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RESEARCH PAPER
Droplet dynamics passing through obstructions in confined
microchannel flow
Changkwon Chung •Misook Lee •Kookheon Char •
Kyung Hyun Ahn •Seung Jong Lee
Received: 19 February 2010 / Accepted: 22 April 2010 / Published online: 7 May 2010
ÓSpringer-Verlag 2010
Abstract Motivated by the previous studies (Lee et al.,
Lab Chip 10:1160–1166, 2010; Link et al., Phys Rev Lett
92:054503-1–054503-4, 2004), the droplet dynamics
passing through obstructions in confined microchannel was
explored both numerically and experimentally. The effects
of obstruction shape (cylinder and square), droplet size,
and capillary number (Ca) on droplet dynamics were
investigated. For the size control, due to an obstruction-
induced droplet breakup, the cylinder obstruction was
found to be advantageous over square type for practical
purposes. The thread breakup was attributed to both normal
and shear components of velocity gradients near the
obstruction, in particular, near the corners of the square. As
a result, the square obstruction was considered to generate
more non-trivial satellite droplets. The droplet size showed
little influence on the droplet dynamics. Considering the
wetting process on the cylinder surface, we explored the
droplet dynamics passing through two successive cylinder
obstructions, where more complicated dynamics was
observed depending on Ca (capillary number *viscous
force / interface tension), cylinder interval, and droplet
size. Here, we propose two requirements for independent
wetting on each cylinder: (i) low Ca droplet should be
manipulated, and (ii) cylinder interval should be larger than
channel width. That is, low Ca droplet could intrude the
region between two cylinders if the cylinder interval was
far enough, while the droplet could not intrude due to
geometric hindrance for close obstructions. In the numer-
ical viewpoint, the proposed requirements were also valid
for multi-cylinder obstructions up to 6. In addition, we
propose a novel design of array structure of cylinders for a
selective wetting, which might be useful to fabricate Janus
particles. We hereby prove by both simulation and exper-
iments that the wetting on the obstruction is controllable by
changing Ca and cylinder design in the multilayer depo-
sition process.
Keywords Droplet microfluidics Droplet flow past
obstructions Multilayer deposition process
Finite element method Front tracking method
1 Introduction
Potentials of lab-on-a-chip technology have been realized
with droplet manipulations in future applications, such as
drug discoveries (Dittrich and Manz 2006), biochemical
assays (Khnouf et al. 2009; Boedicker et al. 2008; Li et al.
2007; Taly et al. 2007; Griffiths and Tawfik 2006; Song
and Ismagilov 2003), photonic crystals (Raven et al. 2006;
Seo et al. 2005), and logic chip devices (Cheow et al. 2007;
Prakash and Gershenfeld 2007). The advantages of low
sample consumption, precise control of reagents, and high
throughput enforce us to expand the applicable scope of
droplet microfluidics from biological assay to tissue engi-
neering, etc. (Huebner et al. 2008; Haeberle and Zengerle
C. Chung K. H. Ahn (&)S. J. Lee
School of Chemical and Biological Engineering, Seoul National
University, Seoul 151-744, Korea
e-mail: ahnnet@snu.ac.kr
M. Lee K. Char
School of Chemical and Biological Engineering, The WCU
Program of Chemical Convergence of Energy and Environment,
Center for Functional Polymer Thin Films, Seoul National
University, Seoul 151-744, Korea
Present Address:
C. Chung
Institute for Chemical Research, Kyoto University, Uji,
Kyoto 611-0011, Japan
123
Microfluid Nanofluid (2010) 9:1151–1163
DOI 10.1007/s10404-010-0636-x
2007). And, it will be essential to understand relevant
physics on droplet microfluidics for various applications.
Droplet manipulation technique can be utilized for
versatile purposes, such as a phase chip (Shim et al. 2007),
Janus particles (Nisisako and Torii 2007; Nie et al. 2006;
Shepherd et al. 2006), etc. (Shah et al. 2008; Teh et al.
2008; Whitesides 2006). For chemical reactions in micro-
channels, several techniques have been proposed, such as
droplet fusion to mix reagents (Liu et al. 2007; Sarrazin
et al. 2006; Song et al. 2006; Kohler et al. 2004), and side
injection of reagents into passing droplets through main
channel (Li et al. 2007). In order to enhance mixing inside
the droplets, use of winding channels (Um et al. 2008;
Bringer et al. 2004), and viscoelastic fluids (Chung et al.
2009c) has also been suggested. A droplet may carry some
materials inside (Abraham et al. 2006; He et al. 2005)or
even smaller droplets, subsequently, multiple emulsions
can be generated with several methods (Nisisako 2008). It
was also reported that a droplet could be used as a
screening device for protein crystallization (Chen et al.
2005; Zheng et al. 2003). In brief, droplet manipulation can
be considered as a core technology for next generation
microfluidic applications.
Droplet manipulations, such as droplet generation,
sorting, merging, and breakup have been developed in
microchannels (Christopher and Anna 2007; Squires and
Quake 2005; Cristini and Tan 2004). Droplets have been
generated in flow-focusing devices (Woodward et al. 2007;
Tan et al. 2006; Yobas et al. 2006; Anna et al. 2003)orby
T-junctions (Priest et al. 2006; Nisisako et al. 2002;
Thorsen et al. 2001). In recent studies, more complicated
designs were proposed for improved manipulation of
droplets. Utilizing the flexibility of PDMS (poly-
dimethylsiloxane) wall, epochal methods of tuning the
direction of main stream and of controlling size of droplets
were presented in modified flow-focusing geometries (Lee
et al. 2007,2009; Lin et al. 2008). In the similar manner,
compressed air was used to break off a thread to generate
droplets in a cross-shaped channel with surface treatment
technique (Su and Lin 2006), or a pneumatic valve was
also utilized to control droplet size in T-junction (Choi
et al. 2010). For droplet fusion in microchannels, several
methods have been proposed using geometrically compli-
cated structures, e.g., a hydrodynamic trap of wide cross-
channel (Tan et al. 2004,2007), a tapered channel (Hung
et al. 2006), a fluid resistance in straight channels (Kohler
et al. 2004), and an array of pillar elements (Niu et al.
