Proceedings of ICNMM2006
Proceedings of ICNMM2006
Fourth International Conference on Nanochannels, Microchannels and Minichannels
Fourth International Conference on Nanochannels, Microchannels and Minichannels
June
19-21,
2006,
Limerick,
Ireland
June
19-21,
2006,
Limerick,
Ireland
ICNMM2006-96248
ICNMM2006-96248
INVESTIGATION OF FOULING IN MICROCHANNELS
Jeffrey L. Perry, [email protected]
Microsystems Engineering
Rochester Institute of Technology
Rochester, NY 14623
ABSTRACT
Particulate fouling in microchannels is a subject that is
largely unexplored. It does, however, have significant
implications for all microchannel flows since the hydraulic
diameters are very small and consequently are susceptible to
excessively large pressure drops. The significant forces for
dilute solutions of silica particles ranging from 3 to 10 µm are
studied in rectangular microchannels made in silicon with a
hydraulic diameter of 106 µm. The effects of zeta potential
which is pH driven, lift force on the particulates and their
fouling characteristics are evaluated by measuring the pressure
drop across the microchannel test section.
INTRODUCTION
Microfluidics is an increasingly studied field because of its
use in practical applications in both biology and
microelectronics. In recent years, the proliferation of MEMS
has resulted in the use of microchannels for many applications.
In particular, with microchannels there has been a great
emphasis on semiconductor chip cooling. Since large pressure
drops are inherent with the use of microchannels it is desired to
minimize further increases in pressure drop that can arise due
to fouling which can severely limit the efficiency of a
microchannel heat exchanger.
The smallest hydraulic diameters, Dh, that have been
previously used in fouling studies that the authors are aware of
were by Yiantsios et al. (1995, 1998, 2003) and Niida et al.
(1989). Yiantsios et al. studied fouling in channels with Dh =
952 µm. Their test section consisted of two glass plates
separated by Teflon spacer strips to create a channel that was
10 mm by 0.5 mm. Similarity, Niida et al. used an observation
cell, made of borosilicate glass with a cross-section of 4 mm by
0.4 mm to provide a Dh of 727 µm. Based on the definitions
provided by both Kandlikar & Grande (2002) and Kandlikar &
Kuan (2006) these are categorized as minichannels. In the
Satish G. Kandlikar, [email protected]
Department of Mechanical Engineering
Rochester Institute of Technology
Rochester, NY 14623
present fouling studies microchannels are being used which
have dimensions of 70 µm x 220 µm (Dh = 106 µm).
In general particulate fouling may be considered a two-step
process. It consists of a transport step, in which particles are
transferred to the channel wall, and a subsequent adhesion step,
which is dominated by the interaction forces between particles
and the wall. An important parameter in both steps is the
particle size. Particles in the colloidal size range (< 1 µm) tend
to be strongly controlled by Brownian diffusivity. However,
particles which are several microns in size are less likely to
experience random displacement caused by Brownian motion.
Table 1 illustrates this by providing the mean displacement, in
one direction for particles ranging from 10 nm to 10 µm.
Consequently, particles in the size range used in this work (3 –
10 µm diameter) will not be affected by random displacements
due to Brownian motion; and therefore fouling as it relates to
this phenomenon may be neglected.
Moreover, it needs to be stated that particle size is a critical
parameter in determining their attachment efficiency. It affects
the magnitude of physicochemical interactions between
particles and channel wall as well as the hydrodynamic forces
that tend to cause particles to detach or prevent them from
adhering.
Table 1: Diffusion coefficients and Brownian displacements
calculated for uncharged spheres in water at 25oC.
