-
1
A SEMINAR REPORT ON
MIXING IN MICROCHANNELS
Submitted in partial fulfillment of the requirements for the
Degree of Bachelor of Technology
---------- Presented & Submitted-----------
By
HARSHIT KUMAR
(Roll No. U10CH038)
B. TECH. IV (Chemical) 7th Semester
Guided by
Dr. V.N.LAD
Assistant Professor
CHEMICAL ENGINEERING DEPARTMENT
Sardar Vallabhbhai National Institute of Technology
Surat-395007, Gujarat, INDIA
DECEMBER - 2013
-
2
Sardar Vallabhbhai National Institute of Technology
Surat-395007, Gujarat, INDIA
CHEMICAL ENGINEERING DEPARTMENT
CERTIFICATE
This is to certify that the B. Tech. IV (7th Semester) SEMINAR
REPORT entitled
Mixing in Microchannels presented & submitted by Mr. Harshit
Kumar, bearing
Admission No. U10CH038, in the partial fulfillment of the
requirements for the award of
degree B. Tech. in CHEMICAL Engineering at Sardar Vallabhbhai
National Institute of
Technology, Surat.
He has successfully and satisfactorily completed his seminar
work.
Dr. V. N. Lad
(Guide)
Assistant Professor
Chemical Engineering Department.
-
3
DEPARTMENT OF CHEMICAL ENGINEERING
Sardar Vallabhbhai National Institute of Technology,
Surat.
This is to certifiy that Mr.Harshit Kumar, registered in
Chemical Engineering Department
of S.V.N.I.T. Surat having Admission No. U10CH038 has
successfully presented his Seminar
of B. Tech. (Chemical) 7th Semester, on 11/12/2013 at 04:00 P.M.
The seminar is presented
before the following members of the Committee.
Sign Date
1) Examiner-1 ____________ ___________ _________
2) Examiner-2 _____________ ___________ _________
The Seminar entitled Mixing in Microchannels is submitted to the
Head ( ChED ) along
with this certificate.
Place: Surat
Date: 11/12/2013
Prof. Z. V. P. Murthy
Head,
Chemical Engineering Department,
SVNIT Surat.
-
4
ACKNOWLEDGEMENT
It gives me great pleasure to present my seminar report on
MIXING IN
MICROCHANNELS. No work, big or small, has ever been done without
the
contributions of others.
I would like to express deep gratitude towards Dr. V. N. LAD,
Assistant
Professor at Chemical Engineering Department, SVNIT, who gave me
their
valuable suggestions, motivation and direction to proceed at
every stage. He
extended towards a kind and valuable guidance, indispensible
help and
inspiration at time in appreciation I offer them my sincere
gratitude.
In addition, I would like to thanks Department of Chemical
Engineering
Department, SVNIT. Finaly, yet importantly, would like to
express my heartfelt
thanks to my beloved parents and my brother for their blessings,
my
friends/classmates for their help and wishes for the successful
completion of
this seminar.
Harshit Kumar
(U10CH038)
-
5
ABSTRACT
The ability to mix efficiently has many uses, particularly in
chemistry and biochemistry. A
promising area involves mixing in microchannelsnarrow grooves of
about 100m in width.
A microchannel which mixes fluids is called a micromixer.There
are two types of mixing
methods in microchannels: active and passive.
In active mixing, fluid is pumped into the channel in such a way
that mixing is induced, say
by a time-dependent forcing. However this is difficult to do on
such tiny scales as
micrometres, and is also undesirable from a manufacturing
standpoint because the design
involves moving parts.
In passive mixing, the shape of the micromixer is designed to
create flow patterns that
naturally mix. For example, this is achieved by placing grooves
on the walls of the channels
which cause chaotic motions of fluid particles. An alternative
approach, used in present work,
is electro-osmosis, where electric fields are used to push the
fluid (Ajdari, 1996).
In this seminar we have discussed different types of fabrication
of micro channels & flow of
fluids in a microchannels like Crossflow and mixing in
obstructed and width-constricted
rotating radial microchannel, Two-fluid mixing in a
microchannel, Single-phase fluid flow
and mixing in microchannels, Gasliquid two-phase flow in
microchannel at elevated
pressure, Liquid mixing in gasliquid two-phase flow by
meandering microchannels.
-
6
CONTENTS
PAGE NO.
ACKNOWLEDGEMENT 4
ABSTRACT 5
LIST OF FIGURES 8
1.Introduction 9
2. FABRICATION OF MICROCHANNELS 10
2.1 Fabrication of the microchannels by optical lithography
10
2.2. Wet chemical etching 11
2.3. Reactive ion etching (RIE) 11
2.4 Room Temperature Microchannel Fabrication for Microfluidic
System 12
2.5 Cylindrical PDMS Microchannel Fabrication by 16
Sacrificial Molding using Caramel
2.6 One-stage fabrication of sub-micron hydrophilic
microchannels on PDMS 17
2.7 Microchannel Fabrication using photomask,SU-8,glass slide
18
3. Equation Derivations 20
3.1 Governing Equations 20
3.2 Velocity Field 21
3.3 Pressure Analysis 24
3.4 Pressure Gradient and Constant Velocity Solution 28
-
7
4. mixing analysis 29
4.1 Crossflow and mixing in obstructed and width-constricted
29
rotating radial microchannel
4.2 Two-fluid mixing in a microchannel 30
4.3 Single-phase fluid flow and mixing in microchannels 31
4.4 Gasliquid two-phase flow in microchannel at elevated
pressure 33
4.5 Liquid mixing in gasliquid two-phase flow by meandering
34
microchannels
4.6 Mixing process of immiscible fluids in microchannels 35
4.7 Mixing of a split and recombine micromixer with tapered
37
curved microchannels
4.8 Pumping and mixing in a microchannel using AC 38
asymmetric electrode arrays
4.9 Parametric study on mixing of two fluids in a 39
three-dimensional serpentine microchannel
4.10 Mixing performance of a planar micromixer with 40
circular obstructions in a curved microchannel
4.11 Single phase electrokinetic flow in microchannels 42
4.12 Fluid mixing in microchannel with longitudinal vortex
generators 43
4.13 Ideal micromixing performance in packed microchannels
44
5. CONCLUSION 45
REFRENCES 46
-
8
List of Figures
Figure
no.
Name of figure Page no.
1 A top down view of the staggered herringbone pattern on
the
floor of the channel
9
2 The microchannels mask 10
3 Sample microchannel 5 after wet etching 11
4 Sample microchannel 3 fabricated by RIE 12
5 Sample microchannel 48 fabricated by DRIE 12
6 The developed microfluidic system 13
7 Microstructure design for micro fluidic system 14
8 Fabrication process flow of region from cross section AA
to
outlet
15
9 Evaporating design on microfluidic system 15
10 Movement of saccharomycetes in microchannel by
evaporating
force
16
11 Microchannels fabricated by proposed method 17
12 Schematic for microchannel fabrication procedure 20
13 A diagram of the herringbone shape with respect to y
24
-
9
1. Introduction
A microchannel is a channel that has a width and height in the
order of micrometers (m).
Conventional mixing methods for larger volumes of fluid are
often not practical at such tiny
scales, so micromixing requires a separate area of research.
There are different methods of generating chaotic flows in
channels, varying from placing
obstacles in the channel (Wang. et.al., 2002) to a very popular
and effective solution called
the staggered herringbone system (Stroock et.al., 2002).
The staggered herringbone system is where grooves in a
herringbone shape are carved into
the floor of the channel (see figure 1). The herringbone pattern
is periodic in the x-direction
and half way through each period the herringbone is flipped
around, hence creating a
staggered pattern. In this system the efficiency of mixing is
far greater than the mixing from
diffusion alone (Johnson et. al., 2002).
Figure 1: A top down view of the staggered herringbone pattern
on the floor of the channel
(Stroock et.al., 2002)
-
10
2. FABRICATION OF MICROCHANNELS
2.1 Fabrication of the microchannels by optical lithography
The first step in the fabrication process consists in the design
of the desired mask. By means
of Raith 150 software we have designed the microchannels mask
with following dimensions:
a) the reservoirs size 1000x1000m; channels size 20x4800m;
distance between channels
20m (fig. 2).
Fig. 2. The microchannels mask
We have fabricated the microchannel by standard procedure of the
optical lithography. The
SiSiO2(SiO2 thickness 5m.) wafer was cleaned primarily by
acetone and isopropanol to
remove the contaminations. The wafer was then covered with
primer and photorezist (AZ
5214E) by spin coating in order to form a thick layer. The spin
coating was imposed at
4000rpm, 40sec. and has produced a layer between 1.2 - 1.3 m
thickness. The photorezist-
coated wafer was then baked 1min. at 120C to evaporate excess
solvent. After baking, the
photorezist is exposed 3sec. to the designed microchannel mask
at 14mW UV light (transfer
the pattern from the mask to photorezist). An another bake
process (2min. at 112C) is
performed before flood exposure so thatthe photorezist becomes
harder and the layer is more
durable for the wet chemical etching or RIE etching. As
developer we have used AZ726 MIF,
and stoped the developing process by immersion the wafer in
deionized water. The such
obtained microchannelsdepth is around 1.22m .
