The Seventeenth International Symposium on Transport Phenomena,
4-8 September, 2006, Toyama, JAPANGROOVE-PATTERNS EFFECTS ON MIXING PERFORMANCE IN A MICRO-MIXER
K. Tatsumi, Y. Tsukanaka and K. Nakabe
Department of Mechanical Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, JAPANABSTRACTThe performances of the block-inserted and grooveembedded rectangular ducts are investigated in themeaning of enhancing the fluid mixing under very low
Reynolds number conditions. Both numerical andexperimental studies have been carried out to discuss
the block and groove pattern effects on the mixing
characteristics and to evaluate the numerical schemeand experimental procedure. The results obtained by thetwo approaches agreed fairly well with each other in aqualitative manner. By applying the block and groove tothe channel, a higher mixing rate was obtained in ashorter length compared to a smooth rectangular duct.
The grooved channel was effective even in the channels
with large aspect ratio. A better mixing was achieved withthe case of asymmetric pattern than the symmetric case.
The difference of the groove width also changed the flow
and mixing characteristics, however, the total
performance eventually did not differ much. At the end of
this paper, the performances of the hook-type groove
case and the oblique groove case are compared.
INTRODUCTION
The development of the Micro Electro Mechanical System(MEMS) technology in the past few decades has risen thefeasibility of miniature-sized devices into which multiple
functions are integrated, so-called Lab-on-a-Chip or Micro
Total Analysis Systems (μ-TAS). The scale of flow
channels in such devices is in the range of 10 ~ 100μm
which accompanies a large decrease of the Reynolds
number and incurs a serious deterioration of fluid mixing.
Therefore, various techniques have been studied basedon both passive and active ways for purposes toeffectively enhance the mixing. In the present article,
several types of micro-channels of different geometry werestudied here as a passive technique: such as block
inserted channels or channels with grooves embedded at
the bottom wall. The velocity and concentration profiles inthese channels are examined in order to provide somehints for designing an effective micro-mixer. These kinds ofrelatively simple structures can be easily fabricated byusing etching process or micro- and nano-printing
processes which enables cost saving of the products.
Geometric conditions of the channel, block and groove,such as channel aspect ratio, groove width or symmetricand asymmetric patterns, were varied and their effects
were examined by both experimental and numericalapproaches. In the numerical study, three-dimensional
computation was conducted for the flow and concentration
fields under laminar and incompressible flow conditions. In
the experiment, the fluid velocity profiles were measured
using a micro Particle Image Velocimetry (μ-PIV) system.
The concentration was estimated from the data obtained
through two types of measuring methods: one is bycounting fluorescent tracer particles fed into the flow, andthe other is by detecting the luminance intensity offluorescent dye mixed in the fluid.

CCD camera

Computer hardware
Laser optics

Syringe pump

Double pulsed Nd:YAG laser

Microscope

Fig. 1. Experimental apparatus.
Numerical Procedure
Finite-Volume Method (FVM) is adopted in the present
three-dimensional numerical computation. The governing
equations of the flow solved in this study are continuity andNavier-Stokes equations. These equations are describedin time-dependent, incompressible form and are shown as
follows:
∂U i
(1)
=0
∂x i
ρ

DU i
∂ ⎛⎜ ∂U i ⎞⎟
∂P
μ
+
=−
Dt
∂x i ∂x j ⎜⎝ ∂x j ⎟⎠(2)

where Ui is the velocity of xi direction. ρ and μ are thefluid density and viscosity, respectively.
To discuss the mixing performance of the channels, thefollowing equation of concentration conservation ofbinary mixture is also calculated in the present
computation.
Dc∂ ⎛ μ ∂c ⎞
(3)
⎜
⎟
ρ
=
Dt

