Nume ical s udy o dc-biased ac-elec okine ic low o e
symme ical elec odes
Wee Yang Ng,
1,2,a)
An onio Ramos,
3,b)
Yee Cheong Lam,
2
and Isabel Rod iguez
1
1
Ins i u e o Ma e ials Resea ch and Enginee ing, Agency o Science,
Technology and Resea ch (A*STAR), 3 Resea ch Link, Singapo e 117602, Singapo e
2
School o Mechanical and Ae ospace Enginee ing, Nanyang Technological Uni e si y,
Nanyang A enue 50, Singapo e 639798, Singapo e
3
Depa amen o de Elec o´nica y Elec omagne ismo, Facul ad de Fı´sica,
Uni e sidad de Se illa, A enida Reina Me cedes s/n, 41012 Se illa, Spain
(Recei ed 6 Augus 2011; accep ed 20 No embe 2011; published online 15 Ma ch 2012)
This pape p esen s a nume ical s udy o DC-biased AC-elec okine ic (DC-biased
ACEK) low o e a pai o symme ical elec odes. The low mechanism is
based on a ans e se conduc i i y g adien c ea ed h ough incipien Fa adaic
eac ions occu ing a he elec odes when a DC-bias is applied. The DC biased
AC elec ic ield ac ing on his g adien gene a es a luid low in he o m o
o exes. To unde s and mo e in dep h he DC-biased ACEK low mechanism, a
phenomenological model is de eloped o s udy he e ec s o ol age, conduc i i y
a io, channel wid h, dep h, and aspec a io on he induced low cha ac e is ics.
I was ound ha low eloci y on he o de o mm/s can be p oduced a highe ol -
age and conduc i i y a io. Such apid low eloci y is one o he highes epo ed
in mic osys ems echnology using elec okine ics. V
C2012 Ame ican Ins i u e o
Physics. [doi:10.1063/1.3668262]
I. INTRODUCTION
Dynamic manipula ion o luids in mic ochannel is c ucial o he de elopmen o lab-on-a-
chip (LOC) de ices.
1,2
One key equi emen o he ac ua ion sys em in LOC de ices is o
a oid mechanical mo ing pa s which can po en ially complica e he ab ica ion and inc ease
he size o he sys em.
3,4
Elec okine ics has been demons a ed as a iable app oach o e ec-
i ely manipula e luids in mic ochannels h ough he use o an elec ical d i ing o ce.
5,6
One
key ad an age lies in i s ease o implemen a ion which makes elec oosmosis (i.e., he use o
DC elec ic ield o d i e luid low, due o he Coulomb o ce on he di use double laye ) one
o he mos widely used pumping app oaches in mic o luidics in addi ion o p essu e-d i en
me hods.
7,8
AC-elec okine ic (ACEK) makes use o AC elec ic ields ac ing on AC cha ge densi y o
induce ec i ied low; wo impo an examples o ACEK a e AC-elec oosmo ic (ACEO) and
AC-elec o he mal (ACET) lows.
9–16
ACEO low is based on he Coulomb o ce ac ing on he
induced cha ge in he double laye in he p esence o a angen ial AC elec ic ield.
10–13
ACET
low is based on he in e ac ion o AC elec ic ields wi h conduc i i y g adien s in he luid
induced by a he mal g adien .
14–16
Mo e ecen ly, a DC-bias AC ol age (V
applied
¼V
DC
þV
AC
cos x ) has been employed
e ec i ely o concen a e pa icles/cells
17–19
and o pumping/mixing
20–23
applica ions in mic o-
luidics. The e has been se e al hypo hesis on he d i ing mechanism o he low induced by
DC-bias AC ol age.
6,18,19
Recen ly, we conduc ed expe imen al in es iga ion o elucida e he
d i ing mechanism o he DC-biased ACEK low phenomenon.
21,24
In he publica ions, we
a)
Elec onic mail: [email p o ec ed].
b)
Elec onic mail: [email p o ec ed].