-
11
2.2. Wet chemical etching
For SiO2etching we have prepared the solution with ammonium
fluoride NH4F (12g) in
water H2O (17ml.). When the salt was melt we put hydrofluoric
acid 38% HF (3ml.). The
sample was immersed in this solution different time (5 min.,
15min., 60 min. respectively)
and then the etching process is stoped by immersing the sample
in deionized water. We can
see that the longer time is the wet etching process the
microchannels profile is changing from
the rectangular shape in the sinusoidal one (fig. 3) due to the
isotropic process imposed by
HF. For microfluidics application this cross-section not exactly
rectangular cannot be
neglected because it adds extra impedance to the flow dueto the
small dimensions used. This
drawback can be fixed by means of reactive ion etching
(RIE).
Fig. 3. Sample microchannel 5 after wet etching a) 5min.
immersion the microchannel depth
is around 1.3m; b) 15min. immersion the microchannel depth is
2.1m;
2.3. Reactive ion etching (RIE)
In contrast with the typically isotropic profiles of wet
etching, the RIE can produce very
anisotropic etch features, dueto the mostly vertical delivery of
reactive ions. Etch conditions
in RIE system (RIE IONVAC) depend strongly on the many process
parameters, such as
pressure, gas flow and RF (radio frequency) power. We performed
the RIE process by mixing
tetrafluoromethane CF4 (20sccm) and O2 (2sccm) at 200W, 20mtorr
for 10min. In this way
the surface quality of the etched microchannels isvery good and
will not affect the flow
behavior, as it still will be laminar flow. In figure 4 is shown
the sample after optical
lithography process and the obtained profile after RIE
process.
-
12
Fig. 4. Sample microchannel 3 fabricated by RIE
For our applications neither this method is too convenient due
to the channels depth not very
high (about 1.3 microm. before photorezist removal), therefore
we tried a deep reactive ion
etching(DRIE) with STS Multiplex ICP AOE system. This machine
consisting of multiplex
ICP AOE (Advanced Oxide Etch) can be setup to process wafers up
to 200 mm, but currently
setup is 100mm wafers size. Against the above described RIE
process, in DRIE we added a
gas flux of octafluorocyclobutane C4F8 (20sccm), set the
pressure at 4mtorr and reduced the
etch time at 6min. A drawback of this method is that it should
be used with a metal mask
layer. The metal layer (Cr 100nm) was evaporated before optical
lithography process. By
means of this method the microchannels depth is around 4m
(fig.5). After lithographic
process we performed an evaporation of the 30nm Au layer and
functionalization itwith 1,6
hexane dithiol in order to facilitate the covalent binding of
the semiconductor nanocrystals to
the solid surface using self-assembled monolayers.
Fig. 5. Sample microchannel 48 fabricated by DRIE: a)
profilometer; b) SEM image
2.4 Room Temperature Microchannel Fabrication for Microfluidic
System
Silicon dioxide has hydrophilic property that was stable and it
is thus preferable for
applications in which devices are used extensively, such as in
high throughput screening.
-
13
SiO2was also known for its superior optical properties, useful
for optical detection and
analysis methods.
The microfluidic system was designed as shown in figure 6(a),
including sample inlets,
particle separation region, and evaporation regions as shown on
figure 6(b).
Figure 6: The developed microfluidic system: (a) Total system
including separate region, and
(b) Evaporation region.
Microchannel with different area of evaporation region was
designed, as shown on figure
7(a). Instead of heater design, external thermal source was used
on the top to change
temperature at the outlet of microchannel for liquid flowing
inside. Generally, the width of
comb was usually smaller than the width of main channel, to
ensure that liquid will be
trapped on the end of microchannel.After processing, evaporating
region of chips was fixed
on silicon bulk which was put on top of hot plate to keep on the
same temperature, is shown
on figure 7(b).
As results, velocity of flow was proportion to area of
evaporating region. It is linear relation
since operating on fixed width of main channel with different
area of evaporating region. The
slope of velocity/evaporating-area ratio will decrease with
width- increasing of main channel.
-
14
Figure 7: Microstructure design for micro fluidic system (a)
Total system including,
Evaporation region, and (b) Chip connected onto bulk silicon and
hotplate.
Glass has material properties that are stable in time and it is
thus preferable for applications in
which devices are used extensively, such as in high throughput
screening. Glass is
hydrophilic, meaning it attracts and holds moisture. Most
plastics, in comparison, are
hydrophobic and need treatment to become hydrophilic. If
hydrophobic surfaces are needed,
we can modify the glass surface by applying a coating to the
channels.
In this process, photoresist AZ9260 was used as sacrificial
layer, which is easy to be
deposited and patterned. Another important issue for this
developed process is to deposit
porous Silicon DI water Comb Hot plate Thermal couple silicon
dioxide film by e-beam
evaporator, which degree of porosity could be controlled by
adjusting deposition rate. By
using this porous property, organic solution can go through
silicon dioxide thin film to
release structure and to form microchannel.
The process flow of microfluidic system was shown on figure 8
(Liu C. S. Y., Dai B.T 2005].
Glass wafer were cleaned in RCA-1 and piranha solutions at 950C.
The clean wafers were
rinsed with deionized (DI) water and dried in pure N2. Then
glass wafer was coated by
HMDS to improve the adhesion between PR and wafer. First, we
patterned AZ9260
photoresist, which was coated with 3000 rpm and exposed under
200 mJ. Then, photoresist
was treated up to 1100for 60 seconds to be reflowed. Secondly,
silicon dioxide/Ti (10000
/1500 ) was deposited by e-beam evaporator on top of PR and
glass substrate. The
deposited structure was strong enough to make etching solution
penetrate to release PR and to
form microchannel. The heaters was deposited and patterned at
the entrance and exit by RIE
etching. The ercentage of oxygen in RIE etching process is very
important. The high
percentages of oxygen will generate too much oxygen ions to
damage PR and metal. If less
oxygen ions exist in chamber, organic residue will not be
removed from surface of wafer.
-
15
Then, microstructures were easily released by acetone or some
organic solvent through
porous SiO2structures.
Figure 8:Fabrication process flow of region from cross section
AA to outlet (a) Start from
Pyrex #7740, (b) Channel definition by AZ9260, (c) SiO2 / Ti
deposition (d) Heater and
temperature sensor formation, (e) Entrance and exit formation,
(f) Structure releasing.
Figure 9(a) and 9(b) are top view of microchannel with heater at
the outlet of microfluidic
system. It shows that fabrication process was easy to integrate
metal onto microchannel
structures. The most important is that microchannel structures
were fabricated by porous
silicon dioxide. Moreover, the whole fabrication process was
down under room temperature,
which is suitable for bio-medical application if bio-related
layer was coated in the middle of
device fabrication.
Figure 9: (a) Evaporating design on microfluidic system, SEM
pictures for (b) heater and
temperature sensor, and (c) entrance of microchannel
In figure 9(c), on the top of microchannel forms curvature at
the sidewall of microchannelit,
that is clearly shown successful microchannel formation after
releasing without damage.
From the results, the maximum height can bre reached up to 7m
and the width can be
created up to 60m, if 1m thin film of silicon dioxide was
deposited as structure material.
After microchannel formation by developed fabrication process,
microscale of particles,
accharomycetes, were used in microfluidic system to prove the
liquid transportation by
evaporating force. By turning on the heater at exit of
microchannel, the evaporation force
-
16
would drive the liquid, as shown on figure 10. The particle
movement is steady with time.
Each photo was taken every 0.28 seconds, and total moving length
is about 0.18 m. By
observing the movement of particles, velocity of saccharomycetes
was estimated up to
500m per second on controlling heater temperature at about
40.
Figure 10: Movement of saccharomycetes in microchannel by
evaporating force
2.5 Cylindrical PDMS Microchannel Fabrication by Sacrificial
Molding
using Caramel
Microfluidic channels fabricated by our sacrificial molding
process are shown in
Fig.11. 3-D channel was made without extra layering process
because our method can meke
3-D caramel template directly.We investigated relativity between
conditions of caramel
patterning and cross-sectional area of fabricated channel
(Fig.13). Cross-sectional
images taken on scanning electron microscope were also shown in
the figure. This is
attributed to surface tension of caramel. After the deposition,
a viscosity of the caramel
became lower by absorption of moisture or application of heat,
thus surface tension made
its shape cylindrical. The cross-sectional shape depends on
initial shape and deformation
time of depositted caramel. The reason why the cross-section
tended to become circular as a
nozzle traveling speed higher is the initial shape was flat at
lower nozzle traveling
speed (Masashi Ikeuchi ).
-
17
Figure 11. Microchannels fabricated by proposed method. (a)
fluorescent image of
channel network filled with rhodamine B solution, (b)
reconstructed image of 3-D
interchange taken on conforcal microscopy (scale bar: 100m).
2.6 One-stage fabrication of sub-micron hydrophilic
microchannels on
PDMS
Polymeric materials such as poly(methylmethacrylate)
(PMMA),polystyrene, polycarbonate
(PC), polyurethane, and poly(dimethylsiloxane) (PDMS) have been
widely used as the
substrate materials for microchannels. Among them, PDMS has
received more attention due
to its outstanding performances such as transparency, high
permeability to gases, high
elasticity, easy processing and seals the channel readily, etc.(
Makamba H. et.al.,2003).