∂x i ⎜⎝ Sc ∂x i ⎟⎠Here c is the mixture fraction of ethanol in water. Sc is
the Schmidt number and the value applied in the present
computation is Sc=657, which represents the diffusion
between ethanol and water.
In the discretization method, 4th-order centraldifference scheme is employed for the diffusion terms
and the 5th-order upwind scheme is employed for theconvective terms. These higher order schemes areapplied in the present code to reduce the discretization
errors, particularly numerical diffusion errors. However, insolving Eq. (3), 1st-order upwind scheme and 2nd-order
central-difference scheme are respectively applied to theconvective and diffusion terms to reduce thecomputational load. A modified version of the SemiImplicit Method for Pressure-Linked Equations algorithm(SIMPLEC) is applied to solve the pressure correction.
To solve the discretized equations, a linear-iterative
method using the modified Tri-Diagonal Matrix Algorithm(TDMA) combined with an Alternating Direction Implicit
Method (ADI) is employed.
Experimental Procedure
Figure 1 shows the experimental apparatus of the μ-PIV
system which is applied in the present study to measure
the velocity of the flow in the micro-channel. An Nd-YAG

The Seventeenth International Symposium on Transport Phenomena,
4-8 September, 2006, Toyama, JAPAN

Table 1. Conditions for block-inserted channels.
h/H w/H L/H AR(=Wd/H) Re
Case-B1 0.4
0.5
3.0
1.0
3.0
Case-B2 0.4
1.0
3.0
2.0
2.0
Case-B3 0.4
1.5
3.0
3.0
1.0

Cover glass
Outlet

Inlet

Channel made of PDMS

2

Fig. 2. Schematic of the micro-channel.
laser (2nd harmonic wavelength=532nm) is connected to a
microscope, through which the laser is emitted to thetargeted channel. Fluorescent micro spheres (Duke
Scientific Corporation R820: radius=0.82μm) are mixed in
the flow as tracer particles and the fluorescence isrecorded by a high resolution CCD camera (TSI
Powerview 4M). The objective lens used in the present
study has a magnification of 40 and numerical aperture of
NA=0.75. The focal depth calculated by the following
equation will be, therefore, Δy=5.7μm [1].
3nλ 2.16d p
(4)
Δy ≅
+
+ dp
NA 2
tanθ
n is the refraction index of the fluid located between thelens and the cover glass, λ is the wavelength of the light,and θ is 1/2 of the apex angle of the cone defined
between the fluorescent particle and the objective lens.
dp is the diameter of the fluorescent tracing particle. Δybecomes the spatial resolution in the depth direction of themeasured cross-sectional flow field. The optical spatial
resolution of the microscope calculated by the following
equation is α=0.41μm.

α=

λ
2NA

(5)

Note that this value is larger than the CCD camera
resolution, 0.18μm.
The schematic view of the micro-channel test section
is shown in Fig. 2. A cover glass is attached to the upperside of the channel and the fluorescence of the particles
is recorded from this side. The channel is made of PDMS
(poly-dimethylsiloxane) and is fabricated by using SU-8
(MicroChem Co.) as a mold. This SU-8 mold is made byan etching process. First a mask on which the groove
patters are printed is prepared by using an enlarger(Fujifilm FD-690) and a high precision photo plate (HRPSN-2 2.5X2.5 30Z). Then, through this mask, the SU-8
layer is exposed to the UV light and the channel patternis printed on the layer. After the post baking and etchingprocesses, an SU-8 mold is completed. PDMS in liquid isthen poured over the SU-8 mold, and is hardened andripped off.
A Y-junction type channel shown in Fig. 2 is used in
the experiment to discuss the mixing performance ofeach channel. Two kinds of measurements wereconducted to evaluate the mixing characteristics at thetest section. One is by feeding fluid containing the
aforementioned fluorescent particles from one side of the
Y-junction (inlet #2 in Fig. 2). In this case, the mixing rate
is obtained by calculating the number density of theparticles in the channel. The other is by feeding fluid
containing Rhodamine B, again from one side of theheader. In this case, the mixing rate is obtained bymeasuring the fluorescence intensity and applying it to
the linear function calibrated by a preliminary experiment.