1932-1058/2012/6(1)/012817/10/$30.00 V
C2012 Ame ican Ins i u e o Physics6, 012817-1
BIOMICROFLUIDICS 6, 012817 (2012)
demons a ed ha he applied DC-bias ol age gi es ise o incipien Fa adaic eac ions a he
elec odes’ su ace.
21,24
Indeed, i was es ed ha hese eac ions cause changes on he local pH
due o he gene a ion o co-ions abo e he elec odes. As a esul , he egion abo e he anode
became acidic due o he inc ease o H
þ
ions, and he egion abo e he ca hode was basic due
o he inc ease o OH
–
ions. In addi ion, i was measu ed ha he basic egion is 11%–12%
mo e conduc i e han he acidic egion.
24
Hi he o, he e is no exis ing heo e ical model o desc ibe he DC-biased ACEK low. In
his pape , we p esen a phenomenological model based on he ac ual conduc i i y di e ence
be ween he anode and he ca hode o gi e a desc ip ion o he luid low. I should be no ed
ha he e ec o DC-bias could no be included by simply adding a DC-bias o he AC ol age
in es ablished ACEO model.
12,13
This is because we do no know wi h ce ain y all he elec o-
chemical eac ions aking place a he elec odes’ su ace. The e o e, we ake he alue o he
inc emen o conduc i i y om expe imen s.
24
Mo eo e , since he DC ol age is jus enough
o gene a e he species, he applied DC ol age is d opped ac oss he double laye and no in
he bulk. A con ec ion-di usion equa ion is used he e o desc ibe he dis ibu ion o conduc i -
i y. The in e ac ion o he elec ic ield wi h he conduc i i y g adien leads o luid low. This
pape will demons a e ha he de eloped model could p edic well he expe imen al obse a-
ions
23,24
namely he single and dominan low o ex and he di ec ion o o ex o a ion. I is
expe imen ally di icul o cha ac e ize he c oss-sec ional luid eloci y p o iles; he e o e a nu-
me ical simula ion se es as a ool o be e unde s and he a ious ac o s a ec ing he induced
low eloci y. Pa ame ic ac o s ( ol age, conduc i i y a io) and geome ical ac o s (wid h,
dep h, and aspec a io) we e a ied in his s udy o unde s and hei e ec s on he induced
DC-biased ACEK low eloci y.
II. NUMERICAL ANALYSIS
DC-biased ACEK low phenomenon was modeled using COMSOL MULTIPHYSICS
V
R
. A phenom-
enological model was p esen ed he e o gi e a desc ip ion o he DC-biased AC-elec okine ic
luid low. The nume ical model is based on he measu ed conduc i i y di e ence be ween he
anode and he ca hode and was used as he basis o he bounda y condi ions o he conduc i -
i y equa ion. I was de e mined ha he liquid abo e he ca hode is mo e conduc i e han he
one on he anode side. AC impedance analysis was adop ed o measu e he conduc i i y le el
abo e he ca hode and he anode. I was ound ha wi h a DC bias o 2 V
DC
, he ca hode is
mo e conduc i e han he anode by 11%–12%.
24
We assume ha he applied DC ol age is jus abo e he h eshold o gene a e Fa adaic
eac ions a he elec odes. In his way, V
DC
is d opped a he elec ode/elec oly e in e ace o
d i e he eac ions and negligible DC ol age is d opped ac oss he bulk elec oly e. No ice ha
he minimum ol age o p oduce elec olysis o wa e is abou 1.23 V. The e o e, we can
neglec V
DC
in he medium and sol e only o he AC po en ial (V
applied
¼V
AC
cos x ). Mo e-
o e , since he equency o he AC signal is much g ea e han he ecip ocal RC ime o
cha ging he double laye ,
10
he AC ol age is d opped mainly ac oss he bulk elec oly e and
negligible AC ol age is d opped a he elec ode/elec oly e double laye s. In addi ion, he
e ec o joule hea ing is igno ed since he conduc i i y used is low.