2008). For droplet breakup at small scales, electrowetting-
on-dielectric (EWOD) technique was proposed to control
the contact angle of the droplet on the surface as an active
method utilizing the external forces (Cho et al. 2003). As a
passive way, droplet breakup was also introduced at
T-junction or near an obstruction in microchannels (Link
et al. 2004), where controlling the droplet size was possible
by changing the length of each channel in T-junction or
position of the obstruction. Recently, the obstacle-mediated
geometry combined with an alternating droplet generation
was introduced to conduct a multilayer deposition process
(Lee et al. 2010). In order to realize the multilayer depo-
sition in the continuous microfluidic framework gives a
fast, efficient automated way comparing to conventional
batch process (Priest et al. 2008; Kim et al. 2005).
Therefore, it will be necessary to understand relevant
physics on the deposition process where the droplets are
passing through obstructions in confined microchannels.
Motivated by the previous studies (Lee et al. 2010; Link
et al. 2004), here, we explore the dynamics of the droplet
passing through obstructions in the microchannel flow by
conducting both simulation and experiment. In our recent
study (Chung et al. 2009a), the dynamics of droplet passing
through a cylinder obstruction was investigated including
the effect of viscoelasticity of the fluid. In the present
study, we will consider the effect of obstruction shape
(cylinder and square) and design, droplet size, and capillary
number (Ca *viscous force/interface tension) on droplet
dynamics. Also, we predict wetting performance of droplet
fluids on the cylinder surface when successive cylinder
obstructions are considered.
This article is organized as follows: in the next section, a
problem definition and governing equations are presented.
In Sect. 3, a brief description is introduced on the experi-
mental conditions. In Sect. 4, we compare droplet
dynamics in two geometries: with a cylinder obstruction
and with a square obstruction. In addition, we present more
complicated dynamics of the droplets passing through
successive cylinder obstructions up to 6 or an array struc-
ture of cylinders, and compare numerical results with
experimental ones. Finally, we propose useful suggestions
in the practical viewpoint.
2 Numerical method
2.1 Governing equations
We consider isothermal and creeping flow of incompress-
ible immiscible two-phase fluids in two-dimensional (2D)
framework. Momentum and continuity equations are as
follows:
rpgsr ruþðruÞT
rjnldxxp
¼0;ð1aÞ
ru¼0;ð1bÞ
where pdenotes the pressure, g
s
the solvent viscosity, uthe
velocity vector, rthe interface tension coefficient, jtwice
the local mean curvature (=total curvature) of the interface,
1152 Microfluid Nanofluid (2010) 9:1151–1163
123
n
l
an outward unit normal vector from the interface, and
d(x–x
p
) the Dirac delta function which is non-zero only at
x=x
p
. Here, xis the position vector in the domain and x
p
is the position vector at the interface. In the creeping flow
regime (Reynolds number 1), Stokes equation (1a)
gives an instantaneously converged solution at every step
for a flow variance induced by capillary forces.
For interface tracking and calculation of interfacial
tension, the front tracking method (Tryggvason et al. 2001)
was employed. For 2D droplet deformation problem, our
formulation of finite element–front tracking method (FE–
FTM) was already verified in the previous studies (Chung
2009; Chung et al. 2008). Following our earlier studies
(Chung et al. 2008,2009b), we kept the size of front ele-
ment in the range 20–50% of the diagonal size (h)ofthe
smallest mesh. In addition, we reconstructed interface
topology to execute breakup or merger only when the
distance between two confronting front elements was
within 50% of h. Therefore, it is expected that the breakup
or merger occurs in the tolerable range. The reader is
referred to our previous study (Chung et al. 2009a) for
details of the interface topology algorithm. In the front
tracking method, the critical distance for the reconstruction
of interface is less than one grid spacing, since it enables us
to control short-range attractive force between interfaces
within mesh size to mimic changes of interface topology
during breakup and merger (Tryggvason et al. 2001). For
the wettability of droplet fluids on the surface of obstruc-
tions, we regarded that no significant change occurs for
the droplet shape and for the fluid dynamics near the
obstructions in the macro scale even though a wetting
occurs. Accordingly, we simply assume that droplet fluid
completely wets the surface of obstructions if a distance
between droplet interface and the surface of obstructions is
\0.5 Dx
max
to get approximated data on the level of wet-
ting degree, where Dx
max
is the characteristic length for the
mesh size. That is, in the numerical viewpoint, droplet
interface simply flows due to local capillary force (i.e.,
does not stick to the surface), while the wetting is measured
in the very near region of the surface of obstructions.
Furthermore, we admit that a direct comparison of 2D
simulation results with experimental observations show
quantitative discrepancies of droplet dynamics, since
interface curvature and viscous drag due to the additional
depth direction should be considered, as reported (Harvie
et al. 2008). In this study, nevertheless, we conduct 2D
simulation due to the limited computational costs to per-
form qualitative analysis. A recent study (Leshansky and
Pismen 2009) reported that 2D flow simulation on the
breakup/non-breakup behaviors of droplets in T-junction
resembles the experimental observation (Link et al. 2004).
Therefore, we believe the 2D analysis would be helpful to
understand relevant physics.
2.2 Problem definition
A schematic diagram of the flow situations passing
through the obstruction in the confined microchannel is
provided in Fig. 1. In order to investigate the effect of the
obstruction shape and the effect of obstruction interval,
we prepare seven types of obstruction: (a) single cylinder
(SC), (b) single square (SS), (c) double cylinders nearby
(DCa), (d) double cylinders far apart (DCb), (e) six cyl-
inders nearby (HCa), (f) six cylinders far apart (HCb), and
(g) an array structure of cylinders. The obstruction with a
characteristic size dis aligned at the center of the chan-
nel. In order to minimize end effect from inlet and outlet,
the length of the channel is as long as 9w,10w,or25w
(for HCa and HCb), where wis the channel width. For the
array structure, l
x
=l
y
=100 is set as shown in Fig. 1d.