Table 2. Conditions for grooved channels.
d/H w/H b/H L/HAR
Case-SHG
1.0
1.0
1.0
3.0
3.0
Case-AHG2
1.0
1.0
1.0
3.0
2.0
Case-AHG3
1.0
1.0
1.0
3.0
3.0
Case-AHG4
1.0
1.0
1.0
3.0
4.0
Case-AHG3b 1.0
1.0
3.0
3.0
3.0

Re
1.5
2.0
1.5
1.2
1.5

Table 3. Experimental conditions.
d/H w/H b/H L/HAR
Case-AHGE 0.7
0.6
0.7
2.2
2.2
Case-AOGE 0.7
0.6
1.3
5.0
2.2

Re
1.5
1.5

H
Wd

h

y

z

O

x

L
Lup

(a) Block-inserted case
w

w
w

H

d

Wd

z

y
x

w

Lup

L

L

b

H
d
Wd

z

w

y
x

Lup

b

L

L

(b) Symmetric groove case (c) Asymmetric groove caseFig. 3. Computational domain.
b
w

w

H
d

Wd

z

w

y
x

Lup

L

b

L

θ

H
d
Wd

z

L

y
x

Lup

(a) Asymmetric hook type groove (b) Oblique groove
Fig. 4. Test section of the experiment.
Although the former case only shows the contribution of
the convection to the concentration field, one can obtaina cross-sectional view of the field in the depth direction
due to the same principle of the flow field measured by
the μ-PIV.
Numerical and Experimental Conditions
Figure 3 illustrates the computational domain of the blockinserted and grooved channel cases. In the block case,
blocks are attached diagonally to the top and bottom walls.
In the grooved channel case, the groove is applied only at
the channel bottom wall, and two types of groove patterns
are studied, i.e. symmetric and asymmetric cases. The
geometric conditions examined in the block-inserted andgrooved channel cases are tabulated respectively in Table
1 and 2. The flow rate and channel height, H, are kept
constant in all cases, and Reynolds number, which isbased on the channel hydraulic diameter, differs when thechannel aspect ratio is changed. At the inlet boundary, auniform velocity flow is assumed to enter thecomputational domain. For the concentration field, thevalues of mixture fractions of c=0 and 1 are applied
respectively to each half side divided by the channel
centerline. Lup shown in Fig. 3 is the distance between theThe Seventeenth International Symposium on Transport Phenomena,
4-8 September, 2006, Toyama, JAPAN

0.06

AnalysisAnalysisAnalysisat y/H=0.1
at y/H=0.3
at y/H=0.5

0.05

U [m/s]

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0
20 21 22 23 24 25 26 27

0.0

z/Wd

Present
Present
Present

0.04

0.0125

0
20

21 22

x/H
0.03

23

24

x/Wd

25 26

27

U (m/s)(a) Experiment(b) Numerical simulation
Fig. 7. Comparison of streamwise velocity distributions in
x-z plane at y/H=0.26 (inside the groove).