In his s udy, a 2D analysis was pe o med o a pai o coplana and symme ical elec o-
des enclosed by a mic ochannel as shown in Fig. 1. To limi he scope in his s udy, he elec-
ode wid h and gap we e ixed a 40 lm and 20 lm, espec i ely, bu he mic ochannel wid h
(W) and dep h (D) we e a ied om 100 o 400 lm and 20 o 200 lm, espec i ely.
A. Elec ical equa ions
Fo an elec oly e, he elec ic po en ial (/) dis ibu ion a any poin in he solu ion can be
ela ed o he elec ic cha ge densi y (qe) which is desc ibed by he Poisson equa ion
ðe~
EÞ¼qe;(1)
012817-2 Ng e al. Biomic o luidics 6, 012817 (2012)
whe e eis he pe mi i i y and ~
E¼ /is he elec ic ield. The mo emen o he ions in he
solu ion will cons i u e o an elec ical cu en
~
J¼Xqinili~
EqiDi niþqini~
V

;(2)
whe e qi(¼zie, wi h zi he ionic alence and e he elemen a y cha ge) is he ion cha ge, niis
he ion numbe densi y, li(¼zieD
i=kT) is he mobili y, Diis he di usion coe icien , and ~
Vis
he eloci y. The i s , second, and hi d e ms ep esen , espec i ely, elec omig a ion (i.e.,
conduc ion), di usion, and con ec ion. Typically o elec oly es, he con ec i e cu en qini~
V
is usually smalle han he conduc ion cu en qiniliEwhich is go e ned by he elec ical Reyn-
olds numbe .
25
In mic osys ems, he elec ical Reynolds numbe is e y small o elec oly e.
Fo semi-insula ing liquids, a conduc i i y smalle han 10
9
S/m would be equi ed in o de o
ha e a con ec i e cu en o he same o de han he conduc ion cu en . In addi ion, he a io
o di usi e cu en o elec omig a ion Di ni
jj=jnili~
Ejis smalle han uni y in he liquid
bulk.
25
Typically, o ol age d op in he bulk much g ea e han 0.025 V, di usion is negligible
as compa ed o elec omig a ion. The a io be ween hese wo cu en s is on he o de o
0.025/V. In ou expe imen s, we apply a ound 10 V 0.025 V. In his si ua ion, we can w i e
~
J¼ ~
E, whe e ¼Pqiniliis he elec oly e conduc i i y. Wi h hese app oxima ions, he
cha ge conse a ion equa ion o he AC po en ial becomes
25–27
ðð þiexÞ UÞ¼0;(3)
whe e Uis he phaso o he elec ical po en ial. Conside a bina y elec oly e (ni¼1), assum-
ing elec oneu ali y,
16
he solu ion conduc i i y can be ep esen ed in he model wi h a
con ec ion–di usion equa ion
27–29
@
@ D 2 þð~
V Þ ¼0;(4)
whe e he second and hi d e ms ep esen , espec i ely, di usion and con ec ion.
B. Mechanical equa ions
In a mic oscale sys em, Reynolds numbe is usually small (<1) and low is lamina in na-
u e. The luid eloci y is go e ned by he Na ie -S okes equa ions, o s eady-s a e solu ions,
we ha e
q ð~
V Þ~
V¼ Pþg 2~
Vþ~
Fe;(5)
FIG. 1. Geome ical con igu a ion and bounda y condi ions o he simula ed DC-biased AC-elec okine ics p oblem.
Bounda y condi ions o igh elec ode (conduc i i y:
Righ
, elec ical: V
GND
, low: no slip), le elec ode (conduc i i y:
Le
, elec ical: V
AC
, low: no slip), and channel walls (conduc i i y: insula ion=symme y, elec ical: elec ical insula ion
low: no slip).
