numerical study on the mixing performance of a...
TRANSCRIPT
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Copyright copy 2012 American Scientific PublishersAll rights reservedPrinted in the United States of America
Journal ofNanoscience and Nanotechnology
Vol 12 4523ndash4530 2012
Numerical Study on the Mixing Performance of a
Ring-Type Electroosmotic Micromixer with Different
Obstacle Configurations
Hyeon-Seok Seo1 Bongtae Han2 and Youn-Jea Kim1lowast1School of Mechanical Engineering Sungkyunkwan University 300 Cheoncheon-dong Suwon 440-746 Korea
2Department of Mechanical Engineering University of Maryland College Park Maryland 20740 USA
A new type of electrokinetic micromixer with a ring-type channel is introduced for fast mixing Theproposed mixer takes two fluids from different inlets and combines them in a ring-type mixing cham-ber The fluids enter two different inlets (inner radius 25 m and outer radius 50 m) respectivelyThe total channel length is 500 m and four microelectrodes are positioned on the outer wall of themixing chamber The electric potentials on the four microelectrodes are sinusoidal with time havingvarious maximum values of voltage zeta potential and frequency Also in order to compare themixing performance with different obstacle configurations we performed a numerical analysis usinga commercial code COMSOL The concentration of the dissolved substances in the working fluidand the flow and electric fields in the channel were investigated and the results were graphicallydepicted for various flow and electric conditions
Keywords Micromixer Mixing Performance Zeta Potential Electric Potential
1 INTRODUCTION
The operation of microfluidic-based ducts nozzles valves
etc cannot always be predicted from conventional macro-
scopic flow models such as the Navier-Stokes equations
with the no-slip boundary condition at the fluid-solid inter-
face unlike that of larger flow devices which is predicted
by these models routinely and successfully The pressure
gradient in a long microduct is non-constant and the mea-
sured flow rate is higher than that predicted by the con-
ventional continuum flow model Moreover surface effects
dominate small devices such as MEMS (Micro Electro
Mechanical Systems)-based devices which are used in
microfluidics1
Microfluidics systems have common properties they
work with laminar flows under reduced thermal gradi-
ents and with small samplereagent volumes properties
that promote effective process control and reproducibil-
ity Microfluidic devices with these properties have been
built for lab-on-a-chip applications where the functions
such as separation mixing reaction synthesis and analy-
sis are performed2 This micro device concept and tech-
nology which has developed rapidly is being applied
increasingly in biological and chemical applications3ndash5 the
lowastAuthor to whom correspondence should be addressed
fabrication of hydrogel for drug delivery systems chemi-
cal and enzyme reactions synthesis of nucleic acids and
analysis of DNA (deoxyribonucleic acid) and protein In
most microfluidic applications eg fast chemical reac-
tions DNA separation and amplification the performance
of the microfluidic system is governed by its mixing
efficiency
The rapid and efficient mixing is important for many
microfluidic applications But it is a challenging process in
many microfluidic systems that perform complex chemical
synthesis and analysis Most existing microfluidic mixing
systems are limited flows in the low Reynolds number
regimes According to scaling law decreasing the mixing
path can shorten the mixing time and enhance the mix-
ing quality For this reason it is important to understand
the mixing process in micromixers To do this one must
be able to characterize and evaluate the outcomes of the
mixing process6
Micromixers can be classified into two types passive
and active7ndash10 The operation principles of the passive-type
mixers are mainly based on fluid stretch folding breakup
and molecular diffusion Some passive micromixers reduce
the diffusion path between fluid streams by splitting and
recombining them
Because of the methods that can easily integrate
electrodes into microfluidic and nanofluidic devices
J Nanosci Nanotechnol 2012 Vol 12 No 6 1533-48802012124523008 doi101166jnn20126188 4523
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
electro-kinetically-driven mixing devices are under exten-
sive investigation for use as active micromixers11 Elec-
troosmosis used to generate electrical potential gradients
has been proposed as a propulsion mechanism for bio-
fluids This mechanism would eliminate the need for a
moving apparatus12 The technology of electrokinetically-
driven mixing devices has led to the need for an efficient
fluid control mechanism for micro-fabricated systems that
perform complex chemical synthesis For example local-
ized flow circulations within the bulk flow near regions of
the microchannel wall with oppositely-charged surface het-
erogeneities were investigated and these circulations were
successfully applied to enhance the species mixing in a
T-shaped micro-mixer13 The results indicated that these
heterogeneous regions reduce the required length of the
mixing channel by 70 Sasaki et al14 reported a novel
micromixer based on AC electroosmosis and analyzed its
performance by experiments according to various param-
eters including applied voltage frequency and solution
viscosity Their results were compared with those obtained
from a theoretical model of the AC electroosmosis mixer
The comparison showed that a larger voltage led to more
rapid mixing The results could be used to estimate the
mixing performance of the AC electroosmosis-based mixer
under various experimental conditions They also provided
guidelines on the use of the micromixer in microfluidic
chemical analysis In addition the electroosmotic effect
results in swelling at the cathode side due to water enrich-
ment and shrinkage at the anode side owing to water deple-
tion these phenomena refer to the openclosed control
of IPMC (Ionic Polymer Metal Composite)-based micro-
valve systems15
Bio-fluids which show non-Newtonian fluid flow
behavior are often used in MEMS-fluidics Due to the
Fig 1 Schematic of the modeled electroosmotic micromixer
importance of Bio-MEMS and lab-on-a-chip technolo-
gies many researchers have recently focused on the
non-newtonian fluid behaviors of electrokinetically-driven
bio-fluids16 Das and Chakraborty17 obtained an analyti-
cal solution describing the transport characteristics of a
non-newtonian fluid flow in a rectangular microchannel
under the sole influence of electrokinetic effects As an
illustrative case study they analyzed the flow behavior
of a blood sample Zhao et al18 analyzed the electroo-
somotic flow of power-law fluids in a slit microchannel
by introducing exact and approximate analytical expres-
sions of shear stress effective viscosity and velocity profile
distribution Akgul and Pakdemirli19 presented analytical
and numerical solutions for electroosmotic flow of a third
grade fluid between micro-parallel plates They analyzed
influences of non-newtonian parameters namely the Joule
heating effect viscosity index and electrokinetic effect on
the velocity and temperature profiles of the fluid
In this study the mixing performance of a ring-type
electroosmotic micromixer was numerically investigated
Also the mixing performance of the mixer with different