0.02
0.01

0.010

Experiment
Simulation
0.25

0.50

0.75

z/Wd

Fig. 5. Time-mean velocity distributions in a rectangular
duct.
wz/Wd=0.6

0.005

1.00

0.000

W [m/s]0.00
0.00

z/Wd=0.5

0.005
0.000

w
Wd

z

y
x

Lup

L

b

z/Wd=0.4

L

Fig. 6. Test section of preliminary test case.
inlet and the blocks or grooves, and is constant as Lup=5.0
for all cases. By the time the flow reaches the blockinserted or grooved area, a certain amount of diffusion
between the two fluids is expected. Compared to themixing produced by the blocks and grooves, however, themixing ratio in this area is considered to be relatively small.
The groove patterns examined in the experiment are
shown in Fig. 4. In this case, the flow and mixing
characteristics of a channel with asymmetric hook-type
grooves same as Fig. 3(c), and oblique grooves are
discussed. 30 grooves are periodically embedded in thewall and the streamwise pitch, p, in both cases are
p/H=3.8. The geometric conditions of the channel are
shown in Table 3. Due to the fabrication process, to createa channel of exact same condition with the numerical
study is difficult. Therefore the conditions shown in Table 2
and 3 are not exactly the same.
RESULTS AND DISCUSSION
Preliminary Test Cases for Evaluation of the
Numerical and Experimental Procedures
In this section, discussion is made on the results of apreliminary test to evaluate the numerical andexperimental procedures applied in the present study.
Two cases are shown here, i.e. a comparison of the μPIV measurement and theoretical analysis of viscous
flow of a smooth rectangular channel, and a comparison
between the numerical and experimental results for theflow in a grooved channel.
Figure 5 shows the cross-sectional distributions of thestreamwise velocity U measured at y/H=0.1, 0.3 and 0.5
of a rectangular smooth channel case. The abscissa is
the spanwise location normalized by the channel width,
Wd, which is approximately 200μm. The channel aspectratio is 2.2. The Reynolds number based on the channel
hydraulic diameter is Re=3.0. For comparison, the resultsof a three-dimensional theoretical analysis in arectangular channel [2] are included in the figure as the

0.005
0.000
23.0

23.5

24.0

x/H

Fig. 8. Comparison of the cross-sectional profile of the
spanwise velocity at z/Wd=0.4, 0.5, 0.6.
2.0

Experiment
Simulation

1.5

φ

H
d

1.0
0.5
0.0
0.0

0.2

0.4

z/Wd

0.6

0.8

1.0

Fig. 9. Comparison of the apparent mixture fraction, φ.
solid lines. The experimental results agree well with thetheoretical ones indicating that an accurate measurementof the three-dimensional velocity distribution is performed
using the present experimental apparatus.
Next, comparison of the velocity and mixture fraction
fields obtained by the numerical computation andexperiment is carried out for the grooved channel. The
test section discussed here is shown in Fig. 6. In thispreliminary test, the channel width is larger than thegroove total spanwise width. This will reduce the groove
effect on the flow and mixing characteristics. However,
the geometric error due to the channel fabrication
process, such as the alignment of the mask, is reduced
as well, and a more accurate comparison with thenumerical computation is possible. The geometricconditions of the groove is same as those shown in Table
2 for both experimental and numerical cases, except thatthe channel aspect ratio and groove streamwise pitch are
AR=Wd/H=5.0 and p/H=5.0. The numbers of theThe Seventeenth International Symposium on Transport Phenomena,
4-8 September, 2006, Toyama, JAPAN
0.5

0.5

Rectangular duct (AR=3)

Rectangular duct (AR=3)

0.4

0.4
Square duct (AR=1)

ΦΦ

Square duct (AR=1)

0.3

Case-B1
Case-B2
Case-B3

0.2
0.0

0.3

0.0

0

5

10

15

x/H

20

25

Fig. 10. Comparison of unmixed rate, Φ, of block
inserted case.
1.0

0.5

z/H

10

15

x/H

20

25

Fig. 12. Comparison of unmixed rate, Φ, between
symmetric and asymmetric groove cases.

1.5

0.5

0.0
0.0

5

y/H

0.5

0

2.0

y/H

y/H

1.0

Case-SHG
Case-AHG3

1.0

0.0
1.0
0.0

(a) Case-B1 (AR=1 )

0.5
0.5

1.0

z/H

1.5

2.0

(b) Case-B2 (AR=2)