012817-3 dc-biased ac-elec okine ic low Biomic o luidics 6, 012817 (2012)
~
V¼0;(6)
whe e q is he luid densi y, Pis he p essu e, gis he dynamic iscosi y, and ~
Feis he elec i-
cal body o ce. The elec ical body o ce on he luid is gi en by he ime-a e age Coulomb
o ce
25–27
~
Fe¼qe~
E

¼1
2Re½qe~
E;(7)
whe e qeis he cha ge densi y phaso , Re[...] ep esen s he eal pa , ~
Eis he complex conju-
ga e o he elec ic ield phaso . In his case, he ime-a e age Coulomb o ce is used in he cal-
cula ion. This is because he ac signals ha e pe iods much sho e han he ypical mechanical
ime o a ia ion o he sys em. Despi e he elec oly e being quasi-elec oneu al, he esidual
cha ge can lead o a signi ican o ce. The cha ge densi y (qe) in he bulk can be ob ained om
Eqs. (1) and (3) leading o a cha ge densi y phaso
26,27
qe¼e
þiex  U:(8)
C. Nume ical me hod and se ings
To sol e o he DC-biased ACEK low, “con ec ion and di usion,” “conduc i e media
DC,” and “incomp essible Na ie -S okes” modules in he COMSOL so wa e we e employed.
COMSOL so wa e employs he ini e elemen me hod (FEM) in sol ing he pa ial di e en ial
equa ions (PDEs). The nume ical scheme disc e izes he de ined spa ial domain in o iangula
ini e elemen s o app oxima e he solu ions o he PDEs. Typical compu a ion consis s o
app oxima ely 1300 iangula elemen s and he minimum elemen quali y is 0.86. Fu he
in es iga ion on he nume ical con e gence was conduc ed. Wi h mesh e inemen up o 5000
o e en 20 000 iangula elemen s, he compu ed eloci y does no change app eciably (less
han 1%).
In he module o “con ec ion and di usion,” cons an conduc i i ies ( 1and 2) we e se
on he wo elec odes and insula ion/symme y on he channel walls. In he module o
“conduc i e media DC,” a ious po en ials we e se on he wo elec odes and elec ical insula-
ion was applied on he channel walls. In he module o “incomp essible Na ie -S okes,” no
slip bounda y condi ions we e se o he elec odes and he channel walls.
In he sol ing p ocess, an i e a i e app oach was adop ed whe e he p oblem was sol ed in
h ee s eps: Fi s , he con ec ion-di usion equa ion was sol ed o he conduc i i y ield,
Eq. (4). Nex , he compu ed conduc i i y solu ion was used o sol e o he elec ical po en ial
ield, Eq. (3). A pa ame ic sol e was adop ed o se he ol age whe e he ol age was
inc eased om ze o o he se ol age le el a a ol age s ep o 0.01 V. Las ly, he compu ed
po en ial solu ion was used o sol e o he elec okine ic low eloci y ield, Eqs. (5) and (6).
The sol ing p ocess was epea ed un il we ob ained a con e ged solu ion whe e he ela i e ol-
e ance is se a 10
3
. The pa ame e s used in he simula ion a e lis ed in Table I.
III. RESULTS AND DISCUSSIONS
A. DC-biased AC-elec okine ic low
Figu e 2shows he simula ed esul s o he eloci y dis ibu ion in he 2D c oss-sec ion
model (W ¼100 lm, D ¼50 lm, elec ode wid h ¼40 lm, and elec ode gap ¼20 lm) o bo h
nega i e and posi i e DC-biased AC-elec okine ic low. The ol age ampli ude used was 10 V
and he conduc i i y le el a he wo elec odes was se wi h a 10% di e ence. In bo h cases, a
single and dominan low o ex was ob ained in he di ec ion om highe conduc i i y (basic,
ca hode) o lowe conduc i i y (acidic, anode). As explained, due o Fa adaic eac ions, a con-
duc i i y g adien is gene a ed om he basic (highe conduc i i y, ne nega i e elec ode) o
012817-4 Ng e al. Biomic o luidics 6, 012817 (2012)
he acidic (lowe conduc i i y, ne posi i e elec ode) domains. When an AC signal is applied,
a ho izon al o ce componen is gene a ed close o he elec ode su ace whe e he ield is
s onges . As such, he luid is ac ua ed om he highe conduc i i y o he lowe conduc i i y
domains close o he su ace o he elec odes; his de e mines he di ec ion o o a ion and
e en ually esul s in a single and dominan o ex o e he elec odes pai .
