NANOPOROUS THERMOELECTRIC KNUDSEN PUMP INTEGRATED WITH
A MICROFLUIDIC CHANNEL
A. Faiz1, and S. McNamara2
Department of Mechanical Engineering, University of Louisville, Louisville, KY USA
2
Department of Electrical and Computer Engineering, University of Louisville, KY USA
1
Abstract: We report on the design, fabrication, and testing of a bi-directional Knudsen gas pump integrated into a
microfluidic channel, utilizing a multifunctional nanoporous Bi2Te3 thermoelectric material. Heater, cooler and
nanoporous channels, which are the main elements for the Knudsen pump operation, are combined in the
multifunctional material. This combination makes the device simple and easy to integrate in microfluidic
applications. Sub-micron sized Bi2Te3 powder was compacted at 6 MPa and sintered at 200°C for 2 hours under
running argon to make the nanoporous sample. The pump generates a maximum pressure of about 520 Pa with an
input power of 1.33 W. Characterization using an IR camera and the four-probe technique is also reported. The
measured flow rate is 1 ȝL/min.
Keywords: Knudsen pump, thermoelectric, sintering, microfluidic, nanoporous.
INTRODUCTION
THEORY
Pumps are an important component of most
microfluidic and lab-on-a-chip devices [1]. However,
most pumps have drawbacks such as large power
consumption, wear and tear due to the moving parts
[2], limitations on the types of fluids that may be
pumped, and difficulty to integrate with MEMS
devices due to the low performance at small scale.
The Knudsen pump features no moving parts, making
integration easier. It is a gas pump which can be used
to pump almost any type of liquid through pneumatic
actuation [3]. The present Knudsen pump is suitable
for low flow rate applications, including microdialysis
[4] and drug delivery devices [5]. Figure 1 shows a
schematic example of a thermoelectric Knudsen pump
in series with a microfluidic channel. The Knudsen
pump consisting of the nanoporous thermoelectric
(TE) material placed inside a macrochannel will
provide pneumatic pressure to move the fluid in the
microfluidic channel. More complicated geometries
can be envisioned in which the pump pushes or pulls
the fluids to different locations in the microfluidic
device.
The Knudsen pump relies on the principal of
thermal transpiration for its operation [6, 7]. If two
chambers filled with the same gas are connected by a
narrow channel, and maintained at different
temperatures (Fig. 2), a net gas flow from the cold
chamber to the hot chamber will be generated. The
induced flow can be explained by the amount of
momentum transferred by gas molecules to the
channel wall. The number of molecules striking the
wall from the hot side is larger than those from the
cold side. This large number of collisions induces a
momentum force in the opposite direction to the
temperature gradient.
Once equilibrium is reached in a closed system, the
relationship between the parameters TC, TH, PC, and PH
is:
PH
T
= H
PC
TC
Equation (1) is obtained by equating the molecular
flux between the two chambers. The pressure must be
in the free molecular flow or transitional flow regimes
for proper operation, ideally requiring pore diameter
on the order of 100 nm or smaller for operation at
atmospheric pressure. Figure 3 shows a schematic of
the device. Once the power is turned on, one side of
the thermoelectric material becomes hot, and the other
side becomes cold. Gas starts to flow through the
nanoporous thermoelectric material from the cold side
to the hot side by thermal transpiration. Switching the
voltage polarity reverses the pumping direction.
Fig. 1: Schematic showing an example of how the TE
based Knudsen pump is combined with a microfluidic
device. The generated pressure causes the fluid to
move inside the microfluidic channel.
978-0-9743611-9-2/PMEMS2012/$20©2012TRF
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PowerMEMS 2012, Atlanta, GA, USA, December 2-5, 2012
sealed set-up, a pressure drop due to gas leaking
through the pores was seen.
Fig. 2: Two chambers at different temperatures,
separated by a narrow channel, through which a net
gas flow from the cold side to the hot side is
established.
Fig. 4: Schematic of the fabrication process to create
the nanoporous Bi2Te3 TE material used in the bidirectional Knudsen pump. Commercial grade doped
Bi2Te3 is ball milled to create a nanopowder. The
latter was pressed in a die to form the compact
sample which is then sintered in a tube furnace under
running argon to obtain the final pellet.
Fig. 3: Schematic showing the working of a
nanoporous TE bi-directional Knudsen pump. Gas
flows from the cold side to the hot side.
EXPERIMENT
A schematic of the fabrication process is shown in
Fig. 4. The device fabrication starts by ball milling
(1200 RPM) of p-type Bi2Te3 pellets under vacuum.
The three dimensions movement of the jar, containing
the balls and Bi2Te3 pellets, provide the balls with
enough inertia to crush the sample material upon
impact. The grinding of about 5 gram-sample was
performed in 15-minute periods separated by 30
minute cool-down periods. After milling for 5 hours,
the powder was then transferred into a 13×13 mm2
square die and uniaxially pressed (6 MPa) for 1 hour.
The compact sample was then placed in a tube furnace
where it was sintered at 200°C for 2 hours and 100
sccm running argon.
A photograph of the sintered sample is shown in
Fig. 5a. An SEM image (Fig. 5b) shows the submicron pores through which gas will flow from the
cold side to the hot side. A test was performed on the
sintered sample to make sure that the pores extend
through the whole thickness. The sample was
mounted with a pressure transducer and a syringe
using a T-connector. Once a pressure is applied to the
5a
5b
Fig. 5: (a) 13 mm pressed square sample sitting on
top of a U.S. dime. (b) SEM image of a nanoporous
Bi2Te3 (scale bar: 2µm). The dark regions are the
pores through which gas flows.