obstacle configurations in the mixing chamber was exam-
ined by numerical analysis using the commercial code
COMSOL Especially the concentration of the dissolved
substances in the fluid was considered according to volt-
age electrode frequency and zeta potential
2 NUMERICAL DETAILS
21 Governing Equations
The complex flow phenomena in the modeled micromixer
were investigated by numerical methods Two-dimensional
Navier-Stokes equations describing fluid behavior were
employed to simulate the mixing of two aqueous fluids in
4524 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Table I The boundary conditions applied to this study
Inlet velocity Electric potential Zeta potential Frequency
Model [ms] (V0 [V] () [V] [Hz]
Rectangular 200 1 2 minus01 minus005 4 8
the designed channel under unsteady-state conditions A
complete description of time-dependent ICEO (Induced-
Charge Electro Osmosis) at large voltages which is
beyond the scope of this study would be required con-
sidering all of the effects together The approximation of
thin double layers which has been applied mostly to
steady-state problems involving non-polarizable objects
is a good starting point Thus an ICEO slip velocity is
very rapidly established in response to an induced zeta-
potential and lsquoouterrsquo tangential field Furthermore despite
double layer and tangential field gradients the classical
Helmholtz-Smoluchowski formula correctly gives the elec-
troosomotic slip velocity20
Because the electroosomotic flow velocity is indepen-
dent of channel size electroosomotic pumping presents a
natural and popular technique for fluid manipulation in
small channels On the other hand when the solidfluid
interface is that of a freely suspended particle the electroo-
somotic slip velocity gives rise to motion of the particle
itself termed electrophoresis20
Fig 2 Grid systems (a) Circular obstacle and (b) Rectangular obstacle
Fig 3 Streamlines in the mixing chamber with circular obstacle and
one cycle of sine curve for V0 = 1 V f = 4 Hz and =minus01 V (a) 0 s
(b) 00625 s (c) 0125 s and (d) 01875 s
The equations used in the above simulations are shown
as follows
[V
t+ V middotV
]=minusp+ 2V +eE (1)
where is the fluid density V is the fluid velocity p is
the static pressure of the flow is the molecular viscosity
of the fluid e is the charge density of the fluid and E is
the intensity of the applied electric field Under a wide
range of conditions the local slip velocity is given by the
Helmholtz-Smoluchowski equation as
Uslip =minusEx
(2)
where is the relative permittivity is the zeta potential
and Ex is the tangential component of the bulk electric
field
Fig 4 Streamlines in the mixing chamber with rectangular obstacle
and one cycle of sine curve for V0 = 1 V f = 4 Hz and = minus01 V
(a) 0 s (b) 00625 s (c) 0125 s and (d) 01875 s
J Nanosci Nanotechnol 12 4523ndash4530 2012 4525
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
The ions in the diffuse part of the double layer are
approximately in thermal equilibrium and tangential con-
centration gradients modify the usual electroosmotic slip
by changing the bulk electric field (concentration polariza-
tion) and by producing diffusion osmotic slip20 We can
express the balance equation for the current density with
Ohmrsquos law as
middot minusV = 0 (3)
where denotes the conductivity of solution
In addition the following convection-diffusion equation
describes the concentration of the dissolved substances in
the fluidc
t+ middot minusDc= Rminusu middotc (4)
where c is the concentration D is the diffusion coeffi-
cient and R is the reaction rate pertaining to the working
fluid When R= 0 the concentration is not affected by any
reactions
Fig 5 Concentration distributions in the modeled micromixer with circular obstacle (a) f = 4 Hz =minus01 V t = 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
The mixing efficiency (m applied to this study is
defined as follows
m equiv(1minus
int cminus cdxint c0minus cdx)times100 (5)
where c is the concentration value of outlet c0 is the initialconcentration value before mixing both of working flu-
ids and c is the completely mixed concentration value
respectively
22 Model and Grid Systems
Figure 1 shows the schematic of an electroosmotic mixer
The mixer takes two fluids from different inlets of 25 min size respectively and combines them into a sin-
gle channel that is 50 m wide The fluids then enter
the central loop where four microelectrodes are posi-
tioned along the outer wall of the loop These micro-
electrodes impose a spatially-varying electric field and
the fluids are manipulated via the electroosmotic slip
4526 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
boundary condition before they enter the outlet channel
The electric potentials produced by the microelectrodes
are time-dependent so the fluids are mixed chaotically
in the mixing chamber In this study we performed a
two dimensional numerical analysis using the commercial
code COMSOL
The electric potentials produced by the four microelec-
trodes produced a time-dependent sinusoidal electric field
for the maximum applied voltages of 2 V and 8 Hz Details
of boundary condition applied to this study are shown in
Table I The potentials of electrodes 1 and 3 were denoted
as V0 sin (213ft and the potentials of electrodes 2 and
4 were minusV0 sin (213ft The working fluid was an elec-
trolyte that possessed the same properties as water ie
it had a relative permittivity of = 783 a conductivity
of an ionic solution of = 011845 Sm and a diffu-
sion coefficient of D= 10minus11 m2s The inlet fluid velocity
was described by a parabolic graph with a mean value of
200 ms (Pe= 7times10minus2 Re= 1times10minus2 and the inletupper
Fig 6 Concentration distributions in the modeled micromixer with rectangular obstacle (a) f = 4 Hz =minus01 V t= 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
and inletlower concentration values were 1 and 0 molm3
respectively The time scale of the transient effect in the
micromixer was set to 012560 s and the total calculation
time was 3 s
In order to investigate the simultaneous effects of
electroosmotic flow and convection-diffusion in the mix-
ing chamber two-dimensional unstructured grids contain-
ing approximately 40000 elements were generated using
COMSOL preprocessor as shown in Figure 2 Especially
a non-uniform grid mesh which is thinner in vicinity of
walls has been used to increase the accuracy of the results
The convergence criteria have been satisfied when the
maximum mass residuals of the grid control volume has
been less than about 10minus7
3 RESULTS AND DISCUSSION
Effective mixing basically involves repeated combinations
of stretching and folding of fluid elements and small
J Nanosci Nanotechnol 12 4523ndash4530 2012 4527
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
scale diffusion Results of the streamlines for two dif-
ferent obstacle configurations in the mixing chamber for
V0 = 1 V f = 4 Hz and =minus01 V are shown in Figures 3
and 4 for one cycle of the sine curve In both cases the
streamlines show similar flow patterns They were influ-
enced by the electric fields that were produced by the indi-
vidual electrodes Also eddy flows were formed around
the electrodes in the mixing chamber The fluid particles
that stayed in the central loop stretched and folded for a
long time before they entered the outlet channel These