Nevertheless, PDMS is extremely hydrophobic, which makes it very
difficult for aqueous
solutions to flow inside the microchannels. In addition, the
absorption function of PDMS
surface may generate fouling on the surface. The hydrophobicity
has long been the bottleneck
to the application of PDMS as a microchannel material(D. Bodas
et. al.,2008). Because of
this, different approaches,such as oxygen plasmas (Fritz J.L.
et.al.,1995), ultraviolet light
(UV) (Lai J.Y. et.al.,1996), corona discharges and so on(8]have
been employed to modify
PDMS to obtain a hydrophilic surface. In all these approaches,
the microchannels were
produced firstly, then the microchannel surfaces modified
indicating a time-consuming and
complicated process. Whats more, the hydrophilicity of the PDMS
surface thus obtained will
not last long, say three weeks. In this communication, a
relatively simple method, i.e., one-
stage fabrication of microchannels was reported, using vacuum
ultraviolet light (VUV)
lithography in vacuum. As demonstrated below, the hydrophilicity
on the PDMS surface can
be kept for a longer term after the treatment.
Sylgard 184, consisting of poly(dimethylsiloxane) and a
reinforcing silica filler was prepared
by carefully mixing the precursors Sylgard 184 A/B at a ratio of
10:1 by mass. The PDMS
precursors were then spin-coated onto the cleaned glass
coverslips at 5000 rps using the
-
18
spincoater (Efimenko. et. al.,2002). The resultant PDMS thin
films were then degassed under
vacuum and cured in an oven at 708C for 3 h to produce
cross-linked PDMS. Then the
PDMS films under a closely contacted photomask, which consisted
of a 3-mm thick quartz
glass plate, that is, 91% transparency at 172 nm, with a 0.1-mm
thick chromium pattern, were
irradiated with the VUV light of 172 nm (Ushio Inc., UER20-172V,
Intensity at the lamp
window = 10 mW/cm2 ) in a vacuum (500 Pa) for 15 min, the
experimental setup is
described in the literature(Sugimura et.al.,2000).
In conclusion, sub-micron hydrophilic microchannels can be
fabricated by vacuum ultraviolet
light (172 nm) lithography. XPS analysis showed that the
chemical composition of the
microchannel surface was changed, and a silicon oxide glass-like
crosslinking structure may
be formed, which can prevent the movement of hydrophilic groups
from the surface to the
bulk and thereby gives rise to the longer hydrophilicity of the
microchannel surface.
2.7 Microchannel Fabrication using photomask,SU-8,glass
slide
Microchannel fabrication begins by creating a reusable master
mold. The mold substrate is a
glass slide. The mold substrate is a glass slide. The slide is
cleaned in a piranha solution
(H2SO4:H2O2) (Chan-Park. et. al.,2004). A rinse in deionized
water follows. The clean glass
slide is dried using filtered-compressed nitrogen, and
dehydrated at 120C for thirty minutes.
Cleaning and dehydrating will prolong the life of the master
mold (MicroChem].
Four mL of Epoxy-based SU-8 photoresist from MicroChem Corp
(Newton, Massachusetts)
is spin-coated at 300 rpm with an acceleration of 83 rpm/s for
10 seconds and then to 3,000
rpm at 415 rpm/s for 30 seconds, per the manufacturers
instructions (MicroChem]. The SU-8
coated glass is then set on a perfectly level surface for 20
minutes to allow the photoresist to
smooth out. This will allow for even heating of the SU-8 in the
steps that follow. The mold is
ramp heated from 50C to 95C at 2C/min for 23 minutes and then
held at 95C for six
minutes. Ramp heating is implemented for all heating processes
to prevent thermal stresses
which may cause cracks in the mold and reduce its life.
A photomask is placed in contact with the SU-8 for the
photolithography procedure. The
photomask was created by first modeling the channel geometry in
CAD and then printing this
geometry on transparent medical film using a high resolution
printer. The photomask must be
in direct contact with the SU-8. If there is any gap between the
mask and the SU-8, a
widening of the pattern on the final mold will result due to
diffraction of the UV light
-
19
exposure which follows (Li P. (2007). The SU-8 is exposed for 45
seconds in an ELC-500
(Bethel, Ct.) UV light exposure chamber. This yields the
necessary 240 mJ/cm2of exposure
energy for a 50 m thick SU-8 film on a glass substrate
(MicroChem].
Post exposure baking takes place immediately after UV light
exposure in order to cross link
the exposed film. The SU-8 slide is ramp heated from 50C to 95C
at 2C/min for 23
minutes and then held at 95C for six minutes. MicroChem SU-8
developer (Newton,
Massachusetts) is used to remove any unexposed SU-8 from the
glass substrate. The mold is
developed for six minutes (MicroChem] while being agitated on a
shaker at 150 rpm. After
an isopropyl alcohol rinse the mold is complete.
Dow Corning Slygard 184 silicone elastomer and curing agent
(Philadelphia, Pa) is
thoroughly mixed 10:1 by weight (Chan-Park. et. al.,2004). The
PDMS is poured on top of
the mold to the desired thickness. The PDMS is degassed in a
vacuum for five minutes and
then the chamber isvented. The PDMS is then heated to 70C for
thirty minutes . After
curing, the PDMS is peeled off of the mold and an inlet and
outlet is created using a biopsy
punch.
The PDMS negative relief and a clean glass slide are placed face
up in a Diener Femto
plasma asher (Reading, Pa.). Vacuum conditions are created and
held for five minutes.
Oxygen at 25 psi is introduced and the plasma asher is run for
three minutes. This procedure
oxidizes the surface of both the PDMS and the glass, and
surface-oxidized PDMS and glass
will form a bond (McDonald et.al.,2002). It is important that no
mechanical stress is applied
to the PDMS or glass; otherwise the surface modification will
diminish. After the two
surfaces are placed in contact with one another the channel is
heated to 70C for ten minutes
to allow for full bonding (McDonald et.al.,2002). The
microchannel fabrication is now
complete.
-
20
Fig 12. Schematic for microchannel fabrication procedure
3. Equation Derivations (Stroock et. al., 2002).
3.1 Governing Equations
The governing equations of the fluid motion are the
Navier-Stokes equation and the
continuity equation
3.1
3.2
where u = (u, v, w), is constant density and is the kinematic
viscosity. For our problem the
flow is steady due to the low Reynolds number, so u/t = 0. Also,
for relatively low
Reynolds number, for flow in a microchannel with a large ratio
of channel length to width,
the inertia effects can be neglected (Stroock et. al.,
2002).
Therefore we neglect u u. In addition, as and are constants, we
rescale p such that p =
p/ . The Navier-Stokes equation then reduces to the Stokes
equation
3.3
There are also the following boundary conditions on the flow in
the microchannel.
3.4a
Equations have been derived by Stroock et. al., 2002.
-
21
3.4b
3.4c
where U (x, y) is the function of x and y which defines the flow
on the base of the channel.
These equations satisfy the condition that there is no through
flow on the walls of the channel
and the no-slip conditions on the floor and ceiling of the
channel. However we have not
applied no-slip boundary conditions on the sides of the channel,
because of the simplification
in the model. We impose a function at the base of the channel
that is just shifted with respect
to a herringbone and not one which is 0 at the sides and hence
at y = /2 and /2 the velocity
u will not be 0. This simplification should not affect the
result too much, as the channel has a
large ratio between width and height and the effects of not
applying no-slip at the side walls
will change very little to the flow in most regions of the
channel.
3.2 Velocity Field
Due to the low aspect ratio between h and , Lubrication theory
or Thin Layer theory can
be applied to (2.3) to obtain equations for u, v and w and hence
an approximate analytical
solution for velocity field can be found.
We begin by setting = h/. As is small, the changes in z are
small compared to those in x
and y. Therefore using Lubrication theory we rescale z such that
z z and hence /z
1 /z. For the same reason w w. Thus equation (3.3) becomes
3.5a
3.5b
3.5c
3.5d
-
22
and (3.2) becomes
3.5e
Note that w w has cancelled the 1 given from /z.
We define vertical averaging as
3.6
From this we find that . Also = 0 due to the boundary
conditions. Hence = 0 implies
3.7
This means that the vertically averaged velocity is
incompressible.
We now assume that /x and /y are order 1. Therefore as 2 1, 2 is
very large andhence
equations (3.5a),(3.5b) and (3.5c) reduce to
3.8a
3.8b
3.8c
In order to have a non-zero flow, equations (3.8a) and (3.8b)
imply that the pressure must be
of order 2 at leading order, but must not depend on z in order
to satisfy (3.8c). Therefore
3.9
where is of order unity.