1
Diameter
Diffusivity at 25oC (m2/s)
10 nm
100 nm
3 µm
5 µm
10 µm
4.9x10-11
4.9x10-12
1.6x10-13
9.8x10-14
4.9x10-14
Average displacement
after 1 hour (µm)
590
190
34
26
19
Copyright © 2006 by ASME
THEORECTICAL APPROACH
A. Forces on a particle
When a particle is in contact or near contact with a
horizontal channel wall, many forces around the particle are
involved in determining whether or not adhesion will occur. In
this study the forces are categorized into two main groups. The
first group is the adhesive forces which are due to van der
Waals forces, Fvdw, and gravity, Fg. The second group is the
removal forces which include the hydrodynamic lift force, FL,
and electro static forces, Fel. The electrostatic forces in actuality
may be attractive or repulsive in nature. However, in these
experiments the conditions were adjusted such that they were
always repulsive by proper pH adjustment. A schematic
showing of all these forces is given in Figure 1. The total force,
FT, on a particle is the sum of the adhesive and removal forces
which is expressed as
(1)
F = F +F −F −F
T
vdw
g
el
L
The more negative FT is, the greater the chance that the
rate of fouling will be less. This translates into smaller pressure
drops across a microchannel test section. However, because
Eq. 1 can be somewhat awkward to represent graphically, the
ratio of the removal forces to adhesive forces is used. This
ratio is defined as RM with
RM =
FL + Fel
Fg + Fvdw
(2)
B. Van der Waals force particle/wall
The van der Waals or London dispersion force is an
attractive force between two atoms or non polar molecules that
arises due to fluctuating dipole moments. In this phenomenon a
fluctuating dipole moment in one molecule induces a dipole
moment in the other which results in a net attraction between
them. The van der Waals force between a sphere and a plate
which takes into account retardation effects is given by
Gregory (1981).
Fvdw


d
A132 d p 

1
1−
, h << p
=

2 
12h  1 + λ 
2
5.32h 

(3)
A132 is the Hamaker constant of particle 1 on wall 2 in medium
3 [A132 = 1.3x10-20 J for a silica (SiO2) particle near a silicon
channel wall in water, Holmberg (2001); Kern (1993)], dp is the
particle diameter, h the minimum separation between the
particle and the wall, and λ is the characteristic wavelength of
interaction which is taken as ≈ 100 nm for most materials
Gregory (1981).
C. Gravity
Gravity in the context of this paper is considered an
adhesive force because on a horizontal surface it can drive a
particle to be in contact with it. The force of gravity of a
particle in water is given as
where for larger values of RM the likelihood of fouling is
decreased.
Fg =
πd 3p ( ρ p − ρ f ) g
6
(4)
where ρp is the density of the particle, ρf is the density of the
fluid and g is the acceleration due to gravity. The gravitation
force, is however often negligible for micron sized particles in
comparison to the surface forces that are present.
Figure 1: Schematic showing the forces on a particle in near
contact with a horizontal channel wall. The drag force on
the particle is not considered because it only works in the
horizontal direction and therefore cannot prevent a particle
from coming into contact with the wall.
D. Electrostatic force particle/wall
Most materials immersed in an aqueous environment
acquire a surface charge due to preferential adsorption of ions
present in the liquid phase or due to dissociation of surface
groups. The surface charge is balanced by a counter-charge of
ions of opposite sign in order to make the system
electrostatically neutral. In this case a so-called double layer is
established. This sets up a potential difference between the
solid surface and a diffuse layer of oppositely charged ions in
solution.
The potential most used in colloidal science for calculating
the forces of repulsion between two surfaces is the zeta
potential (ζ). This is the potential adjacent to a solid interface
referred to as the surface of shear which is used to approximate
the surface potential at the Stern plane. In actuality the zeta
potential is somewhat smaller than the Stern potential (ψd) but
errors associated with making this approximation are usually
small, Shaw (1992). This is depicted in Figure 2. The zeta
potential is easily changed by adjusting the pH. ζ for most
2
Copyright © 2006 by ASME
materials becomes more negative at higher pH and more
positive at lower pH values due to the interaction of the
potentially determining ions in solution (H+ and OH-) that can
effect chemical equilibriums at the surface. Important is the
fact that interpenetration of double layers of like sign (like zeta
potentials) will lead to repulsion.