flow patterns are corresponded with those by Hadigol
et al16 which were performed numerically applied to elec-
troosmotic effect in the microchannel with based on phys-
ical properties of the water This fact indicated a chaotic
advection which in turn expedited the final part of mixing
through molecular diffusion
The concentration distributions in the modeled
micromixer for the two different obstacle configurations
are shown in Figures 5 and 6 It is seen that the perturbed
flows continuously moved along the mixing chamber
and the mixing improved everywhere in the modeled
micromixer because of the stretching and folding behav-
iors of the fluid particles which was induced by the
applied electric field Results also showed that the mixing
Fig 7 Concentration profiles along the horizontal direction of the modeled micromixer from the mixing chamber to the outlet for various conditions
at t = 25 s (a) f = 4 Hz =minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
performance was influenced by the frequency of elec-
tric field and the zeta potential The decreases of the
frequency and the increases zeta potential improved the
mixing efficiency But from the viewpoint of fluid flow
the streamline produced by the circular obstacle in the
mixing chamber was smoother than that produced by the
rectangular one This is because the fluid flow correspond-
ing to the rectangular obstacle in the mixing chamber was
affected by the resistance between it and the surface of the
obstacle
In order to evaluate the mixing performance for two
different obstacle configurations at various values of volt-
ages frequency and zeta potential we set up the data
line in the modeled micromixer as shown in Figure 1
The dissolved-substances concentration data was obtained
along the width line of the outlet region and also from
the centerline along the horizontal direction of the mixing
chamber
Figure 7 shows the concentration profiles along the hor-
izontal direction of the modeled micromixer from the mix-
ing chamber to the outlet for various conditions at t= 25 sThe concentration efficiency reaches over 90 in all cases
which means that each fluid was sufficiently mixed and
moved toward the exit of the micromixer In particular the
4528 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
electro-kinetically-driven mixing devices are under exten-
sive investigation for use as active micromixers11 Elec-
troosmosis used to generate electrical potential gradients
has been proposed as a propulsion mechanism for bio-
fluids This mechanism would eliminate the need for a
moving apparatus12 The technology of electrokinetically-
driven mixing devices has led to the need for an efficient
fluid control mechanism for micro-fabricated systems that
perform complex chemical synthesis For example local-
ized flow circulations within the bulk flow near regions of
the microchannel wall with oppositely-charged surface het-
erogeneities were investigated and these circulations were
successfully applied to enhance the species mixing in a
T-shaped micro-mixer13 The results indicated that these
heterogeneous regions reduce the required length of the
mixing channel by 70 Sasaki et al14 reported a novel
micromixer based on AC electroosmosis and analyzed its
performance by experiments according to various param-
eters including applied voltage frequency and solution
viscosity Their results were compared with those obtained
from a theoretical model of the AC electroosmosis mixer
The comparison showed that a larger voltage led to more
rapid mixing The results could be used to estimate the
mixing performance of the AC electroosmosis-based mixer
under various experimental conditions They also provided
guidelines on the use of the micromixer in microfluidic
chemical analysis In addition the electroosmotic effect
results in swelling at the cathode side due to water enrich-
ment and shrinkage at the anode side owing to water deple-
tion these phenomena refer to the openclosed control
of IPMC (Ionic Polymer Metal Composite)-based micro-
valve systems15
Bio-fluids which show non-Newtonian fluid flow
behavior are often used in MEMS-fluidics Due to the
Fig 1 Schematic of the modeled electroosmotic micromixer
importance of Bio-MEMS and lab-on-a-chip technolo-
gies many researchers have recently focused on the
non-newtonian fluid behaviors of electrokinetically-driven
bio-fluids16 Das and Chakraborty17 obtained an analyti-
cal solution describing the transport characteristics of a
non-newtonian fluid flow in a rectangular microchannel
under the sole influence of electrokinetic effects As an
illustrative case study they analyzed the flow behavior
of a blood sample Zhao et al18 analyzed the electroo-
somotic flow of power-law fluids in a slit microchannel
by introducing exact and approximate analytical expres-
sions of shear stress effective viscosity and velocity profile
distribution Akgul and Pakdemirli19 presented analytical
and numerical solutions for electroosmotic flow of a third
grade fluid between micro-parallel plates They analyzed
influences of non-newtonian parameters namely the Joule
heating effect viscosity index and electrokinetic effect on
the velocity and temperature profiles of the fluid
In this study the mixing performance of a ring-type
electroosmotic micromixer was numerically investigated
Also the mixing performance of the mixer with different
obstacle configurations in the mixing chamber was exam-
ined by numerical analysis using the commercial code
COMSOL Especially the concentration of the dissolved
substances in the fluid was considered according to volt-
age electrode frequency and zeta potential
2 NUMERICAL DETAILS
21 Governing Equations
The complex flow phenomena in the modeled micromixer
were investigated by numerical methods Two-dimensional
Navier-Stokes equations describing fluid behavior were
employed to simulate the mixing of two aqueous fluids in
4524 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Table I The boundary conditions applied to this study
Inlet velocity Electric potential Zeta potential Frequency
Model [ms] (V0 [V] () [V] [Hz]
Rectangular 200 1 2 minus01 minus005 4 8
the designed channel under unsteady-state conditions A
complete description of time-dependent ICEO (Induced-
Charge Electro Osmosis) at large voltages which is
beyond the scope of this study would be required con-
sidering all of the effects together The approximation of
thin double layers which has been applied mostly to
steady-state problems involving non-polarizable objects
is a good starting point Thus an ICEO slip velocity is
very rapidly established in response to an induced zeta-
potential and lsquoouterrsquo tangential field Furthermore despite
double layer and tangential field gradients the classical
Helmholtz-Smoluchowski formula correctly gives the elec-
troosomotic slip velocity20
Because the electroosomotic flow velocity is indepen-
dent of channel size electroosomotic pumping presents a
natural and popular technique for fluid manipulation in
small channels On the other hand when the solidfluid
interface is that of a freely suspended particle the electroo-
somotic slip velocity gives rise to motion of the particle
itself termed electrophoresis20
Fig 2 Grid systems (a) Circular obstacle and (b) Rectangular obstacle
Fig 3 Streamlines in the mixing chamber with circular obstacle and
one cycle of sine curve for V0 = 1 V f = 4 Hz and =minus01 V (a) 0 s