Now equations for u, v and w are found. Equations (3.8a), (3.8b)
and (3.9) imply:
-
23
3.10a
3.10b
First we solve equation (3.10b). Using the boundary conditions,
(3.4a) implies b0 = 0 and
(3.4b) implies
Therefore equation (3.10b) becomes
3.11
To satisfy the boundary condition at the side wall (3.4c), we
require
3.12
Now we solve equation (3.10a). At z = 0, (3.4a) implies u(x, y,
0) = a0(x, y) = U (x, y). At z =
h, (3.4b) implies
SO
Which becomes
3.13
We now derive w using u and v by substituting (3.11) and (3.13)
into (3.5e) to get
is now integrated w.r.t. z to obtain
3.14
-
24
where the constant value has been set to 0 due to the boundary
condition (3.4a). We now
have equations for u, v and w which only depend on x, y, z, P0
and U .
Figure 13: A diagram of the herringbone shape with respect to
y.
3.3 Pressure Analysis
In order to use the u, v and w equations, we now need to find a
solution for P0 . To solve for
P0 we use the vertically averaged equation (3.7) (i.e. ). The
vertical average
of v and u can be easily found
3.15
Where
So 3.16
-
25
Next we substitute (3.15) and (3.16) into the vertically
averaged equation (3.7) to obtain the
Condition
3.17
This can now be solved for P0 and hence analytical solutions can
be obtained for u, v and w.
However first we simplify w by substituting (3.17) into (3.14)
to get
3.18
Which reduced to
Hence w does not explicitly depend on P0.
In order to solve (3.17) for P0 the specific form of U is
needed. Figure 3.1 shows how the
herringbone depends on y within the channel. U is different for
y a and y > a. To represent
the herringbone we define a function (y) such that
Therefore (y) is continuous in y. We now take a Fourier
expansion of U in x, varying the
phase in y following the herringbone pattern,
3.19
where kn= 2n/L. This equation is a sum of terms. Because
equations (3.5a) to (3.5e) are
linear,we now look for a solution for each term, which can then
be superimposed once they
have been found. U0is considered later. We now look at
-
26
3.20
where = 0 gives us the sin term where and = /2 gives us the cos
term
where depend on the step function at the base of the
channel. We may expand (3.20) as
3.21
We further divide this into two terms of the form
3.22
where for = 0 we get the sin cos term and for = /2 we get the
cos sin term in (2.21).
Again we will superimpose the solutions. We have thus reduced
the problem of solving for
the boundary condition (3.19) to four boundary conditions of the
form (3.22), with ( , ) =
(0, 0), (0, /2), (/2, 0), (/2, /2).
Now we let
We now substitute P0 and U into equation (2.17) to get
Therefore
3.23
We noe define
So that
-
27
3.24
We look for a particular solution of the form
With the choice = Q, equation (2.24) becomes
Which implies
Therefore
3.25
Additionally, the complementary solution for is
So the solution for when y a and y > a are
3.26a
3.26b
There are 4 -dependent constants to find; AI , AII , BI and BII
. These constants are
independent of . There are four conditions that we need to
satisfy to find the constants
3.27a
3.27b
-
28
3.27c
3.27d
These conditions ensure that the pressure is continuous over the
microchannel and that there
is no through flow at y = /2 and /2.
.
3.4 Pressure Gradient and Constant Velocity Solution
In order for there to be an overall mean flow in the positive
x-direction, there must be either a
pressure gradient or a nonzero mean velocity induced on the
floor of the channel, in addition
to the herringbone induced velocities. On a global scale the
herringbone velocities average
out because for every forward flow herringbone there is an equal
and opposite backwards
flow herringbone due to the step function imposed. Having a
constant velocity on the base of
the channel is equivalent to having a moving channel floor,
which is only feasible for electro-
osmotically driven flow. This would be impossible with a grooved
floor which would need to
be pressure driven.
The U0 term in the expansion for U is the constant velocity. The
pressure gradient would only
be in the x-direction. Therefore we define the pressure for
pressure driven flow as P0 = rx
where r is positive. This will create a flow in the positive
x-direction as the pressure gradient
(r) is negative, so the pressure reduces as x increases and
hence fluid will flow from high to
low pressure areas.
P0 = rx and U = U0 which implies P0x = r, P0y = 0, P0xx = 0 and
Ux = 0. Therefore the
pressure equation (3.17) holds and the equations for v and w
((3.11) and (3.18) reduce to v =
0 and w = 0. However the equation for u (3.13) becomes
The velocity (u) generated by electro-osmosis is linear in z
(Couette flow) whereas the
constant pressure gradient flow is quadratic in z (Poiseuille
flow). For small z, this implies
that the velocity generated by the constant electro-osmosis is
much greater than pressure-
driven flow. From a manufacturing stand-point the requirement
for a high pressure to drive
the flow is undesirable and electro-osmosis is much easier and
effective to use. As stated in
-
29
the introduction, this project will not look at pressure-driven
flows. We set r = 0 and therefore
the global flow is created by U0 only. However, it is useful to
know that the model can easily
be changed to model pressure driven flow by setting U0 = 0 and r
to the non-zero value of the
pressure gradient. We label the flow in the x-direction due to
U0 as ue:
4. mixing analysis
4.1 Crossflow and mixing in obstructed and width-constricted
rotating
radial microchannel
The crossflow and mixing in rotating radial microchannels with
various obstruction and/or
width-constriction geometries have been investigated to improve
samples/reagents mixing
using a centrifugal microfluidic platform. It is found that a
channel with repeated cycles, or
patterns, of obstruction followed by width-constriction (OWC)
provides the best mixing
result. Crossflow in the microchannel is highly intensified even
at moderate rotation speed
less than 100 rad/s, due to the OWC configuration with increased
mixing from a combination
of (a) local centrifugal acceleration abthat arises from flow
negotiating corners of the
obstructions in the channel, and (b) Coriolis
accelerationacorinduced from throughflow in the
rotating microchannel, which is highly amplified in the two
narrower sub-channels
partitioned by the center obstruction in the channel as well as
the downstream channel with
width constriction. Moreover, mixing is further enhanced with
flow splitting at the stagnation
point of an obstruction followed by flow recombination with
jetjet impingement mixing
downstream of the obstruction and upstream of the width
constriction. Numerical and
experimental models have been developed and their results agree
well with each other. As
much as 95% uniformity in mixing can be achieved for a short
30-mm long radial
microchannel with repeated OWC patterns at a moderate rotation
speed of 73 rad/s withEk=
0.049 and Ro= 15.4. The performance of the rotating OWC channel
far exceeds that of the
stationary OWC channel, the rotating unobstructed/obstructed
microchannel, and the rotating
width-constricted microchannel.
The flow and mixing in rotating obstructed and or
width-constricted radial microchannels
have been investigated by numerical simulation as well as
complementary experiments. The
results have been bench-marked against several results: (a)
rotating radial unobstructed
-
30
channel, (b) stationary radial obstructed/constricted channels,
and (c) rotating channel with
width-constriction in the entire channel. Also, optimization on
obstruction length and spacing
between adjacent obstructions has been made. The results can be
summarized as follows,
(1) The crossflow in the cross-sectional planes of the rotating
radial obstructed channel is
determined by interaction of theacor and localab.
(2) The flow rate in the channel is determined by the channel
length, length of obstruction,
the width-constriction, and the rotation speed. Better mixing
can be obtained from either
smaller obstruction length and/or larger spacing between
adjacent obstructions. The
obstruction acts also as a barrier splitting/delaminating the
flow into two narrow sub-streams,
one of which the two accelerations, Coriolis and local
centrifugal accelerations, add up and
the other for which the two accelerations oppose creating
complicated fluid folding and
mixing.
(3) Improvement can be best achieved in channel with OWC. This
allows jetjet
impingement and enhanced Coriolis effect from narrow channel
with intense recirculation
rate and higher crossflow velocity as well as shorter distance
for the crossflow to carryout
mixing. The latter could not have been achieved just by
patterned obstructions, or width-
constriction.
(4) Higher rotation speed with smaller Ekincreases both acor and
local ab (given increased
throughflow velocity) and reduces viscous friction effect, thus
enhances mixing.
(5) With the special configuration of OWC, only moderate
rotation speed is required to
obtain effective mixing in microchannel. .
The results of the investigation offer a new perspective for
understanding the crossflow and
mixing in the rotating radial obstructed and/or
width-constricted channel. This would be
useful for optimizing mixing in the microchannel, as well as
lending itself to benefiting heat
and other transfer processes. (Leung , Ren .(2013)
4.2 Two-fluid mixing in a microchannel
A numerical study of the mixing of two fluids (pure water and a
solution of glycerol in water)
in a microchannel was carried out.By varying the glycerol
content of the glycerol/water
solution, the variation in mixing behavior with changes in the
difference in the properties of
-
31
the two fluids (e.g., viscosity, density and diffusivity) was
investigated. The mixing
phenomena were tested for three micromixers: a squarewave mixer,
a three-dimensional
serpentine mixer and a staggered herringbone mixer. The
governing equations of continuity,
momentum and solute mass fraction were solved numerically. To
evaluate mixing
performance, a criterion index of mixing uniformity was
proposed. In the systems considered,
the Reynolds number based on averaged properties wasRe=1 and 10.
For low Reynolds
numberRe1, the mixing performance varied inversely with mass
fraction of glycerol due
to the dominance of molecular diffusion. The mixing performance
deteriorated due to a
significant reduction in the residence time of the fluid inside
the mixers.
The mixing of two fluids was numerically modeled for two types
of micromixer: a three-
dimensional serpentine mixer and a staggered herringbone mixer.