24
Fo a nega i e DC-bias AC ol age case (see Fig. 2(a)), he luid lows om igh o le ,
i.e., om highe conduc i i y OH
–
ions ich ca hode o lowe conduc i i y H
þ
ions ich anode,
a egion nea he elec odes’ su ace. This low p oduces a esul an clockwise (CW) o ex
o a ion. Fo a posi i e DC-bias AC ol age case (see Fig. 2(b)), he luid lows om le o
igh , i.e., i is s ill lowing om highe conduc i i y OH
–
ions ich ca hode o lowe conduc i -
i y H
þ
ions ich anode, a egion nea he elec odes’ su aces. This low p oduces a esul an
an i-clockwise (an i-CW) o ex o a ion. As such, he p edic ed esul s on he o ex di ec ion
co obo a e he epo ed expe imen al obse a ions.
23,24
TABLE I. Simula ion pa ame e s.
P ope y Value
Fluid densi y (q)110
3
kg=m
3
Fluid dynamic iscosi y (g)110
3
kg=ms
Rela i e pe mi i i y o KCl (e )80
Pe mi i i y o ee space (e0) 8.85 10
12
F=m
Coe icien o di usion (D)110
9
m
2
=s
Vol age ampli ude (V) 1–20 V
AC equency ( ) 100 kHz
Conduc i i y a elec ode 1 ( 1) 1–10 mS=m
Conduc i i y a elec ode 2 ( 2) 1–10 mS=m
FIG. 2. Simula ed eloci y dis ibu ions. (a) Nega i e DC-bias, 1< 2and (b) posi i e DC-bias, 1> 2. Condi ions: ol -
age ampli ude ¼10 V, conduc i i y di e ence ¼10%, W ¼100 lm, D ¼50 lm, elec ode wid h ¼40 lm, and elec ode
gap ¼20 lm. Fo nega i e DC-bias o (a), plo s o X- eloci y (ho izon al) ac oss (c) channel dep h a a ious loca ions
along he le elec ode, and (d) channel wid h a di e en channel heigh s.
012817-5 dc-biased ac-elec okine ic low Biomic o luidics 6, 012817 (2012)

In gene al, he nega i e and he posi i e DC-bias simula ed esul s a e simila and symme -
ical. The x- eloci ies (Vx) o he simula ed esul s o he nega i e DC-biased case (Fig. 2(a))
we e ex ac ed and plo ed. The ho izon al eloci ies we e plo ed ac oss he wid h and ac oss
he dep h a di e en loca ions on he channel as shown in Figs. 2(c) and 2(d), espec i ely.
F om Figs. 2(c) and 2(d), i can be obse ed ha Vxa e as e on he egion nea e o he
elec ode su ace. This is expec ed as he eloci y is d i en by he g adien s o conduc i i y and
he elec ical po en ial, whe e he conduc i i y and he elec ic ield a e he s onges nea he
su ace a he elec ode gap.
Taking he poin whe e Vx¼0 along he cen e o he channel (y ¼0) as he cen e o he
o ex; he cen e o o ex is a a heigh o 20 lm. This co esponds o 40% (i.e., 20 lm/
50 lm) o he o al channel heigh . De ining H
as he pe cen age o he o ex heigh o he
channel dep h (D), he H
alue compu ed is hus a he high a 40%. Simila ly, we ha e
p e iously epo ed an obse ed high H
alue (>30%) by expe imen al imaging he induced
DC-biased ACEK low o ex.