(b) 00625 s (c) 0125 s and (d) 01875 s
The equations used in the above simulations are shown
as follows
[V
t+ V middotV
]=minusp+ 2V +eE (1)
where is the fluid density V is the fluid velocity p is
the static pressure of the flow is the molecular viscosity
of the fluid e is the charge density of the fluid and E is
the intensity of the applied electric field Under a wide
range of conditions the local slip velocity is given by the
Helmholtz-Smoluchowski equation as
Uslip =minusEx
(2)
where is the relative permittivity is the zeta potential
and Ex is the tangential component of the bulk electric
field
Fig 4 Streamlines in the mixing chamber with rectangular obstacle
and one cycle of sine curve for V0 = 1 V f = 4 Hz and = minus01 V
(a) 0 s (b) 00625 s (c) 0125 s and (d) 01875 s
J Nanosci Nanotechnol 12 4523ndash4530 2012 4525
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
The ions in the diffuse part of the double layer are
approximately in thermal equilibrium and tangential con-
centration gradients modify the usual electroosmotic slip
by changing the bulk electric field (concentration polariza-
tion) and by producing diffusion osmotic slip20 We can
express the balance equation for the current density with
Ohmrsquos law as
middot minusV = 0 (3)
where denotes the conductivity of solution
In addition the following convection-diffusion equation
describes the concentration of the dissolved substances in
the fluidc
t+ middot minusDc= Rminusu middotc (4)
where c is the concentration D is the diffusion coeffi-
cient and R is the reaction rate pertaining to the working
fluid When R= 0 the concentration is not affected by any
reactions
Fig 5 Concentration distributions in the modeled micromixer with circular obstacle (a) f = 4 Hz =minus01 V t = 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
The mixing efficiency (m applied to this study is
defined as follows
m equiv(1minus
int cminus cdxint c0minus cdx)times100 (5)
where c is the concentration value of outlet c0 is the initialconcentration value before mixing both of working flu-
ids and c is the completely mixed concentration value
respectively
22 Model and Grid Systems
Figure 1 shows the schematic of an electroosmotic mixer
The mixer takes two fluids from different inlets of 25 min size respectively and combines them into a sin-
gle channel that is 50 m wide The fluids then enter
the central loop where four microelectrodes are posi-
tioned along the outer wall of the loop These micro-
electrodes impose a spatially-varying electric field and
the fluids are manipulated via the electroosmotic slip
4526 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
boundary condition before they enter the outlet channel
The electric potentials produced by the microelectrodes
are time-dependent so the fluids are mixed chaotically
in the mixing chamber In this study we performed a
two dimensional numerical analysis using the commercial
code COMSOL
The electric potentials produced by the four microelec-
trodes produced a time-dependent sinusoidal electric field
for the maximum applied voltages of 2 V and 8 Hz Details
of boundary condition applied to this study are shown in
Table I The potentials of electrodes 1 and 3 were denoted
as V0 sin (213ft and the potentials of electrodes 2 and
4 were minusV0 sin (213ft The working fluid was an elec-
trolyte that possessed the same properties as water ie
it had a relative permittivity of = 783 a conductivity
of an ionic solution of = 011845 Sm and a diffu-
sion coefficient of D= 10minus11 m2s The inlet fluid velocity
was described by a parabolic graph with a mean value of
200 ms (Pe= 7times10minus2 Re= 1times10minus2 and the inletupper
Fig 6 Concentration distributions in the modeled micromixer with rectangular obstacle (a) f = 4 Hz =minus01 V t= 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
and inletlower concentration values were 1 and 0 molm3
respectively The time scale of the transient effect in the
micromixer was set to 012560 s and the total calculation
time was 3 s
In order to investigate the simultaneous effects of
electroosmotic flow and convection-diffusion in the mix-
ing chamber two-dimensional unstructured grids contain-
ing approximately 40000 elements were generated using
COMSOL preprocessor as shown in Figure 2 Especially
a non-uniform grid mesh which is thinner in vicinity of
walls has been used to increase the accuracy of the results
The convergence criteria have been satisfied when the
maximum mass residuals of the grid control volume has
been less than about 10minus7
3 RESULTS AND DISCUSSION
Effective mixing basically involves repeated combinations
of stretching and folding of fluid elements and small
J Nanosci Nanotechnol 12 4523ndash4530 2012 4527
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
scale diffusion Results of the streamlines for two dif-
ferent obstacle configurations in the mixing chamber for
V0 = 1 V f = 4 Hz and =minus01 V are shown in Figures 3
and 4 for one cycle of the sine curve In both cases the
streamlines show similar flow patterns They were influ-
enced by the electric fields that were produced by the indi-
vidual electrodes Also eddy flows were formed around
the electrodes in the mixing chamber The fluid particles
that stayed in the central loop stretched and folded for a
long time before they entered the outlet channel These
flow patterns are corresponded with those by Hadigol
et al16 which were performed numerically applied to elec-
troosmotic effect in the microchannel with based on phys-
ical properties of the water This fact indicated a chaotic
advection which in turn expedited the final part of mixing
through molecular diffusion
The concentration distributions in the modeled
micromixer for the two different obstacle configurations
are shown in Figures 5 and 6 It is seen that the perturbed
flows continuously moved along the mixing chamber
and the mixing improved everywhere in the modeled
micromixer because of the stretching and folding behav-
iors of the fluid particles which was induced by the
applied electric field Results also showed that the mixing
Fig 7 Concentration profiles along the horizontal direction of the modeled micromixer from the mixing chamber to the outlet for various conditions
at t = 25 s (a) f = 4 Hz =minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
performance was influenced by the frequency of elec-
tric field and the zeta potential The decreases of the
frequency and the increases zeta potential improved the
mixing efficiency But from the viewpoint of fluid flow
the streamline produced by the circular obstacle in the
mixing chamber was smoother than that produced by the
rectangular one This is because the fluid flow correspond-
ing to the rectangular obstacle in the mixing chamber was
affected by the resistance between it and the surface of the
obstacle
In order to evaluate the mixing performance for two
different obstacle configurations at various values of volt-
ages frequency and zeta potential we set up the data
line in the modeled micromixer as shown in Figure 1
The dissolved-substances concentration data was obtained
along the width line of the outlet region and also from
the centerline along the horizontal direction of the mixing
chamber
Figure 7 shows the concentration profiles along the hor-
izontal direction of the modeled micromixer from the mix-
ing chamber to the outlet for various conditions at t= 25 sThe concentration efficiency reaches over 90 in all cases