At the inlet and outlet, a fully developed flow condition is
imposed with a mean velocity
U:Droplet length l
d
is set
as an initial condition. Fluid viscosities are designated as
g
i
, where the subscript irepresents droplet or medium. In
numerical study, we consider the case of equiviscous
droplet with medium, i.e., g
d
=g
m
, although experimental
setup shows g
d
/g
m
*1/27, which will be presented in the
next section. Here, we admit the viscosity ratio should be
the real value for more reliable comparison, however, we
confirmed the droplet dynamics is not so significantly
different in the range. In the numerical viewpoint, fur-
thermore, the equiviscous case takes less computational
costs since a time-consuming matrix assembly process is
only required at the first step whereas it should be con-
ducted every step for droplets with different viscosity.
That is, the efficient calculation compensates for any loss
of the accuracy.
As important dimensionless numbers, droplet length
parameter a
d
, obstruction interval parameter a
i
, and capil-
lary number (Ca) are defined as follows:
ad¼ld
w;ð2Þ
ai¼li
w;ð3Þ
Ca ¼gm
U
r;ð4Þ
where l
i
is a distance between the centers of two cylinder
obstructions.
We used refined meshes as shown in Fig. 2, where
zoomed view near the obstruction is presented. In Fig. 2b,
the corners of the square obstruction are slightly rounded
with a radius of 0.1dto facilitate smooth interface tracking
in the computational domain. Detailed information on
seven meshes is provided in Table 1, including total
number of elements, relevant degrees of freedom (DOF),
Microfluid Nanofluid (2010) 9:1151–1163 1153
123
and the size of element in the structured mesh region
(Dx
max
).
3 Experimental setup
3.1 Materials
In microfluidic experiments, water droplets were allowed
to flow in oleic acid medium. The viscosity of water and
oleic acid (Sigma-Aldrich) was 1 and 27 cp, respectively.
The viscosity was measured using a controlled strain type
rheometer (ARES, TA Instruments) with cone-and-plate
fixture at 25°C. Interface tension was measured as 15.6 g/s
2
between the aqueous dispersed phase and the continuous
medium phase using Surface Tensiomat 21 (Fisher
Scientific).
3.2 Channel fabrication and microscopy
The microchannel was fabricated using the standard soft
lithography method (Stroock and Whitesides 2003;
McDonald et al. 2000). PDMS molds were fabricated by
curing PDMS pre-polymer (Sylgard 184 Silicon elastomer,
Dow Corning) and sealed with a slide glass using O
2
plasma treatment for 45 s (60 W, PDC-32G, Harrick
Scientific, Ossining, NY). The main flow channel was
200 lm wide and 40 lm deep. The volumetric flow rates
were controlled for each channel using syringe pumps.
Continuous phase (oil) and dispersed phase (water) were
pumped using 2.5 ml (1000 series, Needle type) and 500 ll
(1700 series, Needle type) syringes (Hamilton Gastight),
respectively. The syringes were connected to microfluidic
devices by tubing (Tygon Teflon, 30 gauge). Syringe
pumps (Harvard Apparatus, PHD 22/2000 Infuse/withdraw
pumps) were used to infuse water and oil phases into the
channel inlets. The flow images were captured using a
microscope (Olympus IX-71, 20X) and a high speed
camera (Fastcam-ultima152, Photron).
4 Results and discussion
4.1 Effect of obstruction shape
First, we study droplet dynamics in the confined channel
with different obstructions. In order to compare the effect
of the obstruction shape, the transient motion of the mov-
ing droplet is provided in Fig. 3for each channel. The
single droplet experiences complicated deformation, while
passing through the obstruction. As it flows, the droplet
first experiences a steady deformation as a bullet shape
Fig. 1 Schematic diagram of
the droplet flow in confined
microchannel with asingle
cylinder obstruction, bsingle
square obstruction, csuccessive
cylinder obstructions, and dan
array structure of cylinders
1154 Microfluid Nanofluid (2010) 9:1151–1163
123
(Fig. 3a, b; Chung et al. 2008; Bringer et al. 2004), splits
by the obstruction (Fig. 3c, d), merges in the rear side of
the obstruction (Fig. 3e, f), and finally generates satellite
droplets after the breakup of thin thread (Fig. 3g, h). In the
early stages as in Fig. 3a–d, similar behavior is observed
independent of whether the obstruction is cylinder or
square. In Figs. 3e–f, however, significant difference is
observed in the dead zone which is defined as a non-
contact region designated with red circles. In other words,
the dead zone is developed only in the downstream region
of the cylinder obstruction, whereas two dead zones are
developed in both upstream and downstream regions of
the square obstruction. This different development of
dead zones is attributed to geometric origin such that
the droplet tends to flow through the streamline near the
obstruction. That is, we conjecture the droplets with same
Ca would show different behaviors depending on the
intrinsically different flow fields of single phase. Very
basically, we simply compare streamlines of single phase
flows in Fig. 3i, j, where the streamlines for the cylinder
obstruction are closer to the surface of the obstruction
near the front and rear stagnation points. Therefore, in the
viewpoint of the deposition process (Lee et al. 2010), the
cylinder shape is more beneficial since smaller dead zones
are developed.
Here, we also notice that a discrepancy between the
previous study (Link et al. 2004) and this study for the
existence of the front dead zone in SS channel. Link et al.
(2004) showed that the front dead zone was very thin or
was not present; however, the droplets seemed densely
populated in their case. Therefore, over-populated droplets
were considered to induce a pressing force to the
obstruction, as a result, the droplets showed slightly
squeezed shapes before the obstruction, not the bullet shape
which is typically observed in droplet flows. On the other
hand, in this study, a single droplet flows through the
square obstruction without any hindrance by other droplets.
