es 14 and 15),
which simpli ied he cha ac e iza ion p ocess.
4.3. Image p ocessing echnique
Following he p ocedu e desc ibed in sec ion 4.2, 20 images o
he nozzle o be cha ac e ized a e acqui ed and eco ded. Each
o hose images shows he silhoue e o he nozzle me idional
plane b ough ace o ace wi h he came a. The me idional
plane appea s in he image as an almos black objec on a g ay
backg ound. Ad anced image p ocessing echniques ha e
been designed o loca e p ecisely he con ou s delimi ing he
objec s in his ype o images. They p o ide esul s wi h
sub-pixel accu acy when p ocessing images o d ops [20–22],
bubbles [23,24], liquid b idges [25,26], liquid ilms [27,28]
and liquid lenses [29], among o he s. In he p esen wo k,
we used an image p ocessing echnique ecen ly p oposed
o loca e he ee su ace enclosing liquid shapes o ens o
mic ome e s in size [28,32]. This echnique is capable o
‘ es o ing’ blu ed edges o pa ially o e come limi a ions due,
o ins ance, o di ac ion o lack o ocus. Fo he sake o
comple eness, we desc ibe in his sec ion he main aspec s o
ha echnique.
4.3.1. De ec ion o he con ou s. In ou expe imen s, a digi al
image is de ined ma hema ically by he g ay in ensi y ma ix
I(i,j), which akes an in ege alue be ween 0 (black) and
255 (whi e) o each pixel (i, j), whe e iand jco espond
o he ho izon al and e ical di ec ions, espec i ely. The
nozzle con ou s mus co espond o a s ep in he g ay in ensi y
in he di ec ion pe pendicula o hose con ou s. Howe e ,
Figu e 9. Digi al image o he nozzle and he con ou s (whi e lines)
de ec ed a he pixel le el wi h he O su me hod.
he in ensi y change is smea ed ou o e se e al pixels, and
de e mining he posi ion o he con ou s is no ob ious.
In he p esen wo k, he nozzle con ou s we e de ec ed
using a wo-s age p ocedu e. In he i s s age, a se o
pixels {(ic,j
c)}p obably co esponding o he con ou s being
sough was ex ac ed using O su’s me hod [33]. In his
me hod, a h eshold alue o he g ay in ensi y is calcula ed by
assuming ha he his og am o I(i,j) is a combina ion o wo
dis ibu ions co esponding o he objec and he backg ound.
The h eshold alue sepa a es hose wo dis ibu ions in he
his og am and is calcula ed by minimizing he weigh ed sum
o hei a iances. Mo e de ails o he O su me hod can be
ound in he o iginal wo k [33]. Figu e 9shows a digi al
image o he nozzle and he con ou s (whi e lines) de ec ed a
he pixel le el wi h he O su me hod.
The accu acy o O su’s me hod is limi ed o he pixel size.
In he second s age, he local in ensi y h eshold c i e ion is
used a he sub-pixel le el o imp o e he p ecision o he esul .
Fo e e y pixel (ic,j
c), he di ec ion ξno mal o he con ou
is de e mined as ha o he in ensi y g adien . To calcula e
he in ensi y g adien , an ope a o such as he 3×3 Sobel
con olu ion ke nel can be applied o he g ay in ensi y ma ix
I(i,j) p e iously smoo hed wi h a il e , such as he Gaussian
il e . I mus be no ed ha he use o he ho izon al axis i
ins ead o he no mal di ec ion ξin he subsequen calcula ions
yields e y simila esul s and educes he compu a ion ime
signi ican ly.
Once he ξdi ec ion has been de e mined o e e y
con ou pixel (ic,j
c), he sigmoid (Bol zmann) unc ion [20]
g(ξ) =g1−g2
1+exp[(ξ −ξ0)/W]+g2(2)
is i ed o he g ay in ensi y p o ile along he ξaxis. He e, g1
and g2co espond o he pla eau g ay alues a he wo sides o
he edge, Wis a measu e o he edge wid h, and ξ0is he mid-
poin o he p o ile. The con ou poin is gi en by ξ0, o which
(2) akes he alue (g1+g2)/2, and hus he me hod can be
seen as a local h esholding echnique. The igh -hand g aph
in igu e 10 shows he g ay in ensi y p o ile (symbols) along
he dashed line indica ed in he image and he co esponding
sigmoid unc ion i s (solid lines). The e ical dashed lines
indica e he posi ions o he le and igh con ou s, whe e (2)
akes he co esponding local h eshold alues (g1+g2)/2.