which means that each fluid was sufficiently mixed and
moved toward the exit of the micromixer In particular the
4528 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Table I The boundary conditions applied to this study
Inlet velocity Electric potential Zeta potential Frequency
Model [ms] (V0 [V] () [V] [Hz]
Rectangular 200 1 2 minus01 minus005 4 8
the designed channel under unsteady-state conditions A
complete description of time-dependent ICEO (Induced-
Charge Electro Osmosis) at large voltages which is
beyond the scope of this study would be required con-
sidering all of the effects together The approximation of
thin double layers which has been applied mostly to
steady-state problems involving non-polarizable objects
is a good starting point Thus an ICEO slip velocity is
very rapidly established in response to an induced zeta-
potential and lsquoouterrsquo tangential field Furthermore despite
double layer and tangential field gradients the classical
Helmholtz-Smoluchowski formula correctly gives the elec-
troosomotic slip velocity20
Because the electroosomotic flow velocity is indepen-
dent of channel size electroosomotic pumping presents a
natural and popular technique for fluid manipulation in
small channels On the other hand when the solidfluid
interface is that of a freely suspended particle the electroo-
somotic slip velocity gives rise to motion of the particle
itself termed electrophoresis20
Fig 2 Grid systems (a) Circular obstacle and (b) Rectangular obstacle
Fig 3 Streamlines in the mixing chamber with circular obstacle and
one cycle of sine curve for V0 = 1 V f = 4 Hz and =minus01 V (a) 0 s
(b) 00625 s (c) 0125 s and (d) 01875 s
The equations used in the above simulations are shown
as follows
[V
t+ V middotV
]=minusp+ 2V +eE (1)
where is the fluid density V is the fluid velocity p is
the static pressure of the flow is the molecular viscosity
of the fluid e is the charge density of the fluid and E is
the intensity of the applied electric field Under a wide
range of conditions the local slip velocity is given by the
Helmholtz-Smoluchowski equation as
Uslip =minusEx
(2)
where is the relative permittivity is the zeta potential
and Ex is the tangential component of the bulk electric
field
Fig 4 Streamlines in the mixing chamber with rectangular obstacle
and one cycle of sine curve for V0 = 1 V f = 4 Hz and = minus01 V
(a) 0 s (b) 00625 s (c) 0125 s and (d) 01875 s
J Nanosci Nanotechnol 12 4523ndash4530 2012 4525
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
The ions in the diffuse part of the double layer are
approximately in thermal equilibrium and tangential con-
centration gradients modify the usual electroosmotic slip
by changing the bulk electric field (concentration polariza-
tion) and by producing diffusion osmotic slip20 We can
express the balance equation for the current density with
Ohmrsquos law as
middot minusV = 0 (3)
where denotes the conductivity of solution
In addition the following convection-diffusion equation
describes the concentration of the dissolved substances in
the fluidc
t+ middot minusDc= Rminusu middotc (4)
where c is the concentration D is the diffusion coeffi-
cient and R is the reaction rate pertaining to the working
fluid When R= 0 the concentration is not affected by any
reactions
Fig 5 Concentration distributions in the modeled micromixer with circular obstacle (a) f = 4 Hz =minus01 V t = 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
The mixing efficiency (m applied to this study is
defined as follows
m equiv(1minus
int cminus cdxint c0minus cdx)times100 (5)
where c is the concentration value of outlet c0 is the initialconcentration value before mixing both of working flu-
ids and c is the completely mixed concentration value
respectively
22 Model and Grid Systems
Figure 1 shows the schematic of an electroosmotic mixer
The mixer takes two fluids from different inlets of 25 min size respectively and combines them into a sin-
gle channel that is 50 m wide The fluids then enter
the central loop where four microelectrodes are posi-
tioned along the outer wall of the loop These micro-
electrodes impose a spatially-varying electric field and
the fluids are manipulated via the electroosmotic slip
4526 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
boundary condition before they enter the outlet channel
The electric potentials produced by the microelectrodes
are time-dependent so the fluids are mixed chaotically
in the mixing chamber In this study we performed a
two dimensional numerical analysis using the commercial
code COMSOL
The electric potentials produced by the four microelec-
trodes produced a time-dependent sinusoidal electric field
for the maximum applied voltages of 2 V and 8 Hz Details
of boundary condition applied to this study are shown in
Table I The potentials of electrodes 1 and 3 were denoted
as V0 sin (213ft and the potentials of electrodes 2 and
4 were minusV0 sin (213ft The working fluid was an elec-
trolyte that possessed the same properties as water ie
it had a relative permittivity of = 783 a conductivity
of an ionic solution of = 011845 Sm and a diffu-
sion coefficient of D= 10minus11 m2s The inlet fluid velocity
was described by a parabolic graph with a mean value of
200 ms (Pe= 7times10minus2 Re= 1times10minus2 and the inletupper
Fig 6 Concentration distributions in the modeled micromixer with rectangular obstacle (a) f = 4 Hz =minus01 V t= 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
and inletlower concentration values were 1 and 0 molm3
respectively The time scale of the transient effect in the
micromixer was set to 012560 s and the total calculation
time was 3 s
In order to investigate the simultaneous effects of
electroosmotic flow and convection-diffusion in the mix-
ing chamber two-dimensional unstructured grids contain-
ing approximately 40000 elements were generated using
COMSOL preprocessor as shown in Figure 2 Especially
a non-uniform grid mesh which is thinner in vicinity of
walls has been used to increase the accuracy of the results
The convergence criteria have been satisfied when the
maximum mass residuals of the grid control volume has
been less than about 10minus7
3 RESULTS AND DISCUSSION
Effective mixing basically involves repeated combinations
of stretching and folding of fluid elements and small
J Nanosci Nanotechnol 12 4523ndash4530 2012 4527
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
scale diffusion Results of the streamlines for two dif-
ferent obstacle configurations in the mixing chamber for
V0 = 1 V f = 4 Hz and =minus01 V are shown in Figures 3
and 4 for one cycle of the sine curve In both cases the
streamlines show similar flow patterns They were influ-
enced by the electric fields that were produced by the indi-
vidual electrodes Also eddy flows were formed around
the electrodes in the mixing chamber The fluid particles
that stayed in the central loop stretched and folded for a
long time before they entered the outlet channel These
flow patterns are corresponded with those by Hadigol
et al16 which were performed numerically applied to elec-
troosmotic effect in the microchannel with based on phys-
ical properties of the water This fact indicated a chaotic
advection which in turn expedited the final part of mixing
through molecular diffusion
The concentration distributions in the modeled