In these calculations, the
mixing of pure water with a solution of glycerol in water was
investigated for three different
mass fractions of glycerol (/0, 0.2 and 0.4). These fluids were
chosen to test the mixing
behavior of fluids with different properties and a large
concentration gradient. The
dependence of the mixing performance on/ atRe=1 and 10 was
examined. AtRe=1, the
mixing performance of both mixers varied inversely with mass
fraction of glycerol due to the
dominance of molecular diffusion. When the Reynolds number was
increased to 10, the
opposite trend was observed for the serpentine mixer. This
change in behavior was attributed
to the enhancement of flow advection at large/. However, no such
change was observed on
increasing the Reynolds number in the herringbone mixer. In
fact, not only was the expected
enhancement of chaotic advection absent on increasing the Rein
the herringbone mixer, the
mixing performance actually deteriorated due to a significant
reduction in the residence time
of the fluids inside the mixer. (Liu , et.al.,2004) )
4.3 Single-phase fluid flow and mixing in microchannels
In the last decade there has been an exponential increase in
microfluidic applications due to
high surface-to-volume ratios and compactness of microscale
devices, which makes them
attractive alternatives to conventional systems. The continuing
growing trends of microfluidic
highlights the importance to understand the mechanism and
fundamental differences involved
in fluid flow and mixing at microscale. In the present article,
the experimental research
efforts in the area of microscale single-phase fluid flow and
issues associated with
investigations at microscale flow have been summarized. The
experimental data are being
analyzed in terms of friction factor, laminar-to-turbulent
transition, and the effect of
-
32
roughness on fluid hydrodynamics for different cross-sectional
geometries.The differences in
the uncharacteristic behavior of the transport mechanisms
through microchannels due to
compressibility and rarefaction, relative roughness, property
variations and viscous
dissipation effects are discussed. Finally, progress on recent
development of micromixers has
been reported for different micromixer types and designs. The
micromixers have been
quantified based on their operating ranges (in terms of
characteristic dimensionless numbers
such as Reynolds numberRe, Peclet number Pe, and Strouhal number
St) and mixing
characteristics.
Microscale devices are powerful tools for process development
and have been successfully
applied for improvement of established chemical processes in
industry. In recent years
microscale devices have been produced for a wide variety of unit
operations in chemical
industry (such as mixers, reaction vessels, valves, pumps,
extractors, heat exchangers, etc.).
From the patent and research article analysis carried out in the
present review it can be seen
that most of the development is being carried out in the last
decade and it is still in progress.
In last 23 years the focus is more in the field of applications
rather than development of
microscale devices. For the applications in microreaction or
mixing field, it is required to
develop understanding about the fluid flow behaviour and mixing
effects in the microscale
devices. In the present review the experimental research efforts
of fluid flow behavior and
mixing effects reported by various researchers have been
analyzed and discussed.For the
friction factor and transition from laminar-to-turbulent
analysis in microchannels, it was
observed that the good agreement with conventional theory has
been reported by the authors
who have carried out the geometrical measurements before
experiments and accounted for
losses (entrance and exit) during data collection and analysis.
It is demonstrated that the
average roughness parameter is not adequate to characterize the
surface roughness in
microchannels due to scale effects. Though in recent papers the
discrepancies in
microchannels due to dimensional measurements and data
collection and analysis have been
resolved with accurate measurements; more attention is required
for the scale effects
(dho50mm), surface roughness and compressibility effects in
microchannel. Therefore, much
work is required in this area to understand the complete fluid
dynamics in microchannels.
Finally, different designs of micromixers and their operating
conditions have been discussed.
The micromixers were categorized based on their principle of
operation. Though, there are
numerous micromixer designs, still there is a room for new
robust and professional designs. It
is found that micromixing research is focused mostly at the
laboratory scale, and fewer
-
33
efforts are made on pilot-plant and industrial scale. As a
future development it is required to
establish the micromixers as production apparatus in the
chemical industry. Though the
performance of active micromixers is better than passive ones,
benchmarking and application
based pilot-plant studies are still required. For future
development of micromixers it is
required to characterize the mixing with real-case mixing
solutions. (Kumar ,et.al.,2011)
4.4 Gasliquid two-phase flow in microchannel at elevated
pressure
The present study deals with pressure effects on the
hydrodynamic characteristics of gas
liquid two phases within a T-junction microchannel. The
operating pressure is in the range of
0.1-5.0 MPa. Nitrogen and de-ionized water are selected as the
test fluids. The gas Weber
numbers vary from 1.37x10-5to 3.46 at atmospheric pressure and
from 1.70x10-3to 70.32 at
elevated pressure,respectively. The liquid Weber numbers are in
the range of 3.1x10-3-4.9.
The operating pressure plays an important role in gasliquid two
phases flow. Seven typical
flow patterns such as bubbly flow, slug flow, unstable slug
flow, parallel flow, slug-annular
flow, annular flow, and churn flow are observed. Based on the
force analysis of the gas and
liquid phase in microchannel, the formation mechanisms of flow
patterns are discussed at
great length, and the flow pattern maps are divided into five
regions usingWeGSandWeLSas
coordinates. These results are beneficial for future
investigation to understand gasliquid
two-phase mass transfer and reaction characteristics in
microchannel at elevated pressure.
Gasliquid two-phase flow in T-junction rectangular microchannel
with the hydraulic
diameter of 400mm at atmospheric and elevated pressure (1.0-5.0
MPa) has been
investigated. The superficial velocities range from 4.62x10-2to
23.15 m/s for gas and from
2.31x10-2 to 0.93 m/s for liquid. The gas Weber numbers vary
from 1.37x10-5 to 3.46 at
atmospheric pressure and from 1.70x10-3 to 70.32 at elevated
pressure, respectively. The
effect of operating pressure on the liquid Weber numbers can be
ignored, which are in the
range of 3.1x10-3 -4.9.Seven typical flow patterns such as
bubbly flow, slug flow, unstable
slug flow, parallel flow, slug-annular flow, annular flow and
churn flow are also observed in
the T-junction rectangular microchannel at atmospheric and
elevated pressure, respectively. It
is found that the same flow pattern shows different detail
characteristics due to the operating
pressure, which may induce the different gasliquid mass transfer
and reaction performance.
The hydrodynamic characteristics of gasliquid two phases are
mainly affected by the
interfacial tension of gasliquid two phases, the gas inertia
force and the liquid inertia force.
Based on the force analysis of gas and liquid in microchannel,
the formation mechanism and
-
34
process of observed flow patterns are discussed at great length.
The flow pattern maps are
divided into five regions usingWeGSandWeLS as coordinates based
on their formation
mechanisms. The transition lines shift to higher WeGS and
lowerWeLSat elevated pressure
compared to the atmospheric pressure. The transition line, from
zone I to II, shifts to higher
WeGSand lowerWeLSwhen the operating pressure increases from 1.0
MPa to 5.0 MPa.
Other transition lines from zone II to III, from zone III to IV,
and from zone III to V almost
remain unchanged at elevated pressure. It is important to note
that this study gives a
contribution to the influence of operating pressure on the
gasliquid system in T-junction
microchannel. This will serve as the basis for future gasliquid
two-phase mass transfer and
reaction characteristics in microchannel at elevated pressure.
(Zhaoet et.al.,2013)
4.5 Liquid mixing in gasliquid two-phase flow by meandering
microchannels
The influence of the channel radius on the mass transfer in
rectangular meandering
microchannels (width200400um and height of 150um) has been
investigated for gasliquid
flow. Laser induced velocimetry measurements have been compared
with theoretical results.
The symmetrical velocity profile, known from the straight
channel, was found to change to an
asymmetrical one for the meandering channel configuration. The
changes in the secondary
velocity profile lead to an enhanced radial mass transfer inside
the liquid slug, resulting in a
reduced mixing length. In the investigated experimental range
(superficial gas velocity 0.08
m/s and superficial liquid velocity 0.010.07 m/s) the mixing
time was reduced eightfold
solely due to changes in channel geometry. An experimental study
on the liquid slug lengths,
the pressure drop and their relation to the mass transfer have
also been performed.
Experimental results were validated by a simulation done in
Comsol Multiphysics . To obtain
information for higher velocity rates, simulations were
performed up to 0.64 m/s. These
velocity variations in the simulation indicate the occurrence of
a different flow pattern for
high velocities, leading to further mass transfer
intensification.
We investigated mixing in liquid slugs for gasliquid Taylor flow
in straight and meandering
microchannels. Velocity profiles were determined both,
experimentally and numerically, to
explain the mixing results. Mixing length could be decreased by
geometrical adaptions to
12% compared to the straight reactor design. Enhancement of the
radial mass transfer in gas
liquid microreactors was achieved by introducing regular bends.
For a given channel width, a
smaller bend radius provides a more effective mass transfer over
the channel center line.