Thermal infrared (IR) microscopy was used to test
the sintered thermoelectric sample. After soldering the
connection wires, the sample was placed flat on a
heated stage (60°C), and power was applied (1.33 W).
A temperature distribution over the surface of the
sample was measured (Fig. 6), showing cooling (<
60°C) on one side, and heating on the other side
(>60°C). When the voltage polarity is reversed, the
hot and cold regions are reversed.
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Fig. 6: (left) Temperature distribution over the surface of the nanoporous sintered thermoelectric from an IR
camera. (Right) Plot of the temperature versus the distance along the white dashed line; blue curve for the line on
the right side, red curve for the line on the left side after switching the voltage polarity. The sample sits on a 60°C
stage to permit emissitivity corrections to be performed. The measured temperature difference is ǻT§15°C.
The sample was placed inside a channel machined
on a plastic substrate. The channel was drawn using
SolidWorks CAD software. The dimensions are 3 cm
long, 13 mm wide. The drawing was saved as .igs file
and transferred, to the computer connected to the
CNC milling machine with VisualMill 6.0 machining
program. The machine was set to 3-axis milling and
the milling speed was 14000 RPM. The machining
was performed in two parts, horizontal rough
machining and parallel finishing machining. An end
mill (3.175 mm diameter, 38.1 mm long, and 2 flutes)
made out of carbide was used. Epoxy glue was
applied on the sides where the sample touches the
channel. A plastic cover, with glued tube (0.01 ý I.D),
was used to close the channel. The plastic tube will be
connected to the pressure sensor for pressure head
measurement.
To measure the pressure difference that may be
obtained with the pump, a digital pressure sensor with
a dead volume of 0.8 cc is connected to one side of
the pump, and the other side was open to the
atmosphere. A similar pressure sensor was used to
monitor the atmospheric pressure. A custom labView
program was written to plot the room pressure, the
Knudsen pump pressure, and their difference.
Fig. 7: Resistivity of the sintered sample versus the
sintering temperature. 200°C was chosen for sintering
the compact sample since it gives the lowest
resistivity, ȡ, which enhances the TE material figure
of merit Z (Z ‫ ן‬1/ȡ).
IR microscope was also used to investigate the
effect of the input power on the generated temperature
gradient (Fig. 8). The objective behind this
measurement was to check for the saturation power
after which the temperature gradient will not increase.
The curve follows a linear trend. As the power goes
up, the majority carriers (holes), responsible for
carrying the heat from the cold to the hot side, migrate
toward the negative side causing it to heat up, and the
other side (positive polarity) becomes cooler.
The final device (Fig. 9) has a footprint of 3×2 cm2.
Its main components are the nanoporous
thermoelectric material, channel, connection wires,
and the tubing. Plastic material was used for the
channel substrate and cover because it has a lower
thermal conductivity which helps maintain the
temperature gradient necessary for thermal
transpiration.
Fig. 10 shows the pressure that is obtained from the
Knudsen gas pump as a function of time. 1.33 W is
the input power. Pressure is permitted to come to
room pressure before switching the voltage polarity.
RESULTS
The effect of the sintering temperature on the
resistivity was investigated. Resistivity was measured
after each sintering temperature using a 4-probe
machine (Fig. 7). The lowest resistivity was seen at
200°C and that explains the choice of this temperature
as the sintering temperature. A lower resistivity
(higher electrical conductivity) will improve the
figure of merit Z of the thermoelectric material. The
higher the Z value, the better the thermoelectric
material [8].
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nearly linear relationship was found between the
generated temperature gradient and the input power.
The vertical spikes occur when the pump is turned on
or off, and the addition or removal of heat causes a
temporary increase or decrease in pressure due to the
gas expansion or contraction. A syringe pump,
connected along with the Knudsen pump and the
pressure sensor, was used to measure the flowrate.
The Knudsen pump was turned on first. Once the
pressure reached a steady state, the syringe pump was
turned on. Flowrate values from the syringe pump
were varied until the overall pressure went back to
zero. The measured flow rate is l µL/min.
ACKNOWLEDGEMENTS
This research was funded by the Kentucky
National Science Foundation Epscor Program (Award
#0814194) and the National Science Foundation
(Award #CBET-1133877).
Fig. 10: Experimental pressure differential obtained
with the fabricated Knudsen pump shown in Fig. 9.
Fig. 8: Measured ǻT of the sintered square TE sample
versus power. The measurements were obtained using
IR microscopy.
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[6] Kennard E. H. 1938 Kinetic Theory of Gases: with an
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[7] Loeb L. B. 2004 The Kinetic Theory Of Gases Dover
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[8] Ma Y., Hao Q., Poudel B., Lan Y., Yu B., Wang D.,
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Fig. 9: Fabricated nanoporous Bi2Te3 thermoelectric
Knudsen pump. The nanoporous thermoelectric
sample is placed in a rectangular channel. Wires are
soldered on the sides. The pump is sealed using
vacuum epoxy glue.
CONCLUSION
Pressureless sintering was used to fabricate a
nanoporous TE sample which was placed inside a
plastic macrochannel to make a bi-directional
Knudsen pump. The powder was compacted at 6 MPa
and sintered for 2 hours at 200°C under running
argon. The measured flowrate and pressure are 1
µL/min and 520 Pa respectively with an input power
of 1.33 W. The pump has a footprint of 3×2 cm2 and
can easily be integrated with microfluidic devices.
Operation at negative pressure proves that the
Knudsen pump does not work due to gas heating. A
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