micromixer for the two different obstacle configurations
are shown in Figures 5 and 6 It is seen that the perturbed
flows continuously moved along the mixing chamber
and the mixing improved everywhere in the modeled
micromixer because of the stretching and folding behav-
iors of the fluid particles which was induced by the
applied electric field Results also showed that the mixing
Fig 7 Concentration profiles along the horizontal direction of the modeled micromixer from the mixing chamber to the outlet for various conditions
at t = 25 s (a) f = 4 Hz =minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
performance was influenced by the frequency of elec-
tric field and the zeta potential The decreases of the
frequency and the increases zeta potential improved the
mixing efficiency But from the viewpoint of fluid flow
the streamline produced by the circular obstacle in the
mixing chamber was smoother than that produced by the
rectangular one This is because the fluid flow correspond-
ing to the rectangular obstacle in the mixing chamber was
affected by the resistance between it and the surface of the
obstacle
In order to evaluate the mixing performance for two
different obstacle configurations at various values of volt-
ages frequency and zeta potential we set up the data
line in the modeled micromixer as shown in Figure 1
The dissolved-substances concentration data was obtained
along the width line of the outlet region and also from
the centerline along the horizontal direction of the mixing
chamber
Figure 7 shows the concentration profiles along the hor-
izontal direction of the modeled micromixer from the mix-
ing chamber to the outlet for various conditions at t= 25 sThe concentration efficiency reaches over 90 in all cases
which means that each fluid was sufficiently mixed and
moved toward the exit of the micromixer In particular the
4528 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
The ions in the diffuse part of the double layer are
approximately in thermal equilibrium and tangential con-
centration gradients modify the usual electroosmotic slip
by changing the bulk electric field (concentration polariza-
tion) and by producing diffusion osmotic slip20 We can
express the balance equation for the current density with
Ohmrsquos law as
middot minusV = 0 (3)
where denotes the conductivity of solution
In addition the following convection-diffusion equation
describes the concentration of the dissolved substances in
the fluidc
t+ middot minusDc= Rminusu middotc (4)
where c is the concentration D is the diffusion coeffi-
cient and R is the reaction rate pertaining to the working
fluid When R= 0 the concentration is not affected by any
reactions
Fig 5 Concentration distributions in the modeled micromixer with circular obstacle (a) f = 4 Hz =minus01 V t = 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
The mixing efficiency (m applied to this study is
defined as follows
m equiv(1minus
int cminus cdxint c0minus cdx)times100 (5)
where c is the concentration value of outlet c0 is the initialconcentration value before mixing both of working flu-
ids and c is the completely mixed concentration value
respectively
22 Model and Grid Systems
Figure 1 shows the schematic of an electroosmotic mixer
The mixer takes two fluids from different inlets of 25 min size respectively and combines them into a sin-
gle channel that is 50 m wide The fluids then enter
the central loop where four microelectrodes are posi-
tioned along the outer wall of the loop These micro-
electrodes impose a spatially-varying electric field and
the fluids are manipulated via the electroosmotic slip
4526 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
boundary condition before they enter the outlet channel
The electric potentials produced by the microelectrodes
are time-dependent so the fluids are mixed chaotically
in the mixing chamber In this study we performed a
two dimensional numerical analysis using the commercial
code COMSOL
The electric potentials produced by the four microelec-
trodes produced a time-dependent sinusoidal electric field
for the maximum applied voltages of 2 V and 8 Hz Details
of boundary condition applied to this study are shown in
Table I The potentials of electrodes 1 and 3 were denoted
as V0 sin (213ft and the potentials of electrodes 2 and
4 were minusV0 sin (213ft The working fluid was an elec-
trolyte that possessed the same properties as water ie
it had a relative permittivity of = 783 a conductivity
of an ionic solution of = 011845 Sm and a diffu-
sion coefficient of D= 10minus11 m2s The inlet fluid velocity
was described by a parabolic graph with a mean value of
200 ms (Pe= 7times10minus2 Re= 1times10minus2 and the inletupper
Fig 6 Concentration distributions in the modeled micromixer with rectangular obstacle (a) f = 4 Hz =minus01 V t= 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
and inletlower concentration values were 1 and 0 molm3
respectively The time scale of the transient effect in the
micromixer was set to 012560 s and the total calculation
time was 3 s
In order to investigate the simultaneous effects of
electroosmotic flow and convection-diffusion in the mix-
ing chamber two-dimensional unstructured grids contain-
ing approximately 40000 elements were generated using
COMSOL preprocessor as shown in Figure 2 Especially
a non-uniform grid mesh which is thinner in vicinity of
walls has been used to increase the accuracy of the results
The convergence criteria have been satisfied when the
maximum mass residuals of the grid control volume has
been less than about 10minus7
3 RESULTS AND DISCUSSION
Effective mixing basically involves repeated combinations
of stretching and folding of fluid elements and small
J Nanosci Nanotechnol 12 4523ndash4530 2012 4527
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
scale diffusion Results of the streamlines for two dif-
ferent obstacle configurations in the mixing chamber for
V0 = 1 V f = 4 Hz and =minus01 V are shown in Figures 3
and 4 for one cycle of the sine curve In both cases the
streamlines show similar flow patterns They were influ-
enced by the electric fields that were produced by the indi-
vidual electrodes Also eddy flows were formed around
the electrodes in the mixing chamber The fluid particles
that stayed in the central loop stretched and folded for a
long time before they entered the outlet channel These
flow patterns are corresponded with those by Hadigol
et al16 which were performed numerically applied to elec-
troosmotic effect in the microchannel with based on phys-
ical properties of the water This fact indicated a chaotic
advection which in turn expedited the final part of mixing
through molecular diffusion
The concentration distributions in the modeled
micromixer for the two different obstacle configurations
are shown in Figures 5 and 6 It is seen that the perturbed
flows continuously moved along the mixing chamber
and the mixing improved everywhere in the modeled
micromixer because of the stretching and folding behav-
iors of the fluid particles which was induced by the
applied electric field Results also showed that the mixing
Fig 7 Concentration profiles along the horizontal direction of the modeled micromixer from the mixing chamber to the outlet for various conditions
at t = 25 s (a) f = 4 Hz =minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
performance was influenced by the frequency of elec-
tric field and the zeta potential The decreases of the