-
35
Increasing the channel width solely leads to increasing mixing
length. Since the liquid slug
volume increases as well, the mixed volume per mixing time
decreases at increasing channel
widths. Hence an extrapolation to the miniscale (dh1 mm) will be
a promising approach in
future projects. The decrease of mixing length by meandering
channels is caused by an
asymmetrical velocity profile in the channel bend. Compared to
the symmetrical recirculation
in straight channels, the inner vortex moves to the slug back
and shifts across the center line
to the outer half. Depending on the velocity, the vortex at the
outer half may be divided into
two vortexes or diminishes completely. This effect is only
observed at sufficient high
velocities (>0.1 m/s) and corresponds to the Dean vortices
observed for one phase flow in
curved channels. For low Dean numbers (low velocity, small
channel width and large bend
radii, respectively) the asymmetrical velocity profile
diminishes. Observations done at
different positions indicate a fast adaption of the flow profile
on the geometry: As soon as the
slug enters the bend, the asymmetrical profile as it was
proposed from numerical
considerations was observed and the symmetrical profile was
obtained directly behind the
bend. Therefore fast and efficient mixing can be achieved by
changing the flow direction
continuously. The total pressure drop per channel length
increases by applying meandering
structures. However, the pressure drop per mixing length will
decrease by applying
meandering structures. Beside Reactor A (straight channel), all
reactors yield within the
measurement uncertainty in the same pressure drop per mixing
length. Therefore no energy
dissipation occurs by applying meandering channels. In summary,
meandering channels are a
useful tool to enhance mixing in gasliquid flow in
microchannels, whereas large Dean
numbers lead to a more efficient mixing (Fries , et.
al.,2009)
4.6 Mixing process of immiscible fluids in microchannels
The paper is concerned with experimental investigations and
numerical simulations of
immiscible flows in microchannels in the presence of interfacial
surface tension. The aim of
the present study is to model the unsteady dynamics of the
vortical structures and interface
shape in the Y-branching geometries with square cross-sections.
The tested fluids are
Newtonian and weakly elastic polyacrylamide solutions in water
(modelled as shear thinning
CarreauYasuda fluids). The experiments used specially designed
configurations based on
optical and confocal microscopic devices; PIV measurements of
the velocity distributions and
direct visualizations of the interface are obtained. The
simulations performed with the VOF
solver implemented in the FLUENT code are validated by
experiments for small and medium
Reynolds numbers (0.1
-
36
vortices formation in the vicinity of the interface, phenomena
which directly influence the
mixing and diffusion processes within the micro-geometry here
investigated.
The main goal of the present study was to investigate and model
the formation of vortices in
the vicinity of the interface between two immiscible fluids,
during the dislocation of one
liquid by another liquid in a micro-branching geometry. The work
has focused on the 3D
numerical simulations of the unsteady flow patterns in a
micro-bifurcation generated by the
travelling of a separation surface. The VOF subroutine from the
commercial FLUENT code
(unsteady laminar and isochoric solvers) was first tested and
validated against several
experiments, performed with Newtonian and weakly elastic viscous
fluids, on two Y-channel
geometries with square cross-sections. In all cases accurate
representations of the
experimental flow spectra and interface shape are obtained,
which confirms that numerical
computations provide an accurate representation of the real flow
patterns within the channel.
The presence of interfacial surface tension determines the shape
of a clearly defined
separation surface between the contact phases. In its
neighbourhood, transitory 3D-vortices
are formed, a phenomenon which determines the local mixing
within each phase, even at
moderate and low Reynolds numbers. This unsteady complex
hydrodynamics develops
rapidly in a microchannel, but it is well captured and described
in our numerical simulations.
Even if the present studies are limited to only the flows of
immiscible Newtonian and
generalized Newtonian liquids, the results offer a fair
description of the unsteady patterns
developed in micro-bifurcations and their interdependence on the
evolution of the interface
shape. The modelling of the 3D-vortical structures during the
displacement of the primary
phase from the channel contains value information in developing
novel lab-on-a-chip
applications, especially if a diffusion process between phases
follows that dynamical process.
We believe that interfacial surface tension and normal stresses
(together with no-slip
conditions at the walls) might be the major factor which
influences the mixing process of
complex fluids in microchannels at low Reynolds numbers. This
assertion is now being tested
experimentally with work in progress being focused on obtaining
PIV measurements of the
micro-flows velocity distributions in the presence of the
interface between a Newtonian oil
and polymer solutions with different concentrations of
polyacrylamide in water. (Balan et.
al.,2010)
-
37
4.7 Mixing of a split and recombine micromixer with tapered
curved
microchannels
We demonstrate a novel parallel laminar micromixer with
two-dimensional staggered curved
channels with tapered structures. Dean vortex flows are produced
in curved rectangular
channels by centrifugal forces. The split structures of the
tapered channels result in the
uneven split of the main stream and the reduction of the
diffusion distance of two fluids.
Furthermore, when one stream is injected into the other the
impingement effects increase the
mixing strength. Cross-sectional concentration distributions and
particle trajectories are
utilized to examine the flow characteristics inside the curved
microchannel numerically. To
evaluate the mixing performance of the designed micromixer, four
different designs of a
curved channel micromixer are introduced for the purpose of
comparison. The mixing index
of the staggered curved-channel mixer with a tapered channel is
20% higher than those of the
other curvedchannel mixers: i.e., the staggered curved-channel
mixer with sudden contracted
channels, the staggered curved-channel mixer with uniform
channel width and the continuous
curved-channel mixer. However, a comparison of the pressure drop
penalty for the mixing is
also reported. The pressure drop of the staggered curved-channel
mixer with a tapered
channel is about 50% higher than those of the other two
staggered curved-channel mixers.
The effects of various Reynolds numbers (Re) and channel
configurations on mixing
performances are investigated in terms of the experimental
mixing indices and the
computational interfacial patterns. It appears that the Dean
vortex and split and recombine
(SAR) effects provide improved mixing when theReis increased
above 5. At theReof 50, the
channel length necessary for mixing to be achieved is 5 times
shorter compared to the case
where the Reequals 1. The comparison between the experimental
data and numerical results
shows a very similar trend.
The centrifugal forces in curved flow channels cause fluids to
produce Dean vortex flows.
The existence of the secondary flows, the split and recombine
structures of the flow channels,
and the impingement effects result in increased mixing strength.
On the basis of this
principle, a parallel laminar micromixer composed of several
staggered three-quarter ring-
shaped channels and a semicircular channel is designed in our
study. Three- dimensional
computational fluid dynamics simulations are performed to
investigate the mass transfer and
fluidic behavior in a curved microchannel. The cross-sectional
concentration distributions
and the particle trajectories are utilized to examine the mixing
and flow characteristics inside
-
38
the staggered curved microchannel with tapered structures. The
uneven split of two fluids
inside the staggered channels improves the mixing performance.
The effects of various
Reynolds numbers and four different curved-channel
configurations on mixing performances
are investigated in terms of the experimental mixing indices and
the computational interfacial
patterns. The results indicate that for low Reynolds numbers
(o5) the secondary flows are
negligible and only diffusion dominates the mixing performance.
At Reynolds numbers
greater than 10, the interface configuration of two fluids is
affected by the secondary flow
and the lamellar formation. The increased interface area of two
fluids could promote
increased mixing. At the Re of 50, the mixing length at the
third segment corresponding to
the downstream distance of 10.5 mm can be achieved in a distance
5 times shorter than when
the Re equals 1. The simulation results are in good agreement
with the experimental
measurements. The simple two-dimensional microstructure is
easily fabricated and can be
integrated with the pretreatment and/or detection microfluidic
system. (Sheu et.al.,2012)
4.8 Pumping and mixing in a microchannel using AC asymmetric
electrode
arrays
A numerical study of electroosmotic microchannel flow driven by
arrays of AC (alternating
current) asymmetric electrodes was carried out. By installing
asymmetric electrode arrays on
the top and bottom walls of the microchannel, pumping and mixing
flow modes can be
generated. The pumping mode (P) is generated when the sequences
of asymmetric electrode
pairs (narrow to wide) on the top and bottom walls are in phase,
whereas the mixing mode
(M) is generated by switching the sequence of electrode pairs of
the top wall (e.g., wide to
narrow). By combining mixing and pumping modes, enhanced mixing
performance can be
achieved without significantly reducing the flow rate. Among
various combinations
ofPandMmodes, the alternatingPMmode showed the best mixing
performance due to the
iterative convergent and divergent flow motions. The effects of
Peclet number and channel
height on the mixing efficiency were analyzed in detail.
A detailed numerical analysis has been performed to elucidate
the pumping and mixing
modes induced in a microchannel using AC asymmetric electrode
arrays. The asymmetric
electrode arrays were installed on the top and bottom walls of
the channel. The pumping
-
39
mode was obtained when the sequence of electrode pairs on the
top wall was the same as that
on the bottom wall, whereas the mixing mode was generated by
switching the sequence of the
electrode pairs on the top wall. Various combinations of pumping
and mixing modes were
tested to optimize the channel performance in terms of the
mixing efficiency and pumping
flow rate. The species equation was solved with the Stokes
equation to obtain the
concentration and velocity field data. Most of the calculations
were performed at Pe=104.