Therefore, we conjecture the discrepancy comes from the
droplet–droplet interaction.
The shape of obstruction also affects the breakup point.
Figure 4shows transient shapes right after thread breakup.
In Fig. 4b, d, and f, the thread breakup occurs near the
corners of the square obstruction. While, for the cylinder
obstruction, the thread becomes uniformly thinner around
the cylinder, and finally breaks up at the front parts
(i.e., 90°BhB270°) independent of Ca, where the angle
his designated in Fig. 4a. The relevant experimental
Fig. 2 Zoomed view of mesh configuration near the obstruction:
asingle cylinder (SC), bsingle square (SS), cdouble cylinders with
short interval (DCa), and dan array structure of cylinders (C24A)
Table 1 Detailed information of meshes used in this study
Name Elements Nodes DOF Dx
max
/w
SC 14,574 59,196 313,704 0.025
SS 15,017 61,028 323,517 0.025
DCa 16,220 65,939 349,615 0.025
DCb 16,491 67,023 355,306 0.025
HCa 51,600 209,535 1,110,215 0.025
HCb 53,165 223,275 1,182,285 0.025
C24A 27,520 111,753 592,095 0.025
Microfluid Nanofluid (2010) 9:1151–1163 1155
123
observations for the droplet of Ca =0.01 are also shown in
Fig. 4g and h. For SS, we clearly see the thread breaks at
two points, which induces a quite large satellite droplet in
Fig. 4h. Furthermore, two dead zones are also found as
reproduced in Fig. 3f, whereas one dead zone is observed
in Figs. 4g and 3e. Therefore, we claim that our simulation
results describe the experimental observations of droplet
flows qualitatively within 2D framework.
Fig. 3 Transient deformation
of a droplet passing through the
obstruction (a
d
=1.3,
Ca =0.05). Cylinder:
a?c?e?g,square:
b?d?f?h. Time (t)is
non-dimensionalized with w=
U:
iand jare streamlines and
pressure contours for a single
phase flow at each obstruction
Fig. 4 Snapshots of the droplet
after the thread breakup with
increasing Ca (a
d
=1.3).
Ca =0.05 for aand b.
Ca =0.1 for cand d.Ca=0.2
for eand f. The angle his
measured with respect to rear
stagnation point. For cylinder,
the thread breakup occurs at the
front part (90°BhB270°).
For square obstruction, the
breakup occurs near the corners
(h=±45°and ±135°). The
relevant experimental data of
Ca =0.01 are shown after the
thread breakup for SC (g) and
SS (h)
1156 Microfluid Nanofluid (2010) 9:1151–1163
123
In order to elucidate the breakup mechanism, the con-
tours of Newtonian stress induced by velocity gradients
before the thread breakup are provided in Fig. 5. In similar
cases, the thread of the dispersed phase was reported not to
break immediately by the flow due to viscous stabilization
of the interface (Christopher and Anna 2007). As a common
feature for SC and SS channels, the maximum of normal
component of velocity gradients 2goux=oxouyoy
is
two or three times larger than the maximum of the shear
component goux=oyþouyox
near the obstruction
although the distribution details depend on the geometry.
For SC channel, the normal component is highly developed
at h=60°and 120°and the shear component is highly
developed near the region of h=90°. On the other hand,
for SS channel, both the normal and shear components are
highly developed near the corner, leading the thread
breakup at the corner region. Therefore, we conclude that
the thread breakup is attributed to the velocity gradients
induced by the geometric effect of obstructions.
In the practical viewpoint, we need to minimize the
formation of satellite droplets. For cylinder obstruction, it
is expected that two breakup points are developed at
h=±90°, leading only one satellite droplet if the breakup
occurs simultaneously. In contrast, the square obstruction
might induce three satellite droplets, since the thread
breakup occurs at four corners. The reason why two
satellite droplets are generated in Fig. 3h may be attributed
to unsymmetry in the unstructured mesh configuration near
the obstruction as shown in Fig. 2b. In the unsymmetrical
mesh configuration, the interfacial tension is distributed
unsymmetrically in the immersed boundary method (Mittal
and Iaccarino 2005), even though the interface is posi-
tioned strictly at symmetry. Comparing Fig. 3g and h, more
non-trivial satellite droplets are generated in SS channel.
Consequently, it is expected that the cylinder obstruction
gives better size distribution of droplets.
4.2 Effect of droplet size
The effect of initial droplet size on droplet dynamics is also
investigated. We flow the droplets with different size of
a
d
=0.8, 1.3, 3.3, here, each case corresponds to shorter,
similar, and longer droplet comparing with channel width,
respectively. The snapshots of the flow before the thread
breakup are compared in Fig. 6, in which no significant
difference is observed regardless of obstruction shape. The
droplets show similar behaviors and shapes while passing
through the obstructions. Although the maximum a
d
is
shown up to 3.3 in this section due to limitation of the
computational mesh, we expect that even longer droplets
(a
d
C3.3) would also show the same patterns with Fig. 6e
and f. Thus, we claim the size of the droplet has little effect
on droplet dynamics near the obstruction.
4.3 Effect of interval for two successive cylinders
In this section, we investigate droplet dynamics passing
through two successive cylinder obstructions. We compare
two cases by adjusting the cylinder interval, i.e., a
i
=0.75
(DCa) and a
i
=1 (DCb). The effect of Ca on droplet
dynamics in two geometries is shown in Fig. 7. In DCa, the
droplet cannot intrude into the region between two cylin-
ders due to geometric hindrance, and the distance depicted
as an arrow in Fig. 7a is nearly unchanged independent of
Ca. In DCb, however, the droplet can intrude into the
region between two cylinders depending on Ca. As Ca
decreases, the distance between the split droplets becomes
closer, eventually leading to merge as shown in Fig. 7b.