frequency and the increases zeta potential improved the
mixing efficiency But from the viewpoint of fluid flow
the streamline produced by the circular obstacle in the
mixing chamber was smoother than that produced by the
rectangular one This is because the fluid flow correspond-
ing to the rectangular obstacle in the mixing chamber was
affected by the resistance between it and the surface of the
obstacle
In order to evaluate the mixing performance for two
different obstacle configurations at various values of volt-
ages frequency and zeta potential we set up the data
line in the modeled micromixer as shown in Figure 1
The dissolved-substances concentration data was obtained
along the width line of the outlet region and also from
the centerline along the horizontal direction of the mixing
chamber
Figure 7 shows the concentration profiles along the hor-
izontal direction of the modeled micromixer from the mix-
ing chamber to the outlet for various conditions at t= 25 sThe concentration efficiency reaches over 90 in all cases
which means that each fluid was sufficiently mixed and
moved toward the exit of the micromixer In particular the
4528 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
boundary condition before they enter the outlet channel
The electric potentials produced by the microelectrodes
are time-dependent so the fluids are mixed chaotically
in the mixing chamber In this study we performed a
two dimensional numerical analysis using the commercial
code COMSOL
The electric potentials produced by the four microelec-
trodes produced a time-dependent sinusoidal electric field
for the maximum applied voltages of 2 V and 8 Hz Details
of boundary condition applied to this study are shown in
Table I The potentials of electrodes 1 and 3 were denoted
as V0 sin (213ft and the potentials of electrodes 2 and
4 were minusV0 sin (213ft The working fluid was an elec-
trolyte that possessed the same properties as water ie
it had a relative permittivity of = 783 a conductivity
of an ionic solution of = 011845 Sm and a diffu-
sion coefficient of D= 10minus11 m2s The inlet fluid velocity
was described by a parabolic graph with a mean value of
200 ms (Pe= 7times10minus2 Re= 1times10minus2 and the inletupper
Fig 6 Concentration distributions in the modeled micromixer with rectangular obstacle (a) f = 4 Hz =minus01 V t= 05 s (b) f = 4 Hz =minus01 V
t = 25 s (c) f = 4 Hz =minus005 V t = 05 s (d) f = 4 Hz =minus005 V t = 25 s (e) f = 8 Hz =minus01 V t = 05 s (f) f = 8 Hz =minus01 V
t = 25 s (g) f = 8 Hz =minus005 V t = 05 s and (h) f = 8 Hz =minus005 V t = 25 s
and inletlower concentration values were 1 and 0 molm3
respectively The time scale of the transient effect in the
micromixer was set to 012560 s and the total calculation
time was 3 s
In order to investigate the simultaneous effects of
electroosmotic flow and convection-diffusion in the mix-
ing chamber two-dimensional unstructured grids contain-
ing approximately 40000 elements were generated using
COMSOL preprocessor as shown in Figure 2 Especially
a non-uniform grid mesh which is thinner in vicinity of
walls has been used to increase the accuracy of the results
The convergence criteria have been satisfied when the
maximum mass residuals of the grid control volume has
been less than about 10minus7
3 RESULTS AND DISCUSSION
Effective mixing basically involves repeated combinations
of stretching and folding of fluid elements and small
J Nanosci Nanotechnol 12 4523ndash4530 2012 4527
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
scale diffusion Results of the streamlines for two dif-
ferent obstacle configurations in the mixing chamber for
V0 = 1 V f = 4 Hz and =minus01 V are shown in Figures 3
and 4 for one cycle of the sine curve In both cases the
streamlines show similar flow patterns They were influ-
enced by the electric fields that were produced by the indi-
vidual electrodes Also eddy flows were formed around
the electrodes in the mixing chamber The fluid particles
that stayed in the central loop stretched and folded for a
long time before they entered the outlet channel These
flow patterns are corresponded with those by Hadigol
et al16 which were performed numerically applied to elec-
troosmotic effect in the microchannel with based on phys-
ical properties of the water This fact indicated a chaotic
advection which in turn expedited the final part of mixing
through molecular diffusion
The concentration distributions in the modeled
micromixer for the two different obstacle configurations
are shown in Figures 5 and 6 It is seen that the perturbed
flows continuously moved along the mixing chamber
and the mixing improved everywhere in the modeled
micromixer because of the stretching and folding behav-
iors of the fluid particles which was induced by the
applied electric field Results also showed that the mixing
Fig 7 Concentration profiles along the horizontal direction of the modeled micromixer from the mixing chamber to the outlet for various conditions
at t = 25 s (a) f = 4 Hz =minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
performance was influenced by the frequency of elec-
tric field and the zeta potential The decreases of the
frequency and the increases zeta potential improved the
mixing efficiency But from the viewpoint of fluid flow
the streamline produced by the circular obstacle in the
mixing chamber was smoother than that produced by the
rectangular one This is because the fluid flow correspond-
ing to the rectangular obstacle in the mixing chamber was
affected by the resistance between it and the surface of the
obstacle
In order to evaluate the mixing performance for two
different obstacle configurations at various values of volt-
ages frequency and zeta potential we set up the data
line in the modeled micromixer as shown in Figure 1
The dissolved-substances concentration data was obtained
along the width line of the outlet region and also from
the centerline along the horizontal direction of the mixing
chamber
Figure 7 shows the concentration profiles along the hor-
izontal direction of the modeled micromixer from the mix-
ing chamber to the outlet for various conditions at t= 25 sThe concentration efficiency reaches over 90 in all cases
which means that each fluid was sufficiently mixed and
moved toward the exit of the micromixer In particular the
4528 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
scale diffusion Results of the streamlines for two dif-
ferent obstacle configurations in the mixing chamber for
V0 = 1 V f = 4 Hz and =minus01 V are shown in Figures 3
and 4 for one cycle of the sine curve In both cases the
streamlines show similar flow patterns They were influ-
enced by the electric fields that were produced by the indi-
vidual electrodes Also eddy flows were formed around
the electrodes in the mixing chamber The fluid particles
that stayed in the central loop stretched and folded for a
long time before they entered the outlet channel These
flow patterns are corresponded with those by Hadigol
et al16 which were performed numerically applied to elec-
troosmotic effect in the microchannel with based on phys-
ical properties of the water This fact indicated a chaotic
advection which in turn expedited the final part of mixing
through molecular diffusion
The concentration distributions in the modeled
micromixer for the two different obstacle configurations