1.0

0.0

(a) Case-SHG: x/H=8.5(b) Case-SHG: x/H=14.0

2.0

1.0

1.5

y/H

1.0

Um

y/H

1.0

0.5

0.5

c

0.0
0.0

0.5

1.0

1.5

z/H

2.0

2.5

3.0 c

0

(c) Case-B3 (AR=3)
Fig. 11. Mixture fraction contours in y-z plane at
x/H=6.5 (block inserted case).
embedded grooves in the experimental and numericalcases are 30 and 5, respectively. Re is set as Re=1.5 inthese cases.
Figures 7 and 8 show the streamwise velocity, U,
contours on the x-z plane at y/H=0.26 and the crosssectional distributions of the spanwise velocity, W, at
three different spanwise locations, z/Wd=0.4, 0.5 and 0.6.
Note that the results shown in each figure are obtained
from the fourth groove counted from the upstream side of
the channel. In Fig.7, the velocity contours of the twocases agree well. The W distributions of both results
depicted in Fig. 8 also show a reasonable
correspondence. These results evaluate the present
numerical and experimental procedures for velocity
measurements.
Figure 9 shows the cross-sectional distributions of theapparent mixture fraction, φ. φ is obtained by calculating
the number density of the fluorescent particles in theexperiment. In the numerical computation, this value isobtained by calculating the path lines of the particles
injected from numerous locations at the inlet. In bothcases, the results shown in Fig. 9 are obtained byspatially averaging the particle densities at y/H=1.5 in thestreamwise direction in the area of one groove length(2L+b in Fig. 6) at the fourth groove. Furthermore, in theexperiment, time-mean value is calculated by averaging
200 images of different time period. Although somediscrepancy is observed at the maximum and minimum
values, a good agreement is obtained for the location ofeach peak. Therefore, the apparent mixture fraction

0.0
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 cz/H(c) Case-AHG3: x/H=8.5z/H(d) Case-AHG3: x/H=14.0

Fig. 13. Mixture fraction contours and velocity vectors
in y-z plane at x/H=8.5 and 14.0 (grooved channels).
results obtained both by experiment and numericalsimulation can be discussed in a qualitative way.
Discussion on Block-Inserted Channel
Figure 10 shows the streamwise distributions of theunmixed rate, Φ, of the block-inserted case under threedifferent channel aspect ratio, AR, conditions obtained by
the numerical computation. Φ is a dimensionless value
defined as Φ = ∫ ρuξdA/Q . Here, ρ is the fluid density, u isthe local streamwise velocity, and ∫ dA is the integration in
the cross-sectional plane. ξ is calculated as ξ = c − cwhere c is the mixture fraction of ethanol and c is the
mixture fraction when the two fluids are completely mixed
together, i.e. c = 0.5 . The results of the square (AR=1)
and rectangular (AR=3) shape smooth channels are also
shown in the figure for comparison. A smaller Φ is
obtained by case-B1 and case-B3 compared to thesmooth channel case of the same aspect ratio, whichindicates a better mixing performance. Especially for caseB1, a noticeable enhancement is obtained. However, inthe case of case-B3 when the channel aspect ratio is large,
not much effect appears by inserted the blocks in thechannel. Actually, a smaller Φ can be achieved by asmooth square channel case if the mass flow rate is thesame as the present study.
Figure 11 shows the mixture fraction contours of thestreamwise cross-sectional plane at x/H=6.5 (middle of theblock streamwise length) of the block-inserted cases withdifferent AR. Due to the block existence, the interface ofthe two fluids is distorted and expanded which results in an

The Seventeenth International Symposium on Transport Phenomena,
4-8 September, 2006, Toyama, JAPAN
2.0

0.5

Rectangular duct(AR=3)

y/H

1.5

Φ

0.4

0.0

5

Fig. 16. Mixture fraction contours in y-z plane at
x/H=8.5 of case-AHG3b.

10

15

x/H

20

25

0.5

Rectangular duct (AR=3)

1.5

z/H

0.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0z/H(a) case-AHG2 (AR=2)

1.0

1.5

y/H

0

5

10

15

x/H

20

25

(b) case-AHG3 (AR=3)

2.0

1.0

0.5

0.5
0.0

Case-AHG3
Case-AHG3b

0.2

0.0
0.0 0.5 1.0 1.5 2.0

Square duct (AR=1)

0.3

1.0
0.5

0.0

0.4

Φ

2.0

1.5

y/H

y/H

2.0

0.5

0

z/H

Fig. 14. Effect of channel aspect ratio on the unmixed
rate, Φ, for grooved channel cases.