Here, we explain why the merge occurs in the case. Basi-
cally, as Ca decreases (interface tension increases), inter-
face tends to form a circular shape (or spherical shape in
3D case) to reduce interfacial area locally. Accordingly, the
split heads divided by the first cylinder become a circular
Fig. 5 Contours of Newtonian
stress before the thread breakup
(a
d
=1.3, Ca =0.05): normal
component of velocity gradient
2goux
oxouy
oy
in aand b; shear
component goux
oyþouy
ox
in cand
d. Both components of velocity
gradients are non-
dimensionalized with 2g
U=w
Microfluid Nanofluid (2010) 9:1151–1163 1157
123
shape as possible. For DCb, two split heads easily come
closer with growing their sizes (Fig. 7h), whereas the
radius of curvature (r
c
) of head parts grows relatively small
by the geometrical hindrance in DCa (Fig. 7g). As a result,
the low Ca droplet in DCb shows the coalescence between
cylinder obstructions.
As shown in Fig. 7, criteria for the droplet coalescence
between cylinder obstructions could be proposed as fol-
lows: (i) Low Ca droplet should be manipulated, and (ii)
‘‘ r
c
/wC’’ should be roughly satisfied to avoid the geo-
metric hindrance. If we conduct a geometric analysis, for
(ii), the maximum of r
c
can be measured with drawing an
inscribed circle which touches two cylinder obstructions
and channel wall simultaneously. As a result, the maximum
of r
c
/wis estimated as 0.21875 for DCa and 0.29167 for
DCb, respectively. We also confirmed the droplet size is
not the critical factor since growing motion of head parts is
considered as a local behavior. That is, we can expect that
the coalescence of head parts occurs no matter how long
the droplet is, which will be shown in the next section.
Consequently, we propose the optimal requirements for
multilayer deposition on successive cylinder obstructions.
Fig. 6 Effect of droplet size on
the dynamics before the thread
breakup (Ca =0.05). a
d
=0.8
for aand b.a
d
=1.3 for cand
d.a
d
=3.3 for eand f
Fig. 7 Effect of Ca on droplet
dynamics passing through
double cylinders (a
d
=1.3).
DCa for a,c,e, and g. DCb for
b,d,f, and h.gand hshow
droplets of Ca =0.01 passing
the first cylinder with a radius of
curvature (r
c
) of split head parts
1158 Microfluid Nanofluid (2010) 9:1151–1163
123
In addition, the droplet interface at lower Ca is closer to
the surface of the cylinder obstructions independent of
cylinder interval. For instance, the interface of low Ca
droplet (Fig. 7a, b) is closer to the cylinder surface than
that of larger Ca droplet (Fig. 7e, f). For practical cases,
therefore, the wetting of the droplet fluid on the cylinder
surface is expected to increase as Ca decreases. In our
recent study (Lee et al. 2010), we presented that aqueous
polyelectrolyte (PE) droplets were wetting the surface of
obstructions patterned with a photo-curable polymer,
PEGDA (poly(ethylene glycol) diacrylate) which has
negative charges on their surfaces (Kim et al. 2008).
Although the aqueous droplet without PEs was used in this
study, continuous oil phase (oleic acid), in general, does
not readily wet the hydrophilic surface of PEs or pristine
hydrogel obstructions. Accordingly, we believe that the
initial oil phase covering the obstructions, if any, could be
easily removed by the flow of aqueous droplets without any
deleterious effect on the reaction between oppositely
charged PEs. In the numerical viewpoint, therefore, we
could roughly estimate a level of contact on the cylinder
surface. Figure 8shows the contact coverage (%) against
whole surface area of the cylinder depending on Ca and
cylinder interval. For Ca =0.01 in DCb, no significant
difference of the contact is observed between the first and
second cylinders. 100% of coverage could not be detected
due to the existence of dead zone in the rear region of the
first cylinder as shown in Fig. 7b. In the same manner, the
contact process is expected to be repeated in the second
cylinder. In other cases, the contact coverage becomes
lower due to the geometric hindrance and relatively large
viscous force (or large Ca). Therefore, we suggest manip-
ulating the droplets of lower Ca to increase the contact
coverage on the cylinder surface for the deposition process
(Lee et al. 2010).
By conducting relevant experiments as shown in Fig. 9,
it can be confirmed that the droplet dynamics is similar
with simulation results of Fig. 7. We notice that two mi-
crochannel geometries are the same with the recent study
(Lee et al. 2010). In the experimental observation, for
double cylinders with a
i
=0.75, the penetration of the
droplet fluids into the region between two cylinders was
not observed as shown in Fig. 9a1–a3. In contrast for
a
i
=1, the intrusion of the droplet fluid is observed as in
Fig. 9b1–b3 although the merge is not observed like the
numerical simulation (Fig. 7b). This discrepancy may be
attributed to some numerical assumptions, such as 2D
droplet and the critical distance for the droplet breakup or
merger. If the critical distance is shortened (or the mesh is
more refined), the merger in the dead zone is hardly
expected to occur as observed in the experimental result
(Fig. 9b2).
4.4 Effect of interval for six successive cylinders
Here, we show simulation data which confirm that the
cylinder interval for the independent wetting is also valid
for multi-cylinders up to 6. Figure 10 displays the effect of
droplet size on the droplet dynamics passing through suc-
cessive cylinders with different interval. Here, the cylinder
intervals of both HCa and HCb are the same with ones of
DCa (a
i
=0.75) and DCb (a
i
=1), respectively. In the
same manner, therefore, we observe that the penetration of
droplet fluid into the cylinder interval occurs for HCb,
whereas droplet fluid cannot intrude for HCa in the case of
Ca =0.01. Therefore, we confirm the successive wetting
occurs independently if the two requirements are satisfied,
as proposed in the previous section. For HCb (Fig. 10b, d,
f, h), we also confirm that the coalescence occurs always
independent of droplet size in the range of 1.3 Ba
d
B8.3,
where a
d
=8.3 is the maximum in the computational
domain. Comparing to the cases of two successive cylin-
ders, we conclude no significant feature is shown even in
the successive cylinders up to 6. Thus, we suggest that a
scale-up for several successive cylinders would be avail-
able for the practical purpose.