Fel =
4πd p nkTe −κh  Y+2
Y−2 
−
1 + e −κh 1 − e −κh 
κ


ys1 + ys 2
y − ys 2
, Y− = s1
2
2
ze
ze
ys1 = ψ s1 , ys 2 = ψ s 2
kT
kT
Y+ =
κ=
e2
ε rε o kT
(5)
∑n z
2
i i
where n is the electrolyte concentration, k is the Boltzmann
constant, T is the absolute temperature, z is the electrolyte
valance charge, e is the elementary electric charge, κ is the
Debye-Huckel parameter of the electrolyte solution (where 1/κ
is known as the Debye length or diffuse layer thickness), ψs1
and ψs2 are the respective surface potentials involved, εr is the
dielectric constant of the medium, and εo is the dielectric
permittivity of a vacuum.
E. Hydrodynamic lift force particle/substrate
The hydrodynamic lift force for a spherical particle in the
vicinity of the deposition surface is given by Leighton and
Acrivos (1985) who extended the analysis of O’Neill (1968) by
taking into account weak inertial effects. They found that the
lift force on a spherical particle in contact with a fixed plane
wall, in a slow linear shear flow is
τ
FL = 0.58ρ f  w
µ
 f
Figure 2: Schematic representation of the structure of the
electric double layer on a flat surface.
The DLVO theory developed by Derjaguin and Landau
(1941), Verwey and Overbeek (1948), independently describes
the interaction that takes place when two of these double layers
interpenetrate. Hog et al. (1966) were amongst others that
extended the DLVO theory to the interaction of dissimilar
plates and dissimilar spheres at constant surface potential. Their
simplified formulas are however only good for surface
potentials up to ≈ 25 mV. Ohshima et al. (1982), came up with
analytical expressions that can be applied to higher surface
potentials, as is the case here.
The analytical expressions developed by Oshima et al.
(1982) which describe the force between a sphere and a plate
are quite lengthy. Therefore, only the first part of the
expression is given. The comprehensive results can be obtained
by differentiating Eqs. 49-51 from Oshima et al. with respect to
h and taking the limit as one of the radii goes to infinity (Fel = dU/dh, where U is the interaction energy). The force for a
symmetrical electrolyte is
2
 4
 dp


(6)
where µf is the viscosity of the fluid and τw is the shear stress at
the wall. This expression is valid for sufficiently small particle
Reynolds numbers such that the inertial terms in the NavierStokes equations can be neglected. The wall shear stress is
calculated as
τw =
1
fρ f V 2
2
(7)
where f is the Fanning friction factor and V is the mean
velocity. The friction factor is calculated from the Poiseuille
number which is a function of the aspect ratio for a rectangular
channel. It can be determined using Eq. 8 from Shah and
London (1978).
1 − 1.3553α c + 1.9467α c2 


f Re = 24 − 1.7012α c3 + 0.9564α c4 



 − 0.2537α c5


(8)
where αc is the channel aspect ratio. One constraint for this
equation is that the aspect ratio must be less than one. If the
3
Copyright © 2006 by ASME
channel aspect ratio is greater than unity, the inverse is taken
for use in Eq. 8.
EXPERIMENTAL
*
D50 and D90 values refer to the 50 percentile and 90 percentile of the
particle diameters respectively.
Silica
Silicon
20.0
0.0
0.0
Zeta Potential (mV)
A. Materials and Methods
Particulate fouling was studied using the flow loop shown
in Figure 3. A peristaltic pump (Cole-Parmer Masterflex L/S)
was used to drive the fluid which has a rated speed control of ±
0.25%. The peristaltic pump was selected because it is capable
of pumping fluids with a high solids content and can be run dry
to flush the system between runs. The 3 µm diameter silica
particles were obtained from Nanostructured & Amorphous
Materials, Inc., while the 10 µm diameter particles were from
U.S. Silica. The physical properties of the silica are given in
Table 2 while statistical information on their distribution is
listed in Table 3. Using these silica particles dilute suspensions
of up to 0.015 wt % were formulated. Deionized water was
used in all experiments which had a pH of 5.5. The pH was
then adjusted as needed to higher values by the addition of
KOH. The zeta potential values for silica were taken from
Holmberg (2001) and those for silicon came from Binner
(2001). The zeta potential vs. pH curves are given in Figure 4.