When his p ocedu e is applied o each pixel (ic,j
c), he esul
is wo se s o poin s {(xl,z)}and {(x ,z)} ep esen ing he le
and igh nozzle con ou s, espec i ely. In ou calcula ions, i
he dis ance be ween he pixel (ic,j
c)and he co esponding
6
J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
(b)
Figu e 10. Le : digi al image o he nozzle. Righ : he g ay
in ensi y p o ile (symbols) along he dashed line indica ed in he
image, and he co esponding sigmoid unc ion i s (solid lines).
The e ical dashed lines indica e he posi ions o he le and igh
con ou s.
poin calcula ed a he sub-pixel le el is g ea e han wice he
pixel size, hen ha poin is ejec ed. The sub-pixel app oach
signi ican ly imp o es he esul s ob ained a he pixel le el
o mos images. In pa icula , i imp o es he p ecision o he
con ou s de ec ed in sha p images [20–22,25–27,29,34], and
allows one o il e anomalous poin s in low-quali y images
[23,24].
I mus be no ed ha he p esen echnique cons i u es
a use ul al e na i e o mo e s anda d sub-pixel esolu ion
me hods (see e.g. [22,25–27]) unde se e al ci cums ances.
Those me hods gene ally calcula e he local h eshold o he
g ay in ensi y p o ile as he a e age o he wo pla eaus exis ing
a each side o he p o ile, and hen de e mine he con ou poin
by in e pola ing he g ay p o ile in he ansien egion. The
p esen echnique has wo main ad an ages wi h espec o
ha p ocedu e: (i) while ha p ocedu e only il e s he noise
on he wo sides o he edge o calcula e he g ay in ensi y
h eshold, i ing (2) o he en i e g ay in ensi y p o ile il e s
he noise in he ansien egion oo; and (ii) i ing (2) o he
g ay in ensi y p o ile p o ides accu a e esul s e en when he
dis ance be ween he le and igh con ou s is so sho ha
he g ay in ensi y p o iles o e lap, making i di icul o
iden i y he pla eaus in he in e e ence egion. Indeed, his is
he case shown in igu e 10, o which s anda d echniques do
no p o ide sa is ac o y esul s.
4.3.2. Calcula ion o he axisymme ic con ou . As
men ioned in sec ion 2, he necks o he nozzles o med
inside glass capilla ies gene ally ha e la ge cu a u es, and
hus hei shapes a e nea ly axisymme ic. In he p esen
wo k, he symme y axis xs(z) o he nozzle neck was ound
by an elemen al p ocedu e, and he le xl(z) and igh x (z)
con ou s we e o a ed un il xs(z) was almos e ical. Then,
he lack o symme y o he en i e nozzle was e alua ed by
calcula ing he eccen ici y E(z) ≡|x∗
l(z)−xs|−|x∗
(z)−xs|,
whe e x∗
l(z) and x∗
(z) a e he le - and igh - o a ed con ou s,
espec i ely. The eccen ici y E(z) can be seen as a quali y
pa ame e which indica es he deg ee o uni o mi y o he
hea ing used o o m he nozzle. In addi ion, an ‘a e age’
axisymme ic con ou was ob ained om he le - and igh -
o a ed con ou s as F∗=(x∗
l−x∗
)/2.
Figu e 11. Flow cha showing he s ages o he image p ocessing
echnique and he quan i ies ob ained.
4.3.3. Smoo hing he axisymme ic con ou . The me hod
desc ibed in sec ions 4.3.1 and 4.3.2, as applied o ou images,
p o ides a se o poin s {(F ∗,z)} ep esen ing he nozzle
con ou . Because his se mus belong o a smoo h unc ion,
smoo hing echniques can be used o imp o e he esul .
An elemen al smoo hing algo i hm was used o educe he
luc ua ions o he con ou posi ion. I is simila o ha used
in [23,35] o smoo h he ee su ace posi ion o pendan
d ops o measu e he su ace ension. I p oceeds as ollows.
Conside a poin (F ∗,z) belonging o he nozzle con ou .
2M+ 1 con iguous poin s o he con ou a e aken a ound
(F ∗,z).AnO h-o de polynomial i o ha se o poin s is
calcula ed. The o iginal cen al poin (F ∗,z)is eplaced wi h
ha ob ained om he i (F, z). The smoo hed con ou s
{(F, z)} o be p esen ed in sec ion 5.1 we e ob ained by
applying his p ocedu e wi h M=40 and O=3 o he
o iginal con ou poin s {(F ∗,z)}.