The results showed that for a given slip velocity, pumping was
more effective in channels
with smaller heights. For the mixing mode, the shape of the
circulation cell was gradually
distorted as the top wall position was shifted with respect to
the bottom wall. By contrast,
such shifting of the relative positions of the top and bottom
walls had little effect on the
pumping mode. The mixing efficiency (eo) at the outlet decreased
as the Peclet number (Pe)
was increased. As the proportion of mixing modes within a
sequence of mixing and pumping
modes was increased, the flow rate decreased linearly and the
mixing efficiency (eo)
increased. Pumping was prohibited in systems with a very large
proportion of mixing modes.
During each pumping mode, symmetric diverging and converging
flow patterns were
observed; however, a zigzag motion was observed in theMM0 mode.
Three mixing modes
were obtained: convective circulating motion; diffusive motion
arising from forcing the main
flow through a narrow region; and diverging flow motion. The
alternatingPMmode showed
good mixing performance throughout the entire calculation
domain. As the channel height
decreased (H= 20, 10 and 5), almost 90% of the mixing efficiency
was achieved at large
Pe(Pe= 200, 1000 and 7000). Systems with a smaller channel
height and a smaller Pe
exhibited better mixing performance due to the strong diffusion
across the channel height.
(Yoon et.al. 2008)
4.9 Parametric study on mixing of two fluids in a
three-dimensional
serpentine microchannel
A flow analysis method using NavierStokes equations has been
applied to a parametric
investigation of mixing two fluids in a three-dimensional
serpentine microchannel, which has
not been reported so far. The serpentine microchannel with
L-shaped repeating units is
found to be effective in mixing fluids at Reynolds numbers, 1,
10, 35 and 70. Mixing
performance and pressure drop characteristics with two
geometrical parameters, i.e., the ratio
of channel height to channel width and the ratio of the length
of a straight channel in an L-
-
40
shaped unit to the channel width, have been analyzed at four
different Reynolds numbers. A
mixing index has been used to quantify and elucidate mixing
behavior in the microchannel.
The vortical structure of the flow in the channel is also
analyzed to identify the relationship
with mixing performance. The results reveal that mixing and
pressure drop characteristics in
a serpentine channel are very sensitive to the geometric
parameters, showing different
behavior at various Reynolds numbers.
A parametric study on the performance of a three-dimensional
serpentine channel with L-
shaped repeating units has been performed using computational
fluid dynamics. Mixing and
pressure drop characteristics have been investigated in terms of
two geometric parameters
i.e., the ratio of channel height to channel width, h/w, and the
ratio of the length of straight
channel in a L-shaped unit to channel width,d/w, as well as
Reynolds number. The
presence of bends at the end of the straight section of the
L-shaped unit strongly influences
the transverse flow structure in the channel, the vorticity
contours on the planes perpendicular
to the flow direction, and variation of circulation and mixing
index along this region. As the
Reynolds number increases from 1 to 70, both the levels of
circulation and the mixing index
increase throughout most of the channel. The results reveal that
mixing is significantly
dependent on both geometrical parameters. The mixing performance
of the channel is
generally improved with a decrease in the value of d/w. The
mixing index shows a minimum
value at h/w=1.0at higher Reynolds numbers, i.e., 35 and 70, as
the lowest surface to volume
ratio of the channel is found under these conditions, while the
effects ofh/wbecome negligible
at lower Reynolds numbers, i.e., 1 and 10. The pressure drop
characteristic of the serpentine
channel is also sensitive to the two parameters. At lower
Reynolds numbers, variation of the
two geometrical parameters has negligible effects on the
pressure drop. However, the effects
of the two parameters on pressure drop become pronounced at
higher Reynolds numbers. For
a given Reynolds number, the pressure drop increases as both
parameters ,d/w and h/w, are
decreased (Ansari , Kim 2009)
4.10 Mixing performance of a planar micromixer with circular
obstructions in a curved microchannel
A numerical investigation of the mixing and fluid flow in a new
design of passive
micromixer employing several cylindrical obstructions within a
curved microchannel is
presented in this work. Mixing in the channels is analyzed using
NavierStokes
equations and the diffusion equation between two working fluids
(water and ethanol)
-
41
for Reynolds numbers from 0.1 to 60. The proposed micromixer
shows far better
mixing performance than a T-micromixer with circular
obstructions and a simple
curved micromixer. The effects of cross-sectional shape, height,
and placement of the
obstructions on mixing performance and the pressure drop of the
proposed micromixer
are evaluated.
A planar curved laminating passive micromixer that is capable of
mixing at low
Reynolds numbers was proposed in this work. Detailed study of
the effects of
geometry and placement of obstructions on mixing was carried out
using Navier
Stokes analysis. The study was performed using a Reynolds number
range from 0.1 to
60. First, the effect of the cross-sectional shape of the
obstructions on mixing was
investigated. Second, the mixing performances of the
T-micromixer with obstructions
and a simple curved micromixer without obstructions were
compared to that of the
proposed micromixer. Finally, the effects of the obstruction
height and Reynolds
number on mixing performance were evaluated. Micromixers with
circular and
hexagonal obstructions show almost the same mixing performances
regardless of the
Reynolds number, while micromixer with diamond obstructions
shows far less mixing
performance compared to the others except at Reynolds numbers
greater than 50. The
curved channel with circular obstructions shows much higher
mixing performance than
those of the T-micromixer with obstructions and a simple curved
micromixer without
obstructions throughout the Reynolds number range considered.
The proposed
micromixer with circular obstructions shows the best mixing
index at the exit of the
micromixer, 88% among the tested micromixers, at Reynolds
numbers of 0.1 and
greater than 15. The minimum mixing index, 72%, was seen at Re =
5. The pressure
drop increased with an increased number of obstructions.
However, this increase in
pressure drop is not substantial, and can be an acceptable
tradeoff for improved
mixing. The mixing generally increased as the height and number
of the obstructions
increased. However, both of these effects disappeared as the
Reynolds number
approached 60, where the formation of secondary flows due to
channel curvature
dominated the other mechanisms due to obstructions. The proposed
micromixer design
is planar, and hence requires only simple fabrication. (Alam A.
et.al.,2013)
-
42
4.11 Single phase electrokinetic flow in microchannels
This chapter reviews the basics of the electrical double layer
(EDL) and focuses on single-
phase electrokinetic flow in microchannels.
Electrokinetic-driven flow is an important pillar
of microfluidics; key applications on lab-on-a-chip devices
require liquid pumping, mixing,
thermal cycling, and accurate sample dispensing and separating.
A great majority of these
processes are carried out employing electrokinetic processes,
which occur as a result of the
EDL. The two basic electrokinetic phenomena are electrophoresis
and electroosmosis; this
chapter focus on the later. Electroosmosis is the liquid motion
in a microchannel due to
interactions with the EDL under an applied electric field.
Briefly, all charged surfaces will
have an EDL, and under the influence of the applied electric
field, the counterions will move
toward the electrode with the opposite charge, pulling the
liquid with them, resulting in
electroosmotic flow. One of the main advantages of
electroosmotic flow is that it can
generate the required flow rate in very small microchannels,
something that would be
difficult to achieve with pressure-driven flow. Additionally,
plug-type velocity profiles are
obtained with electroosmotic flow, which decreases dispersion in
microsystems.
Electroosmotic flow allows for liquid transport in complex
microfluidic networks, since it
does not require any moving parts. This chapter presents a
detailed analysis and numerical
simulations of electroosmotic pumping in a rectangular
microchannel, a common
configuration in microfluidic devices. The main parameters
affecting electroosmotic flow are
discussed, including the description of the EDL by the
PoissonBoltzmann equation along
with zeta potential, used as the boundary conditions on channel
surfaces. The experimental
techniques for studying electroosmotic flow are also reviewed
and their main characteristics
are highlighted. The nature of electroosmotic flow in
heterogeneous surfaces is discussed,
describing how surface heterogeneity distorts electroosmotic
flow. AC electroosmosis has
unique features and has been used in various applications,
including the generation of bulk
fluid motion by employing specially designed electrodes.
Electrokinetic mixing is an another
attractive use of electroosmotic flow, since, due to the small
dimensions of microfluidic
channels, low Reynolds numbers are obtained and mixing is
strongly dominated by diffusion.
Microfluidic mixing can be enhanced by electrokinetics by
heterogeneous patches that distort
electroosmotic flow. Passive electrokinetic micromixers have
been achieved by adding
regions of positive surface charge to microchannels with
negatively charged surfaces, which
introduces an advective mixing component and increases
circulation, thus significantly
enhancing mixing. An important challenge in lab-on-a-chip
devices is the dispensing of
-
43
minute quantities of liquid to be used as samples in chemical
and biomedical analysis.
Sample loading and dispensing is discussed, including
mathematical model and simulation.
Finally, the effects of Joule heating, heat generation due to
current passing through the buffer
solution, are analyzed in detail, explaining why higher average
velocities are obtained due to
Joule heating. Practice problems are presented to reinforce the
fundamentals of
electroosmotic flow ( Li, 2014).
