Mic owa e-induced wa e lows in mic osys ems
A. Ramos,a兲A. Robles, P. Ga cía-Sánchez, and M. J. F ei e
Depa amen o de Elec ónica y Elec omagne ismo, Uni e sidad de Se illa, A da. Reina Me cedes s/n,
Se illa 41012, Spain
共Recei ed 3 Decembe 2008; accep ed 21 Decembe 2008; published online 14 Janua y 2009兲
Al e na ing cu en elec ic ields a e o inc easing impo ance o he de elopmen o mic o luidic
pumps. We epo how mic owa e ields can induce wa e low in mic osys ems, i espec i e o
saline concen a ion. A d op o wa e is placed on wo pa allel coplana mic oelec odes ha a e
ene gized by a mic owa e gene a o . Fluid low is obse ed and he luid eloci y is abou he same
o wo elec oly es wi h e y di e en saline concen a ions. Elec ically induced g adien s o
empe a u e p oduce spa ial a ia ions in mass densi y and dielec ic pe mi i i y leading,
espec i ely, o buoyancy and dielec ic o ces in he liquid. The obse ed luid low pa e ns
demons a e ha bo h e ec s a e aking place a di e en leng h scales: he dielec ic o ces
domina e a leng hs o he o de o 100
␮
m o smalle , while buoyancy domina es a ound 1 mm.
©2009 Ame ican Ins i u e o Physics.关DOI: 10.1063/1.3070521兴
Con ol and manipula ion o wa e is an impo an e-
qui emen o he lab-on-chip echnology.1Among he mos
p omising echniques o handle small amoun s o liquid a e
hose ha employ elec ical o ces di ec ly applied o he
liquid. Elec ohyd odynamic 共EHD兲ac ua ion p esen s he
ad an ages o ol age-based con ol, dominance o elec ical
o ces a he mic ome e scale, and absence o mo ing pa s.
The e o e, se e al possible ways o EHD ac ua ion in mic o-
sys ems ha e been explo ed such as elec o-osmosis,2ac
elec o-osmosis,3elec o he mal induc ion pumping,4and
ion-d ag pumping.5
Mic owa e elec ic ields ha e ecen ly been used in mi-
c osys ems o con olled dielec ic hea ing6o o eagen
de ec ion wi hin mic ochannels.7In his le e , we expe i-
men ally demons a e he use o mic owa e ields o elec-
o he mal ac ua ion o wa e in mic osys ems. The mic o-
wa e ields hea he luid gene a ing g adien s in mass
densi y and dielec ic pe mi i i y. The luid is hen se in o
mo ion due o buoyancy g=⌬
␳
gand dielec ic o ces
E=−1
2E2ⵜ␧. The main ad an age o his kind o EHD ac-
ua ion is ha wa e saline solu ions can be pumped wi h
almos no dependence on saline concen a ion since he
hea ing is based on wa e dielec ic loss a mic owa e
equencies.8O he kinds o EHD pumping o wa e a e sui -
able o ce ain anges o conduc i i y: ac elec o-osmosis
is sui able o elec oly es wi h low ionic s eng h
共
␴
ⱕ0.01 S/m兲, while ac elec o he mal induc ion pumping
is sui able o highe ionic s eng h 共
␴
⬎0.01 S/m兲. The la -
e can be used o liquids wi h smalle conduc i i y bu
using ex e nal hea ing. In addi ion, he equency o he sig-
nal mus be changed depending on conduc i i y o achie e
he bes pumping pe o mance in bo h kinds o ac ua ion.