4.5 Selective wetting for array structure of cylinders
Interestingly, a different design of cylinder array can be
utilized for a selective wetting of the droplet fluids without
a droplet breakup. Here, we present a 2 94 array structure
as an example of the complicated design. As shown in
Fig. 11, both numerical simulation and experimental
observations confirm that the droplet is passing through the
center path following main streamlines due to parabolic
velocity profiles. In addition, the droplet could not pene-
trate into the interval between neighboring cylinders as the
Ca
0.00 0.01 0.02 0.03 0.04 0.05 0.06
contact coverage (%)
0
20
40
60
80
100
DCa (1st cylinder)
DCa (2nd cylinder)
DCb (1st cylinder)
DCb (2nd cylinder)
Fig. 8 Contact coverage of droplet fluid on the cylinder surface as a
function of Ca for different cylinder interval
Microfluid Nanofluid (2010) 9:1151–1163 1159
123
Fig. 9 Experimental results:
droplet dynamics passing
through two successive
cylinders nearby (a
i
=0.75) in
a1–a3, and two cylinders far
apart (a
i
=1) in b1–b3
(Ca =0.01). Droplet phase is
water, and medium phase is
oleic acid
Fig. 10 Effect of droplet size
passing through the six
successive cylinder obstructions
with different interval
(Ca =0.01). HCa (a
i
=0.75)
for a,c,e, and g, and HCb
(a
i
=1) for b,d,f, and h
Fig. 11 Transient motions of
the droplet passing through the
array structure of cylinders
(Ca =0.01). a,c,e, and gare
simulation results (a
d
=1.3),
and b,d,f, and hare relevant
experiments
1160 Microfluid Nanofluid (2010) 9:1151–1163
123
penetrating flow is expected to be weak comparing to the
main stream in transient situation, even though the cylinder
distance (l
x
) is quite large comparing to the radius of
cylinder. As a result, each row of cylinders is like a
hydrodynamic wall for the droplet only, not for medium.
Therefore, we expect that the wetting occurs selectively
(i.e., nearly half part of each cylinder), if the droplet has a
wetting material inside. Numerically, we confirmed that the
contact coverage of the droplet fluid is nearly unchanged
even if the droplet size varied in the range of 1.3 B
a
d
B4.3 (cf. the allowable maximum of a
d
=4.3 in this
computational domain). Thus, we propose a complicated
design based on the array structure of cylinders might be
applicable and possible to extend for Janus particles
(Walther and Muller 2008) by conducting the selective
wetting on the surface of cylinders.
5 Concluding remarks
We investigated droplet dynamics passing through
obstructions in the confined microchannel. For practical
purposes, such as the multilayer deposition process (Lee
et al. 2010) and droplet size control (Link et al. 2004), the
cylinder obstruction shows better performance than the
square obstruction since more non-trivial satellite droplets
are produced and additional dead zone is observed near the
front stagnation point in the square obstruction. Through
numerical simulation, we confirm that both normal and
shear components of velocity gradients induce thread
breakup due to the geometric effect of each obstruction. In
particular, the square obstruction facilitates thread breakup
near the corner regions since both components of velocity
gradients are highly developed at the corner.
For the multilayer deposition process, we proposed two
requirements for an efficient wetting on the surfaces of
multiple cylinders based on the simulation results and the
geometric analysis. Low Ca droplets and enough interval of
cylinders (i.e., roughly a
i
C1) were necessary for the
independent wetting. Also, we notice that droplet size did
not play a significant role on the droplet dynamics. This
implies that we could not realize additional droplet breakup
to reduce droplet size in the successive cylinder design.
The array structure of smaller cylinders was proposed for a
selective wetting, while no breakup of droplet was expec-
ted. In the viewpoint of droplet breakup, thus, more com-
plicated designs (e.g., a zigzag patterning of small
obstructions) might be helpful to control the size distribu-
tion of droplets in microfluidics, which is another inter-
esting issue.
We hope that this study expands our knowledge on the
droplet flows in the complicated geometry, and contributes to
better design of practical frameworks in droplet microfluidics.
Acknowledgments This study was supported by the National
Research Foundation of Korea (NRF) grant (No. 0458-20090039 and
The Acceleration Research Program R17-2007-059-01000-0) funded
by the Korea Ministry of Education, Science, and Technology (MEST),
and the WCU (World Class University) Program of Chemical Con-
vergence for Energy and Environment (R31-10013). The authors also
would like to acknowledge the support from KISTI Supercomputing
Center (KSC-2008-S02-0011), and the referees for valuable comments.
References
Abraham S, Jeong EH, Arakawa T, Shoji S, Kim KC, Kim I, Go JS
(2006) Microfluidics assisted synthesis of well-defined spherical
polymeric microcapsules and their utilization as potential
encapsulants. Lab Chip 6:752–756
Anna SL, Bontoux N, Stone HA (2003) Formation of dispersions
using ‘‘flow focusing’’ in microchannels. Appl Phys Lett 82:364–
366
Boedicker JQ, Li L, Kline TR, Ismagilov RF (2008) Detecting
bacteria and determining their susceptibility to antibiotics by
stochastic confinement in nanoliter droplets using plug-based
microfluidics. Lab Chip 8:1265–1272
Bringer MR, Gerdts CJ, Song H, Tice JD, Ismagilov RF (2004)
Microfluidic systems for chemical kinetics that rely on chaotic
mixing in droplets. Phil Trans R Soc Lond A 362:1087–1104
Chen DL, Gerdts CJ, Ismagilov RF (2005) Using microfluidics to
observe the effect of mixing on nucleation of protein crystals.