The mean temperature of the fluid was kept at ambient
conditions (27 ± 2 oC) and the flow rate was 10.49 ml/min for
all trials. This gave a flow rate 0.144 ml/min and a Reynolds
number of 18.4 in the microchannels. After each run the silicon
chip was removed from its test section and cleaned by spraying
it down with deionized water. This was done to ensure that
there was no build up of particles in the channels that could
adversely affect subsequent experiments.
Table 3: Statistical distribution of silica particles
Particle diameter
3 µm
10 µm
D50* (µm)
2.8
3.6
D90* (µm)
6
7.8
2.0
4.0
6.0
8.0
10.0
12.0
-20.0
-40.0
-60.0
-80.0
-100.0
pH
Figure 4: General zeta potential vs. pH curves for silica and
silicon.
Figure 3: Experimental flow loop used in microchannel
fouling studies. ∆P is a differential pressure transducer
while T1 and T2 are inlet and outlet temperature
thermocouples.
B. Data Acquisition
A data acquisition (DAQ) system monitors the
thermocouples and pressure transducers in the flow loop. The
DAQ is based upon the signal conditioning SCXI system from
National Instruments. This system conditions all incoming
signals and gives the ability to have high channel counts. The
DAQ system used is capable of sampling at a rate of 100,000
samples per second. The fast sampling is used to increase the
accuracy. The procedure for data collection begins with the
sampling rate. The channels are sampled at a rate of 1.0 kHz.
The data collected is in a waveform. The channel information
contains both amplitude and frequency information. For each
experimental data point 500 samples from every channel are
collected (pressure, temperature, etc.). The uncertainty in the
temperature, flow rate and pressure measurements are given in
Table 4. The pressure uncertainty is larger than it might be for a
gear type pump. This is because with a peristaltic pump the
rollers that move the fluid create pulsations. Even so the
uncertainty in the pressure measurement was only 360 Pa.
Table 2: Physical properties of silica particles
Particle diameter
3 µm
10 µm
3
Average Density (g/cm )
2.40
2.65
Percent Purity
99.94
99.4
Table 4: Uncertainty in experimental measurements
Parameter
Uncertainty
Temperature
0.05 oC
Flow Rate
0.03 ml/min
Pressure
360 Pa
4
Copyright © 2006 by ASME
Test Section Design
The design of the test section used to conduct the
experiments is discussed here. The test section is located in the
flow loop schematic and provides support for the device. In
addition, it is a platform that contains the electrical and fluidic
connections necessary for data acquisition.
This is shown in Figure 7. The cover piece has the same overall
dimensions as the silicon substrate. The thickness of the cover
plate is 600 µm. The cover piece is laser drilled with two holes
to match with the location of the inlet and outlet headers. The
diameter of the plenum holes is 1.5 mm.
C. Test Device
The geometry of the microchannels that have been
fabricated is presented in Table 5. Figure 5 shows the location
of the geometric variables used in Table 5 where a is the
microchannel width, s is the fin thickness separating the
microchannels, b is the depth of the microchannels, L is the
total flow length of the microchannels and n is the number of
microchannels. The total width and length of the microchannel
array is 8 and 10 mm respectively.
s
a
Figure 6: Picture of silicon microchannels.
b
Figure 5: Schematic of the geometrical parameters of the
microchannels.
Figure 7: Diagram of silicon microchannels with Pyrex
cover plate. Together these form the complete test device.
Table 5: Channel geometries of test device
b (µm)
a (µm)
s (µm)
pitch (µm)
n
L (mm)
220
70
40
110
73
10
The microchannels were fabricated in silicon using deep
reactive ion etching (DRIE) because very high aspect ratios
with straight sidewalls can be achieved with this etching
technique. 8-inch wafers were used in the fabrication so the
unetched substrates have a thickness of 725 µm. Figure 6
shows an example of the silicon microchannels. There are also
inlet and outlet headers formed in the silicon. The back side of
the header is rounded to help direct the flow and minimize
stagnation regions. Finally, the entrance to each channel is
rounded to reduce the pressure drop due to entrance effects.