4.4. Calcula ion o he h ee-dimensional shape
As explained in sec ion 4.2, 20 images co esponding o an
equal numbe o nozzle me idional planes we e acqui ed and
eco ded in he measu ing p ocess. Following he p ocedu e
desc ibed in sec ions 4.3.1 and 4.3.2, he le and igh
con ou s delimi ing hose me idional planes we e de e mined
and o a ed o he e ical posi ion.
In o de o ob ain he 3D shape o he nozzle, he o a ed
con ou s x∗
l(z) and x∗
(z) mus be e e ed o a common sys em
o coo dina es. As men ioned in he p e ious sec ion, he
nozzles analyzed we e almos axisymme ic in he egion close
o hei necks. The e o e, he symme y axes calcula ed om
ha egion o he me idional planes mus coincide. In addi ion,
he heigh zco esponding o he minimum wid h o he nozzle
mus also be he same o all he images o he nozzle. We used
hese wo condi ions o e e he con ou s x∗
(z) and x∗
l(z) o
he 20 images o a common coo dina e sys em. In his way, he
se o poin s in he 3D space belonging o he nozzle con ou
7
J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
Figu e 12. Le xl(z) and igh x (z) nozzle con ou s, eccen ici y E(z), and axisymme ic con ou F(z)co esponding o he digi al image
shown in he igu e.
Figu e 13. Le xl(z) and igh x (z) nozzle con ou s, eccen ici y E(z), and axisymme ic con ou F(z)co esponding o he digi al image
shown in he igu e.
Figu e 14. Le xl(z) and igh x (z) nozzle con ou s, eccen ici y E(z), and axisymme ic con ou F(z)co esponding o he digi al image
shown in he igu e.
Figu e 15. Le xl(z) and igh x (z) nozzle con ou s, eccen ici y E(z), and axisymme ic con ou F(z)co esponding o he digi al image
shown in he igu e.
could be ob ained easily. The inal esul was a con inuous
su ace calcula ed by in e pola ing ha se o poin s.
Figu e 11 is a low cha showing he s ages o he
image p ocessing echnique and he quan i ies ob ained in he
analysis.
5. Cha ac e iza ion esul s
In o de o illus a e he capabili ies o he me hod p oposed
in his pape , we show in his sec ion he esul s ob ained
o se e al nozzles. Figu es 12–15 show he le xl(z) and
igh x (z) nozzle con ou s, he nozzle eccen ici y E(z)
and he smoo hed axisymme ic shape F(z) calcula ed o
a me idional plane o ou nozzles, while he 3D shape o
wo nozzles is plo ed in igu e 16. The nozzles analyzed in
igu es 12,13 and 16 we e manu ac u ed in ou labo a o y,
while igu es 14 and 15 show he esul s o wo cus om ip
ype II nozzles manu ac u ed by Eppendo AG.
5.1. Two-dimensional (axisymme ic) esul s
Figu e 12 shows he shape o a highly con e ging nozzle wi h
a neck adius smalle han 5 μm. The eccen ici y had no
spa ial s uc u e and was less han 200 nm o e he en i e
sec ion analyzed, which e lec s he high deg ee o symme y
achie ed in he manu ac u ing p ocess. A e y smoo h con ou
F(z)was inally ob ained a e p ocessing he image.
Figu e 13 shows he shape o a con e ging-di e ging
nozzle wi h a neck adius o abou 30 μm. The eccen ici y
had ha dly any spa ial s uc u e and was smalle han 5 μm,
8
J. Mic omech. Mic oeng. 20 (2010) 075035 J M Mon ane o e al
Figu e 16. 3D esul s ob ained o an axisymme ic (le ) and
de ec i e ( igh ) nozzle.
less han 2% o he maximum diame e . In he image, one
can app ecia e he exis ence o small blo ches close o he
nozzle con ou . They p obably co espond o bubbles o med
in he mel ing p ocess and apped when he glass solidi ied.
These s ains cons i u ed an obs acle o accu a e de ec ion
o he nozzle con ou s. Ne e heless, he image p ocessing
echnique o e came his di icul y and s ill p o ided a smoo h
axisymme ic con ou F(z).
In igu es 14 and 15, we plo he esul s ob ained o wo
nozzles wi hou colo ing hem. As men ioned in sec ion 4.2,
back-ligh illumina ion p oduced he silhoue e e ec o e y
small nozzles by simply pu ing hem in he glyce in ba h.