J Am Chem Soc 127:9672–9673
Cheow LF, Yobas L, Kwong DL (2007) Digital microfluidics: droplet
based logic gates. Appl Phys Lett 90:054107
Cho SK, Moon HJ, Kim CJ (2003) Creating, transporting, cutting, and
merging liquid droplets by electrowetting-based actuation for
digital microfluidic circuits. J Microelectromech Syst 12:70–80
Choi JH, Lee SK, Lim JM, Yang SM, Yi GR (2010) Designed
pneumatic valve actuators for controlled droplet breakup and
generation. Lab Chip 10:456–461
Christopher GF, Anna SL (2007) Microfluidic methods for generating
continuous droplet streams. J Phys D 40:R319–R336
Chung C (2009) Finite element–front tracking method for two-phase
flows of viscoelastic fluids. Ph.D. thesis, Seoul National University
Chung C, Hulsen MA, Kim JM, Ahn KH, Lee SJ (2008) Numerical
study on the effect of viscoelasticity on drop deformation in
simple shear and 5:1:5 planar contraction/expansion microchan-
nel. J Non-Newtonian Fluid Mech 155:80–93
Chung C, Ahn KH, Lee SJ (2009a) Numerical study on the dynamics
of droplet passing through a cylinder obstruction in confined
microchannel flow. J Non-Newtonian Fluid Mech 162:38–44
Chung C, Kim JM, Ahn KH, Lee SJ (2009b) Numerical study on the
effect of viscoelasticity on pressure drop and film thickness for a
droplet flow in a confined microchannel. Korea–Australia Rheol
J 21:59–69
Chung C, Kim JM, Hulsen MA, Ahn KH, Lee SJ (2009c) Effect of
viscoelasticity on drop dynamics in 5:1:5 contraction/expansion
microchannel flow. Chem Eng Sci 64:4515–4524
Cristini V, Tan YC (2004) Theory and numerical simulation of
droplet dynamics in complex flows: a review. Lab Chip 4:
257–264
Dittrich PS, Manz A (2006) Lab-on-a-chip: microfluidics in drug
discovery. Nat Rev Drug Discov 5:210–218
Griffiths AD, Tawfik DS (2006) Miniaturising the laboratory in
emulsion droplets. Trends Biotechnol 24:395–402
Haeberle S, Zengerle R (2007) Microfluidic platforms for lab-on-a-
chip applications. Lab Chip 7:1094–1110
Microfluid Nanofluid (2010) 9:1151–1163 1161
123
Harvie DJE, Cooper-White JJ, Davidson MR (2008) Deformation of a
viscoelastic droplet passing through a microfluidic contraction.
J Non-Newtonian Fluid Mech 154:67–79
He MY, Edgar JS, Jeffries GDM, Lorenz RM, Shelby JP, Chiu DT
(2005) Selective encapsulation of single cells and subcellular
organelles into picoliter- and femtoliter-volume droplets. Anal
Chem 77:1539–1544
Huebner A, Sharma S, Srisa-Art M, Hollfelder F, Edel JB, Demello
AJ (2008) Microdroplets: a sea of applications? Lab Chip
8:1244–1254
Hung LH, Choi KM, Tseng WY, Tan YC, Shea KJ, Lee AP (2006)
Alternating droplet generation and controlled dynamic droplet
fusion in microfluidic device for CdS nanoparticle synthesis. Lab
Chip 6:174–178
Khnouf R, Beebe DJ, Fan ZH (2009) Cell-free protein expression in a
microchannel array with passive pumping. Lab Chip 9:56–61
Kim HJ, Lee K, Kumar S, Kim J (2005) Dynamic sequential layer-by-
layer deposition method for fast and region-selective multilayer
thin film fabrication. Langmuir 21:8532–8538
Kim P, Baik S, Suh KY (2008) Capillarity-driven fluidic alignment of
single-walled carbon nanotubes in reversibly bonded nanochan-
nels. Small 4:92–95
Kohler JM, Henkel T, Grodrian A, Kirner T, Roth M, Martin K,
Metze J (2004) Digital reaction technology by micro segmented
flow: components, concepts and applications. Chem Eng J
101:201–216
Lee CH, Hsiung SK, Lee GB (2007) A tunable microflow focusing
device utilizing controllable moving walls and its applications
for formation of micro-droplets in liquids. J Micromech Micro-
eng 17:1121–1129
Lee C-Y, Lin Y-H, Lee G-B (2009) A droplet-based microfluidic
system capable of droplet formation and manipulation. Micro-
fluid Nanofluid 6:599–610
Lee M, Park W, Chung C, Lim J, Kwon S, Ahn KH, Lee SJ, Char K
(2010) Multilayer deposition on patterned posts using alternating
polyelectrolyte droplets in a microfluidic device. Lab Chip
10:1160–1166
Leshansky AM, Pismen LM (2009) Breakup of drops in a microflu-
idic T junction. Phys Fluids 21:023303
Li L, Boedicker JQ, Ismagilov RF (2007) Using a multijunction
microfluidic device to inject substrate into an array of preformed
plugs without cross-contamination: comparing theory and
experiments. Anal Chem 79:2756–2761
Lin YH, Lee CH, Lee GB (2008) Droplet formation utilizing
controllable moving-wall structures for double-emulsion appli-
cations. J Microelectromech Syst 17:573–581
Link DR, Anna SL, Weitz DA, Stone HA (2004) Geometrically
mediated breakup of drops in microfluidic devices. Phys Rev
Lett 92:054503-1–054503-4
Liu K, Ding HJ, Chen Y, Zhao XZ (2007) Droplet-based synthetic
method using microflow focusing and droplet fusion. Microfluid
Nanofluid 3:239–243
McDonald JC, Duffy DC, Anderson JR, Chiu DT, Wu HK, Schueller
OJA, Whitesides GM (2000) Fabrication of microfluidic systems
in poly(dimethylsiloxane). Electrophoresis 21:27–40
Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev
Fluid Mech 37:239–261
Nie ZH, Li W, Seo M, Xu SQ, Kumacheva E (2006) Janus and
ternary particles generated by microfluidic synthesis: design,
synthesis, and self-assembly. J Am Chem Soc 128:9408–9412
Nisisako T (2008) Microstructured devices for preparing controlled
multiple emulsions. Chem Eng Technol 31:1091–1098
Nisisako T, Torii T (2007) Formation of biphasic Janus droplets in a
microfabricated channel for the synthesis of shape-controlled
polymer microparticles. Adv Mater 19:1489–1493
Nisisako T, Torii T, Higuchi T (2002) Droplet formation in a
microchannel network. Lab Chip 2:24–26
Niu X, Gulati S, Edel JB, deMello AJ (2008) Pillar-induced droplet
merging in microfluidic circuits. Lab Chip 8:1837–1841
Prakash M, Gershenfeld N (2007) Microfluidic bubble logic. Science
315:832–835
Priest C, Herminghaus S, Seemann R (2006) Generation of mono-
disperse gel emulsions in a microfluidic device. Appl Phys Lett
88:024106
Priest C, Quinn A, Postma A, Zelikin AN, Ralston J, Caruso F (2008)
Microfluidic polymer multilayer adsorption on liquid crystal
droplets for microcapsule synthesis. Lab Chip 8:2182–2187
Raven JP, Marmottant P, Graner F (2006) Dry microfoams: formation
and flow in a confined channel. Eur Phys J B 51:137–143
Sarrazin F, Loubiere K, Prat L, Gourdon C, Bonometti T, Magnaudet
J (2006) Experimental and numerical study of droplets hydro-
dynamics in microchannels. AIChE J 52:4061–4070
Seo M, Nie ZH, Xu SQ, Lewis PC, Kumacheva E (2005) Microflui-
dics: from dynamic lattices to periodic arrays of polymer disks.
Langmuir 21:4773–4775
Shah RK, Shum HC, Rowat AC, Lee D, Agresti JJ, Utada AS, Chu
LY, Kim JW, Fernandez-Nieves A, Martinez CJ, Weitz DA
(2008) Designer emulsions using microfluidics. Mater Today
11:18–27
Shepherd RF, Conrad JC, Rhodes SK, Link DR, Marquez M, Weitz
DA, Lewis JA (2006) Microfluidic assembly of homogeneous
and Janus colloid-filled hydrogel granules. Langmuir 22:8618–
8622
Shim JU, Cristobal G, Link DR, Thorsen T, Jia YW, Piattelli K,
Fraden S (2007) Control and measurement of the phase behavior
of aqueous solutions using microfluidics. J Am Chem Soc
129:8825–8835
Song H, Ismagilov RF (2003) Millisecond kinetics on a microfluidic
chip using nanoliters of reagents. J Am Chem Soc 125:14613–
14619
Song H, Li HW, Munson MS, Van Ha TG, Ismagilov RF (2006) On-
chip titration of an anticoagulant argatroban and determination
of the clotting time within whole blood or plasma using a plug-
based microfluidic system. Anal Chem 78:4839–4849
Squires TM, Quake SR (2005) Microfluidics: fluid physics at the
nanoliter scale. Rev Mod Phys 77:977–1026
Stroock AD, Whitesides GM (2003) Controlling flows in microchan-
nels with patterned surface charge and topography. Acc Chem
Res 36:597–604
Su YC, Lin LW (2006) Geometry and surface-assisted micro flow
discretization. J Micromech Microeng 16:1884–1890
Taly V, Kelly BT, Griffiths AD (2007) Droplets as microreactors for
high-throughput biology. ChemBioChem 8:263–272
Tan YC, Fisher JS, Lee AI, Cristini V, Lee AP (2004) Design of
microfluidic channel geometries for the control of droplet volume,
chemical concentration, and sorting. Lab Chip 4:292–298
Tan YC, Cristini V, Lee AP (2006) Monodispersed microfluidic
droplet generation by shear focusing microfluidic device. Sens
Actuat B 114:350–356
Tan YC, Ho YL, Lee AP (2007) Droplet coalescence by geometri-
cally mediated flow in microfluidic channels. Microfluid Nano-
fluid 3:495–499
Teh SY, Lin R, Hung LH, Lee AP (2008) Droplet microfluidics. Lab
Chip 8:198–220
Thorsen T, Roberts RW, Arnold FH, Quake SR (2001) Dynamic
pattern formation in a vesicle-generating microfluidic device.
Phys Rev Lett 86:4163–4166
Tryggvason G, Bunner B, Esmaeeli A, Juric D, Al-Rawahi N, Tauber
W, Han J, Nas S, Jan YJ (2001) A front-tracking method for the
computations of multiphase flow. J Comput Phys 169:708–759
1162 Microfluid Nanofluid (2010) 9:1151–1163
123
Um E, Lee DS, Pyo HB, Park JK (2008) Continuous generation of
hydrogel beads and encapsulation of biological materials using a
microfluidic droplet-merging channel. Microfluid Nanofluid
5:541–549
Walther A, Muller AHE (2008) Janus particles. Soft Matter 4:663–668
Whitesides GM (2006) The origins and the future of microfluidics.
Nature 442:368–373
Woodward A, Cosgrove T, Espidel J, Jenkins P, Shaw N (2007)
Monodisperse emulsions from a microfluidic device, character-
ised by diffusion NMR. Soft Matter 3:627–633
Yobas L, Martens S, Ong WL, Ranganathan N (2006) High-
performance flow-focusing geometry for spontaneous generation
of monodispersed droplets. Lab Chip 6:1073–1079
Zheng B, Roach LS, Ismagilov RF (2003) Screening of protein
crystallization conditions on a microfluidic chip using nanoliter-
size droplets. J Am Chem Soc 125:11170–11171
Microfluid Nanofluid (2010) 9:1151–1163 1163
123