The powe densi y dissipa ed as hea o an ac ield Eo
angula equency
␻
due o dielec ic loss is Pdiel =1
2␧⬙
␻
E2,
and due o Ohmic cu en s is POhm=1
2
␴
E2, whe e ␧⬙is he
imagina y pa o he complex dielec ic pe mi i i y and
␴
is
he elec ical conduc i i y. The e o e, dielec ic hea ing
domina es o e Joule hea ing o ␧⬙
␻
⬎
␴
. Fo ins ance, he
dielec ic loss ac o ␧⬙
␻
a 3 GHz and 20 °C esul s in an
equi alen conduc i i y o 2.2 S/m. 共The equi alen conduc-
i i y is 0.24 S/m o a equency o 1 GHz a 20 °C.兲The
hea ing and he expec ed low induced by ac elec ic ields a
3 GHz a e abou he same o wa e solu ions wi h conduc-
i i ies smalle han 2.2 S/m. The e o e, mos biological lu-
ids could be pumped wi h he same beha io using he same
applied signal. Fo highe conduc i i y, he hea ing will in-
c ease bu he e ec would be simila . We p opose ha mi-
c owa e wa e ac ua ion can be o use o he lab-on-chip
echnology.
The expe imen al se up is shown in Fig. 1. A squa e luid
chambe was buil wi h polydime hylsiloxane 共so polyme
used in mic o luidics兲. The bo om o he chambe is a plana
glass subs a e wi h wo pa allel pla inum mic oelec odes
ab ica ed on i . The lid is a glass co e slip. The elec odes
a e 100 nm hick and 500
␮
m wide sepa a ed by a 10
␮
m
a兲Elec onic mail: [email p o ec ed].
FIG. 1. Scheme o he expe imen al se up o he obse a ion o mic owa e
induced lows. Fluid low is gene a ed on op o wo coplana mic oelec-
odes. The de ice is connec ed o a mic owa e gene a o h ough a ans-
mission line.
APPLIED PHYSICS LETTERS 94, 024104 共2009兲
0003-6951/2009/94共2兲/024104/3/$23.00 © 2009 Ame ican Ins i u e o Physics94, 024104-1
09 June 2025 13:40:47
gap. KCl wa e solu ions we e pipe ed in o he chambe .
Fluo escen la ex pa icles 共500 nm diame e 兲we e sus-
pended in he solu ion and used as low ace s. Fluid low
was obse ed a e applica ion o ac elec ic ields om 1 o
4 GHz. The mic owa e sou ce comp ises an Agilen PNA
E8363B au oma ic ec o ne wo k analyze used as a mic o-
wa e gene a o and connec ed o a mic owa e ampli ie AR
5S164. The de ice was connec ed o he ampli ie h ough a
coaxial ansmission line.
Figu e 2共a兲p esen s he measu ed eloci y agains e-
quency o cons an powe Pin =0.16 W o he inciden wa e
o wo saline solu ions. The heigh o he chambe is
737
␮
m, su icien ly high o conside ha he luid mo ion is
mainly due o buoyancy 共see below兲. Typically, wo symme -
ic olls we e obse ed on op o elec odes. Fo
⬎1.5 GHz, he eloci y is oughly he same o he wo
wa e solu ions. A equencies om 1 o 4 GHz, mic owa e
wa eleng hs a e o he o de o 10 cm, much g ea e han he
dimensions o he de ice 共⬃2mm兲. The e o e, simple ci -
cui heo y is alid o he analysis o he mic ode ice and a
ol age di e ence can be assumed o be applied be ween he
pa allel elec odes. The a ia ion in luid eloci y wi h e-
quency can be unde s ood om he equency a ia ion o
he ol age be ween elec odes. Ou de ice will beha e as a
load impedance Zconnec ed o he end o he ansmission
line, which has a cha ac e is ic impedance o Z0=50 ⍀.A
mic owa e equencies he connec ion pads beha e mainly
as an induc o 共o induc ance L兲, which is connec ed o he
wo coplana mic oelec odes ha , wi h he wa e d op on
op, beha e as a leaky capaci o 共wi h esis ance Rand ca-
paci ance Cin pa allel兲. The esis ance Ris no a cons an 共i
is in e sely p opo ional o
␴
+␧⬙
␻
兲. The de ice impedance
is gi en by Z=i
␻
L+R/共1+i
␻
CR兲. The ol age V=V++V−
and he elec ical cu en I=共V+−V−兲/Z0a he end o he
ansmission line a e ela ed by V=ZI, whe e V+is he am-
pli ude o he inciden wa e p o ided by he sou ce and V−is
he ampli ude o he wa e e lec ed by he de ice. The ol -
age a he elec odes ela i e o V+is hen VCR/V+
=2ZCR/共Z+Z0兲, wi h ZCR=R/共1+i
␻
CR兲 he impedance o
he leaky capaci o . Figu e 2共b兲shows he ol age a he
elec odes as a unc ion o equency o easonable alues o
L,R, and C, compu ed wi h ini e elemen s o he ac ual
de ice. I also shows he heo e ical ol age equi ed o gen-
e a e he measu ed eloci ies by buoyancy. The ag eemen is
sa is ac o y.