The radius of curvature of the channels is one half the fin
thickness, s. The temperature and pressure are measured in the
plenums. The plenums were carefully designed to allow for
sufficient volume to reduce the fluid velocity. This ensures that
only the static pressure is measured since the dynamic pressure
component is very small. The silicon chip is sealed with a
Pyrex cover to form a fully functional microchannel device.
D. Test Section
The test section was constructed with black Delrin
(DuPont trade name for acetal polyoxymethylene) which is an
acetal resin. It is a lightweight polymer that is very stable and is
capable of being machined to fairly high tolerances. The test
fixture is comprised of the following major parts: a main block,
pogo block, bottom retaining plate, device retaining plate and
mounting plate. The pogo block is part of the test section where
high current pogo probes may be place for electrical
connections to the backside of the chip. This however, was not
utilized in the present investigation because a heat flux was not
being applied to the microchannel chip. The pogo block is
placed in the main block and secured with a bottom retaining
plate. A Teflon spacer is placed between the pogo block and
silicon chip for added support. Figure 8 shows the pogo probe
block with the pogo probes inserted into it. The pogo probe
block is inserted into the main block shown in Figure 9. The
entire test section assembly can be seen in Figure 10.
A critical part of the test fixture assembly is the device
retaining plate shown in Figure 11. It provides the clamping
force on the microchannel test section and fluidic connections.
5
Copyright © 2006 by ASME
This piece is made of Lexan (trade name) which is an optically
clear polycarbonate material. The fluid enters the piece and
moves into an inlet plenum. The fluid then enters the test
device and leaves through the exit plenum. Figure 12 illustrates
the stacked layer of materials used between the pogo block and
device retaining plate. There are three thin pieces of silicon
rubber membrane 200 µm thick which resides between (1) the
pogo block and Teflon spacer, (2) the Teflon spacer and silicon
chip and, (3) the test device and device retaining plate. The
silicon rubber membranes help provided compliance during
assembly. With it a good seal is provided and breaking of the
test device is prevented.
Two miniature thermocouples are placed in the plenums.
The thermocouples have a small bead diameter of 0.5 mm in
order to minimize their effect on flow disturbance. In addition,
they are coated with an epoxy which prevents their corrosion.
Figure 10: Test fixture assembly.
Pogo probe
block
Pogo probes
Figure 8: Pogo probe block with probes inserted.
Figure 11: Device retaining plate.
Figure 9: Main block which pogo probe block fits into from
underneath to help support microchannel chip.
Silicon rubber membrane
Pyrex cover
Silicon microchannel chip
Teflon spacer
Pogo probe block
Figure 12: Side view of material stack with silicon
membrane material to provide a good seal and prevent
fracturing of the test device while under compression.
6
Copyright © 2006 by ASME
RESULTS AND DISCUSSION
The experimental results are given in Figures 13 – 16
while Figures 17 – 19 display the corresponding theoretical
curves related to the removal and adhesive forces acting on the
particles. The theoretical curves were calculated for a
temperature of 25oC which corresponds within the
experimental range of the data. Figures 13 and 14 show an
expected trend with particulate concentration for the 3 and 10
µm diameter spheres. The fouling rate is seen to increase at
greater particle concentrations. A comparison of the figures
demonstrates that the larger particles can be present at higher
concentrations than smaller sizes particles and still maintain a
lower rate of fouling or pressure drop after a given amount of
time. Both figures show that the fouling rate is not constant
and the pressure drop fluctuations become more erratic at
higher particle concentrations. This can easily be observed
from the characteristic “saw tooth” curve. This is the result of
built up deposits that become dislodged from time to time.
There is some visual evidence that this is occurring in the
microchannels. Due to the erratic nature of fouling, significant
fluctuations in pressure drop are seen. This necessitates a fair
number of experimental runs to develop correlations to
accurately predict this phenomenon.