1.0

0.5

0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0

Case-AHG2
Case-AHG3
Case-AHG4
0

1.0
0.5

Square duct(AR=1)
0.3

0.2

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

z/H

c

0

(c) case-AHG4 (AR=4)
Fig. 15. Mixture fraction contours in y-z plane at x/H=8.5(channel aspect ratio effect).
enhancement of the mixing performance. For larger AR
cases, however, the interface per flow volume becomes
small, and the influence of the block effect on the interface
becomes relatively small. Therefore, it appears that theblock-inserted cases are not effective in larger aspect ratio
channels.
Discussion on Symmetric and Asymmetric Grooved
ChannelsFigure 12 shows the unmixed ratio, Φ, for case-SHG andcase-AHG3. Same as Fig. 10, the results of the smoothchannel cases are shown together in the figure.
Comparing case-SHG with the smooth channels, caseSHG takes a smaller Φ than the rectangular duct case
(AR=3), however, shows a larger Φ than the square duct
(AR=1) case. On the other hand, Φ of case-AHG3 issmaller than the square duct case at the downstream of
the groove.
Figure 13 shows the cross-sectional view of thevelocity vectors and mixture fraction contours at x/H=8.5
and 14.0. From the velocity vectors at x/H=8.5, where the
spanwise groove exists, generation of a secondary flow
passing along the groove can be observed. Due to theconvection produced by this secondary flow motion, theinterface of the fluids is distorted and expanded. The fluidof higher or lower concentration is brought to the interface
which increases the concentration gradient namely the
diffusion flux at the interface. These are believed to be thereasons why a better mixing is obtained by the grooved
channel cases. However, at x/H=14 the secondary velocity

Fig. 17. Effect of spanwise groove width, b, on theunmixed rate, Φ.
components are small and the vortices do not maintainitself. The decrease ratio of Φ is, therefore, not large at thedownstream of the grooves.
Under the condition of low Reynolds number as Re≈1,
the secondary flow is relatively small for case-SHG, and abetter performance is obtained by case-AHG3 whichaccompanies a surface extension effect of the interface
additional to the increase of the diffusion flux at theinterface.
Effects of Channel Aspect Ratio and Spanwise Groove
Width
In this section, discussion is carried out on the AR and b
effects on the flow and mixing characteristics of theasymmetric groove case. The streamwise distributions ofΦ and mixture fraction contours at the cross-sectional
plane of x/h=8.5 are respectively shown in Figs. 14 and 15
for the conditions of AR=2, 3 and 4. Same as the smoothchannel case, Φ becomes smaller as AR increases since
the interface becomes relatively small compared to thechannel cross-sectional area. Focusing on case-AHG4,even though the aspect ratio is AR=4, Φ is equivalent tothat of a square smooth channel, and is, furthermore,
smaller than that of case-SHG or case-B2 whose aspectratios are smaller (AR=3 or 2). This indicates thatassociated with the spanwise flow, mixing enhancement
effect can be expected with the asymmetric groove caseeven for large channel aspect ratios.
Since the spanwise flow shows a significant
contribution to the mixing characteristics as describedabove, the effect of the width of the spanwise groove, b, isdiscussed next. Fig. 16 shows the c contours of the y-z
plane at x/H=8.5 of case-AHG3b whose b is three times
larger than case-AHG3. In Fig. 17 is shown the Φdistributions of case-AHG3 and case-AHG3b. Comparing
the results shown in Figs. 15 (b) and 16, one can see thatthe surface is distorted more in case-AHG3, whichindicates that a stronger spanwise flow is produced at theThe Seventeenth International Symposium on Transport Phenomena,
4-8 September, 2006, Toyama, JAPAN
1.5

Case-AHGE
Case-AOGE

φ

1.0

0.5

0.0
0.0

0.2

0.4

0.6

z/Wd

0.8

1.0

Fig. 18. Apparent mixture fraction, φ.