24
This high cen e o o ex implies ha he low mechanism is
bulk d i en. In he li e a u e, ACET low which is bulk induced gene ally has a o ex cen e
be ween 30% and 40% o he channel heigh .
14–16
B. E ec o ol age and conduc i i y a io
The applied ol age and he conduc i i y a io a ec he eloci ies o he low induced in
he sys em. He e, he conduc i i y a io (c) is de ined as he a io o he highe conduc i i y
( 2) o he lowe conduc i i y ( 1). To quan i y he eloci ies o he low a a ious condi ions
( ol age, conduc i i y a io), he a e age eloci y ampli ude in he c oss-sec ion domain was
compu ed and de ined as
27
Va e ¼1
AððVdxdy;(9)
whe e V¼jVðx;yÞj is he eloci y ampli ude a ðx;yÞand A(m
2
) is he a ea o he c oss-
sec ion domain. Simila ly, he adop ed geome y o be s udy we e W ¼100 lm, D ¼50 lm,
elec ode wid h ¼40 lm, and elec ode gap ¼20 lm. The a e age eloci y ampli udes o nega-
i e DC-bias a di e en pa ame e s ( ol age, conduc i i y a io) we e calcula ed and p esen ed
in Fig. 3.
Figu e 3(a) shows ha he a e age eloci y ampli udes inc ease wi h he applied ol age a
a ious conduc i i y a ios. The highes eloci ies ob ained o c¼1.1, 1.3, and 1.5 a 20 V
we e 2.78 mm/s, 7.64 mm/s, and 11.78 mm/s, espec i ely. Nex , by ixing he ol age ampli ude
a 10 V, he e ec o conduc i i y a io on eloci y was in es iga ed. Figu e 3depic s esul s
o a ious conduc i i y a ios. I indica es a clea end ha a highe applied ol age and/o
highe conduc i i y a io will esul in a as e low eloci y. F om Fig. 3(a), he simula ed
eloci y a 10 V and c¼1.1 is 695 lm/s, which compa es a o ably wi h he expe imen al
measu ed eloci y o 700 lm/s.
24
I should be no ed ha he conduc i i y g adien / a io gene a ed by he DC-bias Fa adaic
cha ging has a limi a ion. This is because elec olysis and elec odes deg ada ion will occu a
oo high ol age. The e o e, he conduc i i y a io ia his me hod is limi ed by he le el o
DC-bias (i.e., <3V
DC
). Ne e heless, o acili a e an unde s anding o mechanism, simula ion
is conduc ed o conduc i i y a io up o 10 which is he ypical a io adop ed in elec okine ic
ins abili y (EKI) low phenomenon.
30–32
F om Fig. 3(d), he achie ed eloci y a 20 V and
c¼10 was ex emely as , 14.44 mm/s. As a compa ison wi h a mo e complex
nume ical model,
33
i was epo ed ha he achie ed eloci y was up o ens o mm/s (i.e., a
0.5 10
5
V/m and c¼10). Thei p edic ed eloci y is o he same o de o magni ude as
ob ained by he cu en model. In addi ion, his esul implies ha apid induced low can be
achie ed by inco po a ing a mic oelec ode (wi h applied AC ol age) wi h manually induced
conduc i i y s eams. Typically, he EKI con igu a ion in oduces he high AC ol age h ough
012817-6 Ng e al. Biomic o luidics 6, 012817 (2012)
bulk elec odes om he ese oi s. In eg a ed mic oelec odes can indeed supply elec ic ield
o he same o de o magni ude (10
4
–10
5
V/m) due o he educed elec odes gap.
C. E ec o channel wid h, dep h, and aspec a io
Channel dimensions can a ec he e ec i eness o luid manipula ion in he mic ochannel.