Figure 15 illustrates that for identical concentrations
smaller particles will result in greater fouling. This is primarily
because the lift force significantly decreases for smaller particle
sizes since it is related to the fourth power of the particle
diameter. This is quite evident by comparing Figures 17 and
18. The lift forces for both particle sizes are listed in Table 6.
Table 6: Lift force for various particle sizes
Particle diameter (µm)
Lift Force (N)
3
7.50x10-12
10
9.26x10-10
The effect of pH on fouling is significant. This is observed
in Figure 16 for the 3 µm particle diameter. The pressure drop
decreases from about 110 to 37 kPa (66 %) after 24 hours of
operation. This is because of the increased electrostatic forces
between the particles and the wall which provides a greater
removal force. The effect of increasing Fel with pH is
observable in Figure 19 for the 3 µm particle. This effect is not
seen at all separation distances.
However, from the
experimental data it would appear that it is the value of RM for
separation distance under 80 nm which is important. This is
most likely because at shorter distances the force of repulsion
from Fel is greater.
As can be seen from all theoretical curves the effect of
gravity was negligible compared to the other forces under
consideration. This is because the particles in this study were
too small and hence did not possess enough mass for the force
of gravity to play a significant role.
Figure 13: Test section pressure drop vs. time for different
particle concentrations of 3 µm diameter spheres, pH = 5.5.
Figure 14: Test section pressure drop vs. time for different
particle concentrations of 10 µm diameter spheres, pH =
5.5.
Figure 15: Test section pressure drop vs. time for 3 and 10
µm particle sizes with identical particle concentrations of
0.0037 wt%, pH = 5.5.
7
Copyright © 2006 by ASME
Figure 16: Test section pressure drop vs. time for 3 µm
particle size with a concentration of 0.0037 wt%, for pH
values of 5.5, 7.5 and 10.3.
Figure 18: Force vs. sphere-plate distance for 10 µm
particle with a pH of 5.5.
1400
1200
1000
800
600
RM
pH = 5.5
pH = 7.5
pH = 10.3
400
200
0
0
20
40
60
80
100
120
140
160
180
200
-200
-400
Distance (nm)
Figure 19: RM vs. sphere-plate distance for 3 µm particle
for pH values of 5.5, 7.5 and 10.3.
Figure 17: Force vs. sphere-plate distance for 3 µm particle
with a pH of 5.5.
CONCLUSIONS
From the results of this fouling study the two most
important factors were found to be the particle size and solution
pH. The larger the particle size the larger the lift force
available to help repel particles from the channel walls. The
effect of pH was significant as well. Fouling was mitigated by
using solutions with higher pH values. A 66 % decrease in the
pressure drop was observed after 24 hours of operation when
the pH was increased from 5.5 to 10.3 for the 3 µm particle
size.
8
Copyright © 2006 by ASME
ACKNOWLEDGEMENTS
The authors are thankful for the support of the
Microsystems Engineering program and Thermal Analysis and
Microfluidics Laboratory at the Rochester Institute of
Technology. The second author acknowledges the IBM Faculty
Award in support of this work.
NOMENCLATURE
a
A
b
D50
D90
Dh
dp
e
f
Fel
Fg
FL
FT
Fvdw
g
h
k
L
n
Re
RM
s
T
U
ys
z
Greek
αc
δ
εo
εr
κ
λ
µf
ρf
ρp
τw
ψd
ψo
ζ
channel width, m
Hamaker constant, J
channel depth, m
50 percentile of particle diameter
90 percentile of particle diameter
hydraulic diameter, m
diameter of particle, m
elementary electric charge, c
Fanning friction factor
electro static force, N
gravitational force, N
lift force, N
total force acting on particle, N
van der Waals force, N
acceleration of gravity, m/s2
minimum separation between the particle and wall, m
Boltzmann constant, J/K·molecule
channel length, m
electrolyte concentration, ions/m3
Reynolds number
ratio of the removal forces to adhesive forces
fin thickness, m
absolute temperature, K
interaction energy, J
dimensionless surface potential
electrolyte valance charge
channel aspect ratio = a/b
Stern layer thickness, m
dielectric permittivity of a vacuum, F/m2
dielectric constant of the medium
Debye-Huckel parameter, 1/m
characteristic wavelength of interaction, m
viscosity of fluid, kg/m-s
density of fluid, kg/m3
density of particle, kg/m3
shear stress at channel wall, N/m2
Stern potential, V
surface potential, V
zeta potential, V
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