are shown in Figures 5 and 6 It is seen that the perturbed
flows continuously moved along the mixing chamber
and the mixing improved everywhere in the modeled
micromixer because of the stretching and folding behav-
iors of the fluid particles which was induced by the
applied electric field Results also showed that the mixing
Fig 7 Concentration profiles along the horizontal direction of the modeled micromixer from the mixing chamber to the outlet for various conditions
at t = 25 s (a) f = 4 Hz =minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
performance was influenced by the frequency of elec-
tric field and the zeta potential The decreases of the
frequency and the increases zeta potential improved the
mixing efficiency But from the viewpoint of fluid flow
the streamline produced by the circular obstacle in the
mixing chamber was smoother than that produced by the
rectangular one This is because the fluid flow correspond-
ing to the rectangular obstacle in the mixing chamber was
affected by the resistance between it and the surface of the
obstacle
In order to evaluate the mixing performance for two
different obstacle configurations at various values of volt-
ages frequency and zeta potential we set up the data
line in the modeled micromixer as shown in Figure 1
The dissolved-substances concentration data was obtained
along the width line of the outlet region and also from
the centerline along the horizontal direction of the mixing
chamber
Figure 7 shows the concentration profiles along the hor-
izontal direction of the modeled micromixer from the mix-
ing chamber to the outlet for various conditions at t= 25 sThe concentration efficiency reaches over 90 in all cases
which means that each fluid was sufficiently mixed and
moved toward the exit of the micromixer In particular the
4528 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Seo et al Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer
Fig 8 Concentration profiles along the vertical direction of the outlet region of mixing chamber for various conditions at t = 25 s (a) f = 4 Hz
=minus01 V (b) f = 8 Hz =minus01 V (c) f = 4 Hz =minus005 V and (d) f = 8 Hz =minus005 V
oscillation of flow increases with the increase of frequency
which means that it hinders stable mixing At constant zeta
potential value the concentration distribution is the most
stable for the case of 4 Hz which means that the fluids were
well mixed at the proper frequency rather than at high fre-
quencies At constant frequency the mixing performance
was influenced by the zeta potential value When the elec-
trodes were applied with low voltages the agglomeration of
fluid particle increased with the decrease of the zeta poten-
tial value So we may deduce that the mixing efficiency
with f = 4 Hz and = minus01 V was the most stable com-
pared those of the other cases The concentration value at
the applied voltage of 2 V was higher than that at 1 V
However there was little difference in the mixing efficiency
according to the obstacle configuration
Figure 8 shows the concentration profiles along the ver-
tical direction of the outlet region of the mixing chamber
for various conditions at t = 25 s Numeric number plusmn25
along the horizontal axis denotes the high and low limits of
width (see Fig 1) At the frequency value of 8 Hz the con-
centration distributions indicate a similar pattern through
the channel width in all cases (see Figs 8(b and d)) How-
ever at f = 4 Hz the concentration profiles indicate a
high mixing performance over the channel width and the
mixing efficiency increases about 30 compared with that
of the case of f = 8 Hz (see Figs 8(a and c)) Especially
for the case of f = 4 Hz and = minus01 V the con-
centration distribution is the most stable and the mixing
efficiency remains almost over 85 all over the channel
width Even with the change of the obstacle configuration
the mixing characteristics change very little with respect
to concentration
4 CONCLUSION
An electroosmotic actuated active ring-type micromixer
was designed and investigated numerically for two differ-
ent obstacle configurations in the mixing chamber Of par-
ticular concern was the concentrations of the fluids in each
condition for various values of voltage frequency at the
electrodes and zeta-potential The following conclusions
were obtained
(1) Chaotic behavior was confirmed by the stretching and
folding of the material lines due to the applied electric
fields
(2) In the evaluation of the concentration value accord-
ing to frequency and zeta potential the mixing was the
most active for the case of f = 4 Hz and = minus01 V
J Nanosci Nanotechnol 12 4523ndash4530 2012 4529
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012
Delivered by Ingenta toSung Kyun Kwan University
IP 115145156117Mon 09 Jul 2012 070343
RESEARCH
ARTIC
LE
Numerical Study on the Mixing Performance of a Ring-Type Electroosmotic Micromixer Seo et al
compared with those of the other cases As the applied
voltage at electrodes increased the mixing performance in
the micromixer increased
(3) From the viewpoint of fluid flow the circular obstacle
showed a smoother pattern than the rectangular one but
there was little difference in the mixing efficiency between
the two obstacle configurations
By taking these findings into account one can design
effectively the other types of active micromixer Further
improvements of the mixing efficiency will be possible by
considering a novel design such as locations of electrode
on the obstacle instead of the outer wall of the mixing
chamber
Acknowledgments Financial aid from the Korea
Ministry of Education through the Brain Korea 21
Project [HRD Center for Convergence Mechanical Sys-
tem Design] is gratefully acknowledged The correspond-
ing author (YJK) also acknowledges the financial support
of the Sungkyunkwan University for his sabbatical year
References and Notes
1 M Gad-el-Hak The MEMS Handbook MEMS Introduction and
Fundamentals Taylor amp Francis London (2005)2 H A Stone A D Stroock and A Ajdari Annu Rev Fluid Mech
36 381 (2004)
3 T Khaleque S Abu-Salih J R Saunders and W Moussa
J Nanosci Nanotechnol 11 2470 (2011)4 W Ehrfeld V Hessel and H Lowe Microreactors Wiley-VCH
Boston (2002)5 D R Reyes D Iossifidis P A Auroux and A Manz Anal Chem
74 2623 (2002)6 J Aubin M Ferrando and V Jiricny Chem Eng Sci 65 2065
(2010)7 H H Bau J Zhong and M Yi Sens Actuators B 79 207 (2001)8 L Fu R Yang C Lin and Y Chien Electrophoresis 26 4605
(2005)9 C Hong J Choi and C H Ahn Lab-on-a-Chip 4 109 (2004)
10 S Park J K Kim J Park S Chung C Chung and K J Chang
J Micromech Microeng 14 6 (2004)11 S H Yoon S Kumar G H Kim Y S Choi and T W Kim
J Nanosci Nanotechnol 8 3427 (2008)12 M Longaretti G Marino B Chini J W Jerome and R Sacco
J Nanosci Nanotechnol 8 3686 (2008)13 D Gobby P Angeli and A Gavriilidis J Micromech Microeng
11 126 (2001)14 N Sasaki T Kitamori and H B Kim Anal Sci 26 815 (2010)15 J S Yun K S Yang N J Choi H K Lee S E Moon and D H
Kim J Nanosci Nanotechnol 11 5975 (2011)16 M Hadigol R Nosrati A Nourbakhsh and M Raisee J Non-
Newtonian Fluid Mech 166 965 (2011)17 S Das and S Chakraborty J Anal Chim Acta 559 15 (2006)18 C Zhao E Zholkovskij J H Masliyah and C Yang J Colloid
Interf Sci 326 503 (2008)19 M B Akgul and M Pakdemirli J Non-Linear Mech 43 985
(2008)20 T M Squires and M Z Bazant J Fluid Mech 509 217 (2004)
Received 28 October 2011 Accepted 14 February 2012
4530 J Nanosci Nanotechnol 12 4523ndash4530 2012