As such, he e ec s o he channel wid h (W), dep h (D), and aspec a io (i.e., AR ¼D/W) on
he a e age o ex low eloci y (Va e) we e in es iga ed. Simila ly, he elec ode wid h and
gap we e ixed a 40 lm and 20 lm, espec i ely. The ol age ampli ude used was 10 V and
conduc i i y a io was a c¼1.1. Figu e 4(a) shows he a e age eloci y ampli udes (Va e)as
he wid h o he channel (W) a ies om 100 lm o400lm, a ixed dep h o ei he 50 lmo
100 lm. I can be obse ed ha he Va e gene ally dec eases as he W inc eases. This is because
he e is a limi whe e he induced DC-biased ACEK low can d ag he su ounding luids in o
mo ion.
34
The e o e, he e is an op imum ange whe e he luids can be e ec i ely ac ua ed,
de e mined by he d i ing eloci y (i.e., eloci y nea he su ace o he elec odes). As W
inc eases (see Fig. 4(a)), he eloci ies a e only con ined wi hin he cen al egion o he mic o-
channel, and hus, he ac ua ion e icien gene ally dec eases. These indings ha e implica ion
on he design o pump and mixe de ices, as i would be p e e ed o loca e he elec odes in
close p oximi y o he pumping/mixing egion. The inse in Fig. 4(a) shows he co esponding
H
pe cen age o he simula ed da a poin s. The end indica es ha he o ex cen e heigh
s ays ela i ely cons an (28%–40%) o di e en channel wid h (100–400 lm) in es iga ed.
This is because o he ixed channel dep hs (50 lm, 100 lm) adop ed.
Figu e 4(b) shows he a e age eloci y ampli udes (Va e) as he dep h o he channel (D)
a ies om 20 lm o200lm, a a ixed wid h o ei he 100 lm o 200 lm. The a e age eloc-
i y inc eases o a maximum and hen dec eases wi h inc easing channel dep h. I can be
obse ed ha he e is an op imal dep h whe e a maximum a e age eloci y is ob ained. The
maximum eloci ies we e 748 lm/s (a W ¼100 lm, D ¼100 lm, AR ¼1) and 698 lm/s (a
FIG. 3. A e age eloci y ampli ude a di e en (a) applied ol age, (b) conduc i i y a io, up o 1.1, (c) conduc i i y a io,
up o 2, and (d) conduc i i y a io, up o 10. Con igu a ions: W ¼100 lm, D ¼50 lm, elec ode wid h ¼40 lm, and elec-
ode gap ¼20 lm.
012817-7 dc-biased ac-elec okine ic low Biomic o luidics 6, 012817 (2012)
W¼200 lm, D ¼150 lm, AR ¼3/4) o he ixed wid hs in es iga ed. No e ha when he
c oss-sec ion is la ge, he luid eloci y does no ex end e y a om he gap be ween elec o-
des. This means ha he a e age eloci y should dec ease, since egions a om he gap has
e y small eloci y. I he c oss-sec ion is small (sho heigh ), he eloci y is educed because
o iscous ic ion wi h he walls. The e o e, he e is a maximum in be ween he wo limi s. In
addi ion, he maximum a e age eloci y gene ally occu s a channel AR close o 1, his gi es
us clue on designing he geome y o he pump wi h be e e iciency. The esul indica es ha
o la ge channel c oss-sec ion (AR 1) he induced low would no ex end a om he elec-
ode su ace, hence will no be e icien . Fo small channel c oss-sec ion (AR 1), he induced
low eloci y is dec eased om expec ed due o iscous ic ion.
Nex , he inse in Fig. 4(a) shows he co esponding H
pe cen age o he simula ed da a
poin s. The H
pe cen age gene ally dec eases wi h inc easing dep h. Simila ly, his is because
he induced DC-biased ACEK low also has a limi in se ing he luids in mo ion in he y-
di ec ion (dep h-wise). In Fig. 4(b), i should be no ed ha o he ixed wid h o 200 lm, he
channel AR <1, and he ob ained H
pe cen age is s ill conside ably high (>23%). Fo he
ixed wid h o 100 lm, as he geome ical con igu a ion changes om a la mic ochannel
(AR <1) o a all mic ochannel (AR >1), a d ama ic d op in he H
pe cen age is obse ed.