Figu e 2can be used as a calib a ion cu e o in e he
ol age a he elec odes as a unc ion o equency o a
gi en inciden powe Pin=V+
2/2Z0. Figu e 3shows he ex-
pe imen al luid eloci y as a unc ion o es ima ed dissi-
pa ed powe Pdis=共PinVCR/V+兲2共Z0/R兲 o wo channels wi h
di e en heigh s 共287 and 737
␮
m兲. The expe imen al e-
loci ies we e ob ained a ying he inciden powe 共0–3 W兲
o gi en equencies 共1, 2, and 3 GHz兲and saline concen-
a ions 共de-ionized wa e and KCl solu ion o conduc i i y
128 mS/m兲. We can see ha he expe imen al eloci ies ha e
collapsed in o a single cu e, independen o equency.
Compu a ions o he eloci y using ini e elemen s a e also
shown.9The di e ence be ween expe imen al and nume ical
esul s a low powe s o he 287
␮
m channel heigh can be
a ibu ed o he ac ha he calib a ion cu e was ob ained
om he 737
␮
m channel heigh measu emen s.
Fo he compu a ions, we ha e sol ed he elec ic, em-
pe a u e, and eloci y ields in he chambe . Because he
wa eleng h is much g ea e han mic ode ice dimensions,
he elec ic po en ial is sol ed. Complex pe mi i i y in di -
e en domains 共wa e , glass兲a e used in o de o accoun o
he dielec ic esponse a mic owa es,
ⵜ·关共
␴
+i
␻
␧
˜
兲ⵜ
␾
兴=0 ␧
˜
共
␻
兲=␧⬘共
␻
兲−i␧⬙共
␻
兲.共1兲
A 20 °C, he eal pa ␧⬘is app oxima ely 80␧0 o equen-
cies below 5 GHz 共 ela i e a ia ion ⬍5%兲. On he o he
hand, he imagina y pa ␧⬙depends on equency in he
ange o ou expe imen s 共1–4 GHz兲. The empe a u e ield
is go e ned by
kⵜ2T+1
2共
␴
+
␻
␧⬙兲E2=0, 共2兲
neglec ing con ec ion o hea . Finally, he luid eloci y is
ob ained om S okes equa ions o an incomp essible luid,
␩
ⵜ2u−ⵜp+ g+具 E典=0 ⵜ·u=0, 共3兲
whe e pis he p essu e and
␩
is he iscosi y. The dielec ic
o ce exp ession is usually ob ained om he modynamic a -
gumen s wi h s a ic ields. We ha e assumed ha he dielec-
ic o ce exp ession is alid wi h ␧=␧⬘since 1
2␧⬘E2accoun s
o he elec ical ene gy s o ed in he dielec ic. Fo simplic-
FIG. 2. 共Colo online兲共a兲Veloci y measu ed a a gi en poin 共x=200
␮
m,
z=100
␮
m兲as a unc ion o equency o wo wa e solu ions 共inciden
mic owa e powe is 0.16 W兲.共b兲Es ima ed ol ages a elec odes as unc-
ions o equency o gene a ion o he obse ed luid eloci ies by buoy-
ancy and expec ed ol age a he elec odes om he ci cui analysis
关L=2.3⫻10−8 H, C=10−12 F, and R=885/共␧⬙
␻
兲⍀兴Rand Ca e com-
pu ed wi h COMSOL MULTIPHYSICS o he ac ual de ice. Lis es ima ed om
analy ical solu ion o he induc ion pe uni leng h o wo in ini ely long
s ips.