The esul ing images we e sha p and could be acqui ed and
accu a ely p ocessed in a ew minu es. The spa ial s uc u e
o he eccen ici y e ealed a ce ain lack o symme y o he
nozzles.
5.2. Th ee-dimensional esul s
As explained in sec ion 4.4, he 3D shape o he nozzle can
be isualized by combining di e en me idional planes. By
way o illus a ion, igu e 16 shows he esul s ob ained o an
axisymme ic (le ) and de ec i e ( igh ) nozzle. In he la e
case, non-uni o m hea ing caused no iceable asymme ies a
om he neck, whe e he e ec o su ace ension was less
impo an .
Es ablishing he accu acy o he esul s p esen ed in his
sec ion is a e y ha d ask e en when eso ing o a des uc i e
echnique. In his case, one would i s ly cu away he
ou e wall o he glass capilla y un il making he nozzle
me idional c oss-sec ion isible. I can be easily e i ied ha
he dis ance be ween he nozzle me idional plane and he
on plane ob ained a e polishing he capilla y cu would
be ≃(2F|F−F∗|)1/2, whe e F∗would be he appa en
nozzle con ou exhibi ed ( igu e 17). We will assume ha
he e o assigned o ou cha ac e iza ion me hod is o he
o de o 1 pixel size, i.e. 0.1 μm in mos o he images (see
sec ion 4.1). I F∼10 μm (see igu es 12,14, and 15),
hen mus be smalle han (2×10 ×0.1)1/2=1.41 μm.
O he wise, he alida ion me hod would lead o e o s la ge
han hose o ou me hod. Un o una ely, we do no ha e access
o such a glass polishing echnique o achie e he equi ed
p ecision.
Figu e 17. The dis ance be ween he nozzle me idional plane and
he on plane ob ained a e polishing he capilla y.
6. Conclusions
In his pape , we ha e discussed in de ail a new con igu a ion
o capilla y FF using lame-shaped glass mic o-nozzles [18].
The main ad an ages o e ed by hese nozzles o e he classical
PO con igu a ion [1] a e: (i) hey a e ex ao dina ily smoo h
e en a he mic ome e scale, (ii) one can eadily ob ain nozzles
wi h neck diame e s in he ange o a ew ens o mic ons,
(iii) hey demand gas low a es (ene gy) signi ican ly smalle
han hose equi ed by he PO con igu a ion and (i ) hey a e
anspa en . Howe e , highly demanding applica ions equi e
a p ecise cha ac e iza ion o hei 3D shape by means o non-
des uc i e echniques. In con as o he case wi h he classical
PO con igu a ion, his cha ac e iza ion is no i ial ask,
mainly due o he op ical dis o ion caused by he capilla y.
Fo he pu poses o his quan i a i e cha ac e iza ion, we ha e
p oposed a non-des uc i e me hod o measu e he 3D shape
o mic o-nozzles o med inside capilla ies made o anspa en
ma e ials. The me hod is based on he conjunc ion o op ical
imaging and ad anced image p ocessing echniques. Sec ion 5
shows he esul s ob ained o se e al nozzles. The con ou s
delimi ing he me idional planes o he nozzles analyzed
we e p ecisely de e mined. Submic ome e luc ua ions we e
ob ained in hose con ou s o all he cases conside ed.
Also, he mic oscopic cha ac e iza ion me hod desc ibed
in his pape can be used in e y a ied applica ions.
Speci ically, i can be used o de e mine he shape o e y
small channels used in mic o luidics, in which many o he
echnologies used o p oduce mic oje s, d ops, capsules and
bubbles equi e nozzles om ens o hund eds o mic ons in
size, and he ole played by he nozzle shape may become
c i ical o a ain sa is ac o y esul s.
Acknowledgmen s
This esea ch was suppo ed by he Minis e io de Educaci´
on y
Ciencia (Spain) h ough g an no DPI2007-63559. Pa ial
suppo om he Jun a de Ex emadu a h ough g an no
GRU07003 is also acknowledged. We a e e y g a e ul o D
Con ado Fe e a o discussions and expe imen al assis ance.
Re e ences
[1] Ga˜
n´
an-Cal o A M 1998 Gene a ion o s eady liquid
mic o h eads and mic on-sized monodispe se sp ays in gas
s eams Phys. Re . Le . 80 285–8
9