ξ

1.0

0.5

Case-AHGE
Case-AOGE
0.0
0.0

0.2

0.4

0.6

z/Wd

0.8

1.0

Fig. 19. Mixture fraction, ξ, obtained by measuring
the fluorescence intensity of Rhodamine B.
spanwise groove and more fluid is transported from one
side of the channel to the opposite side. By these effects,
decrease of Φ shown in Fig. 17 is larger at 8<x/H<9 in thiscase than case-AHG3b. In case-AHG3b the interface isless expanded and the gradient of Φ is smaller at thesame region. However, since b is increased the value
decreases constantly in the area of 8<x/H<11 at which the
spanwise groove is located. The contribution of these two
effects to Φ, respectively appearing in case-AHG3 andcase-AHG3b, are approximately the same. Therefore,
consequently Φ at the downstream of the grooves arenearly identical and the difference of the mixing
performance is small.
Comparison of Hook-Type and Oblique Grooves
In this section, discussion is carried out for theexperimental results of the mixing characteristics of ahook-type asymmetric groove and oblique groove. Figures
18 and 19 show the cross-sectional distributions of the
mixture fraction of each groove case. Figure 18 shows theapparent mixture fraction, φ, which is calculated bymeasuring the number density of the fluorescent particles
at the plane of y/H=1.5. Figure 19 depicts the mixture
fraction, ξ, calculated by measuring the fluorescenceintensity at the same location. Both values are spatiallyaveraged in the streamwise direction for one groove length(=2L+b) and time-averaged by averaging the data of 200
images. Comparing φ and ξ for case-AHGE, although both
values are calculated at the same streamwise location, ξ
has a smoother distribution compared to that of φ. This isbelieved to be ascribable to the diffusion effect of
Rhodamine B and to the fact that the measured
fluorescence intensity is the summation of the light in thedepth direction. Nevertheless, the characteristics of each
distribution roughly agrees with each other, at least in aqualitative sense.

Comparing the results of case-AHGE and case-AOGE,
a more uniform distribution is obtained by case-AOGE for
both φ and ξ which indicates that a better mixing is
produced by this case. Although not shown here, the flowrate in the groove in the spanwise direction in case-AOGE
is larger than case-AHGE which indicates a larger fluid
transport resulting in a mixing enhancement. It is believedthat the increase of the spanwise flow is attributed to theinclination of the groove and to the increase of the groove
width.
CONCLUSIONS
Flow and mixing characteristics of a micro-channel withblocks and grooves applied to the walls have been
discussed by numerical and experimental approaches.
The major conclusions drawn from the present study is asfollows:
1. The results of the velocity fields measured by the μ-PIV
for the flow in a rectangular smooth channel showed an
excellent agreement with the three-dimensional analyticalresults. The apparent mixture fraction obtained bymeasuring the number density of the fluorescent tracing
particles in the grooved channel corresponded fairly wellwith the results of the numerical simulation.
2. In the case of the block-inserted channel, a good mixing
was obtained for the square channel. However, theperformance significantly deteriorated as the channel
aspect ratio (AR) increased indicating that the blockinserted case is not effective for channels of large AR.
3. For the case of grooved channel, an effective mixing
was obtained even when AR is large. The grooved
channel of AR=4 produced a comparable performance tothe square smooth channel and block-inserted case of
AR=2.
4. Comparing the performances of the grooves ofsymmetric and asymmetric patterns, a better mixing was
obtained by the asymmetric groove case. This is
ascribable to the spanwise flow which distorted andexpanded the interface of the two fluids.
5. Under the condition of the present study, the width of
the spanwise groove consequently did not affect the
mixing performance if compared at the downstream of thegroove. This is due to the trade-off problem between theincrease of the area of larger fluid mixing, and theenhancement of spanwise fluid transport produced by thegroove.
6. Comparing the results of the hook type asymmetricgroove and the oblique groove cases, the latter caseshowed a better performance.
REFERENCES
1. C. D. Meinhert, S.T. Wereley and M. H. B Gray,
Volume illumination for two-dimensional particle image
velocimetry, Measurement Science and Technology 11,809-814 (2000).
2. D. G. Drake, On the Flow in a Channel due to aperiodic pressure gradient, Quarterly J. of mechanics
and applied mathematics, 18, 1-10 (1965).
ACKNOWLEDGEMENT
The work is partially supported through the project“MEMS Open Network Engineering System of Design
Tools (MEMS-ONE)” by Micromachine Center (MMC).