FIG. 3. 共Colo online兲Veloci y as a unc ion o es ima ed dissipa ed powe
in he de ice o di e en equencies and wa e solu ions: 共a兲channel wi h
heigh equal o 287
␮
m and 共b兲 o 737
␮
m. Con inuous lines: compu ed
eloci y as a unc ion o dissipa ed powe o ␧⬙
␻
+
␴
=0.4 S/m.
024104-2 Ramos e al. Appl. Phys. Le . 94, 024104 共2009兲
09 June 2025 13:40:47
i y, in he compu a ions we ha e assumed ha inc emen s o
empe a u e a e small. The e o e, physical p ope ies a e
conside ed cons an , independen o empe a u e, excep
o he o ce e ms in S okes equa ions 共Boussinesq app oxi-
ma ion兲: g=共d
␳
/dT兲⌬Tgand E=−1
2E2共d␧/dT兲ⵜT, whe e
o wa e a 20 °C 共1/
␳
兲d
␳
/dT=−2.6⫻10−4 K−1 and
共1/␧兲d␧/dT=−4⫻10−3 K−1.
The a io be ween g a i a ional and dielec ic o ces is o
he o de o g/ E⬃gl3⌬
␳
/0.5V2⌬␧ 共wi h las he ypical
leng h兲,10 and his a io dec eases apidly wi h dec easing l.
Figu e 4shows expe imen al pa icle pa hs o he wo de-
ices wi h channel heigh s o 287 and 737
␮
m a a plane
90
␮
m high om he le el o elec odes. The luid mo ion
pa allel o he gap be ween he elec odes is mainly o igi-
na ed by he dielec ic o ce, while he mo ion pe pendicula
o he gap is mainly due o buoyancy.11 When he chambe is
small he mo ion due o dielec ic o ces s a s o domina e.
The heo y o small empe a u e inc emen s p edic s ha
luid eloci y due o buoyancy should be p opo ional o he
dissipa ed powe , while he eloci y due o he dielec ic
o ce should be p opo ional o he dissipa ed powe squa ed.
Fo a channel wi h heigh 287
␮
m, Fig. 3shows ha he
eloci y inc eases mo e han linea ly wi h dissipa ed powe
o Pdis⬎0.02 W.
In conclusion, we ha e demons a ed he pumping o
wa e in a mic ode ice by he elec o he mal ac ion o mi-
c owa e elec ic ields. Buoyancy and dielec ic o ces se
he liquid in o mo ion. We ha e shown semiquan i a i e
ag eemen be ween expe imen and heo y in e ms o e-
quency and ol age dependence. The abili y o pump wa e
solu ions wi h di e en conduc i i ies 共including bio luids兲
in a mic osys em has many po en ial applica ions in he lab-
on-chip echnology.
We acknowledge he inancial suppo o he Spanish
go e nmen agency DGCyT 共Con ac No. FIS2006-03645兲
and Jun a de Andalucía 共Con ac No. FQM-241兲. A. Robles
acknowledges inancial suppo o MIT-Spain P og am In-
e nship.
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11See EPAPS Documen No. E-APPLAB-94-006903 o a ideo showing
he luid mo ion a wo di e en heigh s abo e he elec odes. Fo mo e
in o ma ion on EPAPS, see h p://www.aip.o g/pubse s/epaps.h ml.
FIG. 4. 共Colo online兲Pa icle pa hs and compu ed eloci ies a a plane
90
␮
m high om elec ode le el. Channel wi h heigh s o 287
␮
m共up兲
and wi h 737
␮
m共down兲.
024104-3 Ramos e al. Appl. Phys. Le . 94, 024104 共2009兲
09 June 2025 13:40:47