4.12 Fluid mixing in a microchannel with longitudinal vortex
generators
A heat transfer enhancement technique based on longitudinal
vortex generators (LVGs) has
been well established for large-scale heat exchangers. Motivated
by the success of the LVGs,
this paper is intended as an investigation of micromixers based
on the T-shaped channel with
rectangular winglet pairs (RWPs) mounted on the bottom of the
main channel. The RWPs
stay with an angle of attack to the main flow direction and
generate longitudinal vortices to
enhance fluid mixing. The effects of geometrical parameters on
the performance of
micromixers with micro-scale LVGs are investigated by numerical
simulations and the
Taguchi method. The validity of numerical simulations is
examined by comparing the
numerical and experimental results. The results obtained for a
wide range of Reynolds
numbers show that the mixing efficiency of the micromixer with
divergent RWPs is greater
than that of the micromixer without RWPs for convection-dominant
cases as well as
diffusion-dominant cases. A static Taguchi analysis shows that
the relative effectiveness of
the geometrical parameters can be ranked as: asymmetry index
> angle of attack > winglet
height > winglet spacing. Based on the relative influence of
the geometric parameters, we can
obtain an optimal parameter group on the parameter selected
range.
Numerical simulations on fluid mixing in the T-shaped channel
with micro-scale RWPs
mounted on the bottom of the channel are carried out. Besides,
we fabricate the micromixer
by a lithography process and the fluid mixing in the micromixer
is observed by using a
confocal spectral microscope imaging system. The numerical and
experimental results are in
agreement qualitatively. The Taguchi method is applied to find
out the better combination of
the geometrical parameters. The results show the following
trends. (i) When the Reynolds
number is large enough, the RWPs generate longitudinal vortices
which enhance fluid mixing
effectively. (ii) The results obtained for a wide range of
Reynolds numbers show that the
-
44
mixing efficiency of the micromixer with divergent RWPs is
greater than that of the
micromixer without RWs for convectiondominant cases as well as
diffusion-dominant cases.
(Hsiao et.al., 2014)
4.13 Ideal micromixing performance in packed microchannels
In this work, the hydrodynamics and the micromixing
characteristics in the packed and non-
packed microchannels were studied experimentally at low Reynolds
numbers (8300). The
mixing performances in microchannels were observed with
high-speed CCD camera, and
were evaluated in terms of a segregation index by the
Villermaux/Dushman method. The
fluid elements were drastically stretched, folded, and sheared
with the effects of micro-
particles in packed microchannels, resulting in extremely
shorter diffusion distance and larger
effective interfacial area, and much higher micromixing
efficiency compared with those of
non-packed microchannels. Under enough packing length and
appropriate packing position of
micro-particles, the ideal micromixing performance could be
obtained in packed
microchannels. Furthermore, the micromixing time in packed
microchannels was determined
based on the incorporation model, and its value was in the range
of 00.1 ms.
The hydrodynamics and the micromixing characteristics in the
packed and non-packed
microchannels were investigated by highspeed imaging techniques
and Villermaux/Dushman
method, respectively. From the observation of the hydrodynamics,
it is seen that the mixing
of miscible liquidliquid two phases was dependent on the packing
length of micro-particles
in the packed microchannel. As the same as the macromixing (or
mesomixing), the
micromixing performance in the packed microchannel was improved
obviously compared
with the non-packed microchannel. The reason is that the fluid
elements were stretched,
folded, and sheared with the effects of micro-particles in
packed microchanels, resulting in
much shorter diffusion distance and larger effective interfacial
area. In particular, increasing
the packing length and decreasing the distance between
T-junction and the threshold of the
packing section were both beneficial to the micromixing
performance in packed
microchannels, and the ideal micromixing could be obtained under
enough packing length
and appropriate packing position of micro-particles. The
micromixing time in
microchannels was also evaluated based on the incorporation
model, and its value was in the
range of 010-4s. The extremely low tm also provides a new
approach for studying the ultra-
fast reaction kinetics. (Su et. al.,2011)
-
45
5.conclusion
Throughout this seminar the aim has been to model flow in a
microchannel analytically. We
used electro-osmotically induced flow from a herringbone pattern
on the floor of the channel.
We then continued to find some of the mixing properties of these
flows. We have only
concentrated on simple configurations and have found some good
results. We successfully
manipulated the governing equations of the flow and imposed the
boundary conditions to get
an analytical solution for the velocity field.We have only
modelled some simple
configurations of microchannels here. There are many studies
that could follow from this
seminar.We have presented the lithographic techniques for the
fabrication of the
microchannels, relying on the wet chemical etching and dry
etching (optical lithography,
RIE, deep RIE).
References
Ajdari A., Electro-Osmosis on Inhomogeneously Charged Surfaces,
Physical Review
Letters, 75, 755-758 (1995)
Alam A., Afzal A., Kim K.Y., chemical engineering research and
design (2013)
Ansari M.A., Kwang-Yong kim, Chemical Engineering Journal 146
(2009) 439448
Balan C.M., Broboana D., Balan C., International Journal of Heat
and Fluid Flow 31 (2010)
11251133
Bodas D., Rauch J.Y., Malek C.K., Eur. Polym. J. 44 (2008)
2130.
Chan-Park M.B., Zhang J., Yan Y., Yue C.Y., Fabrication of Large
SU-8 mold with High
Aspect Ratio Microchannels by UV Exposure Dose Reduction,
Sensors and Actuators B:
Chemical, vol 101, pp 175-182, 2004.
Efimenko K., Wallace W.E., Genzer J., Colloid Interface Sci. 254
(2002) 306.
Fries D.M., Rohr P.P.V., Chemical Engineering Science 64 (2009)
1326 1335
-
46
Fritz J.L., Owen M.J., Adhes J.. 54 (1995) 33.
Hsiao K.Y., Wu C.Y., Huang Y.T., Chemical Engineering Journal
235 (2014) 2736
Ikeuchi M., Ikuta K, , Koyata Y.,Advanced Science and
Technology, the University of
Tokyo, Tokyo, Japan
Johnson T. J., Ross D.and Locascio L. E. Rapid Microfluidic
Mixing, Anal. Chem.2002,
74, 45-51, (2002)
Kaji N., Tezuka Y., Takamura Y., Ueda M., Nishimoto T.,
Nakanishi H., Horiike Y., Baba
Y., Anal. Chem. 76 (2004) 1522.
Kim D.S., Lee H.S., Lee J., Kim S., Lee K.H., Moon W, Kwon T.H.,
Microsyst. Technol. 13
(2007) 601606.
Kim D.S., Lee S.H., Ahn C.H.,Lee J.Y., T.H. Kwon, Lab Chip
6(2006) 794802.
Kim P., D.H. Kim, Kim B., Choi S.K., Lee S.H., Khademhosseini
A., Langer R., Suh K.Y.,
Nanotechnology 16 (2005) 24202426.
Kumar V., Paraschivoiu M., Nigam K.D.P., Chemical Engineering
Science 66 (2011) 1329
1373
Lai J.Y., Lin Y.Y., Denq Y.L., Shyu S.S., Chen J.K., Adhes Sci.
Technol. 70 (1996)231.
Lee H.U., Cho D.W., in: Proceedings of the First International
Conference on
Micromanufacturing, IL, USA, September 1315, 2006, p. 186.
Leung W.W.L., Ren Y., International Journal of Heat and Mass
Transfer 64 (2013) 457467
Li D.,Heat Transfer and Fluid Flow in Minichannels and
Microchannels(Second
Edition),2014,pages 175-219
Li P., Standard Fabrication Procedure for Soft Lithography,
unpublished, 2007.
Liu C. S. Y., Dai B.T., "Fabrication challenges for a
complicated micro-flow channel system
at low temperature process," 2005.
Liu Y.Z., Kim B.J., Sung H.J., International Journal of Heat and
Fluid Flow 25 (2004) 986
995
Makamba H., Kim J.H., Lim K., Park N., Hahn J.H.,
Electrophoresis 24 (2003) 3607.
-
47
McDonald J.C., Whitesides G.M., Poly(dimethylsiloxane) as a
Material for Fabricating
Microfluidic Devices, Accounts of Chemical Research, vol 35 no
7, pp 491-499, July 2002.
MicroChem, SU-8 Permanent Epoxy Negative Photoresist- Processing
Guidelines for: SU-8
2025, SU-8 2035, SU-8 2050 and SU-8 2075, unpublished.
Ou J., Perot B., Rothstein J.P., Phys. Fluids 16 (2004)
46354643
Sheu T.S., Chen S.J., Chen J.J., Chemical Engineering Science 71
(2012) 321332.
Stroock A. D., Dertinger S. K. W., Ajdari A., Mezic I., Stone H.
A., Whitesides G. M.,
Chaotic Mixer for Microchannels, Science, 295, 647-651
(2002)
Sugimura H. , Ushiyama K., Hozumi A., Takai O., Langmuir 16
(2000) 885.
Su Y., Chenn G., YuanQ., Chemical Engineering Science 66 (2011)
29122919
Tada T., Poborchii V.V., Kanayama T., Microelectron. Eng. 63
(2002)259265.
Wang H., Iovenitti P., Harvey E., Masood S. Optimizing layout of
obstacles for enhanced
mixing in microchannels, Smart Materials and Structures, 11,
662-667, (2002).
Yoon M.S., Kim B.J., Sung H.J., International Journal of Heat
and Fluid Flow 29 (2008)
269280
Zhao Y., Chenn G., Ye C., Yuan Q., Chemical Engineering Science
87 (2013) 122132
Place: Surat