This also sugges s ha he design o mic ochannel geome y should adop a squa e (AR ¼1) o
la (AR <1) ype o channel c oss-sec ion o elec okine ic low ac ua ion o be mo e
e ec i e.
FIG. 4. A e age eloci y ampli ude wi h a ying channel (a) wid h, o a ixed dep h o 50 lm o 100 lm, and (b) dep h,
o a ixed wid h o 100 lm o 200 lm. Inse shows H
alue o each da a poin . Condi ions: ol age ampli ude ¼10 V, con-
duc i i y di e ence ¼10% (c¼1.1), elec ode wid h ¼40 lm, and elec ode gap ¼20 lm.
012817-8 Ng e al. Biomic o luidics 6, 012817 (2012)
As obse ed in Fig. 4(b), he channel AR can a ec he manipula ion o luid inside a
mic ochannel. He e, we in es iga e he eloci y o he induced low in a channel o a ious
ARs (1/2, 1/3, 1/4, and 1/5), bu we es ic ed ou s udy o AR <1 ( la mic ochannel), he p e-
e ed channel con igu a ion. Figu e 5shows he a e age eloci y ampli udes in di e en chan-
nel wid hs o a ious cons an channel ARs. Figs. 5(a)–5(d) show he plo s o AR o 1/2, 1/3,
1/4, and 1/5, espec i ely. Wi h a dec ease in AR om 1/2 o 1/5, he Va e gene ally dec eases.
The AR measu es he la ness o he mic ochannel, hus a lowe AR indica es ha W is much
la ge han he D. No e in Fig. 4(a) wi h ixed D, he compu ed a e age eloci y is also ound
o dec ease wi h inc easing W. The e o e, he end in Figs. 4(a) and 5a e he same depic ing a
dec easing AR wi h ixed D and inc easing W.
Typically in such con igu a ion, he induced DC-biased ACEK low has a limi ed ac ua ion
ange as discussed p e iously o Fig. 4(a). I should be no ed ha he H
pe cen age emains
ela i ely high a 27%–39%, 30%–42%, 33%–44%, and 35%–45% o AR o 1/2, 1/3, 1/4,
and 1/5.
IV. CONCLUSIONS
In his pape , a nume ical model desc ibing DC-biased AC-elec okine ic low has been
p esen ed. “Con ec ion and di usion,” “conduc i e media DC,” and “incomp essible Na ie -
S okes” modules we e adop ed in he COMSOL so wa e. The phenomenological model is based
on expe imen ally measu ed conduc i i y g adien gene a ed upon he applica ion o a DC-bias
o one o he elec ode pai s. The simula ed esul s indica e good co ela ion wi h epo ed
expe imen s in e ms o low induced o ex cha ac e is ics, magni ude, and o a ing di ec ion.
I was con i med ha he low di ec ion was om he highe conduc i i y o he lowe conduc-
i i y egions nea he su aces o he elec odes and hus o ming a single and uni ied o ex
ac oss he wid h o he mic ochannel. Pa ame ic s udies we e conduc ed by a ying he ol -
age, conduc i i y a io, channel wid h, dep h and aspec a io. I was ound ha he low eloc-
i y induced in DC-ACEK can each alues in he ange mm/s by selec ing an app op ia ed
highe ol age and conduc i i y a io. In addi ion, i was ound ha mic o channels wi h squa e
dimensions (AR ¼1) a e mo e e icien o op imum low eloci y.
FIG. 5. A e age eloci y ampli ude a di e en channel aspec a ios (a) AR ¼1=2, (b) AR ¼1=3, (c) AR ¼1=4, and (d)
AR ¼1=5. Inse shows H
alue o each da a poin . Condi ions: ol age ampli ude ¼10 V, conduc i i y di e ence ¼10%
(c¼1.1), elec ode wid h ¼40 lm, and elec ode gap ¼20 lm.
012817-9 dc-biased ac-elec okine ic low Biomic o luidics 6, 012817 (2012)