This document discusses the design and operation of a thermal bi-morph valve operated microthruster, intended for space exploration and microfluidic applications. The microthruster operates on the principle of thermal bimorph actuation, utilizing silicon and aluminum materials, achieving a thrust of 0.31μN with a power consumption of 6.32mW. Key aspects include the fabrication process and optimization techniques to ensure the microthruster's effective performance in handling liquid propellants in a zero-gravity environment.

1. Thermal Bi-Morph Valve Operated Microthruster
By: Sai Siva Kare UIN 661961324,
The University of Illinois at Chicago, Department of Mechanical Engineering
Abstract
Space exploration is one of the most interesting and
challenging subject in science. Challenging because
the equipment used in exploration is highly complex.
Like conventional satellite they need propulsion
system for obtaining desired attitude. This has paved
way for designing micro propulsion systems called
microthrusters. The device discussed here work on
the principle of thermal bimorph actuation. The top
beam element selected is silicon whereas the bottom
beam is of aluminum. Applying voltage potential in
aluminum beam results into heating of the beam,
which results into expansion of aluminum. Due to
difference between coefficient of expansion of
aluminum and silicon, aluminum expands more
compared to silicon thus resulting into bending. This
bending opens inlet port of a converging-diverging
nozzle, simultaneously heating the liquid propellant.
For temperature of Aluminum reaching to 227°C
(dT=200°C) maximum tip deflection of cantilever
was observed to be 2.5µm. The inlet of nozzle has
cross sectional area of 2500µm2 whereas throat area
is 738.74 µm2
, the exit section area is designed to be
2216.22 µm2
. Analytical calculation shows a thrust of
0.31µN is possible with this device and a power
consumption of 6.32 mW is observed. The temperature
obtained in the aluminum beam is approximately 300°C
when a dc voltage of 0.35V is applied. Various references
are taken in order to minimize assumptions and take the
project closer to reality. Also some optimization and
compensation has been done using MATLAB to further
reduce assumed parameters. To my best knowledge this
device is first of its kind which can be used to handle
liquid material safely, avoiding any spillage and exposure
to radiation in zero gravity environment. This specific
design is chosen to demonstrate that its possible to
fabricate nozzles normal to the substrate and control its
characteristic. An array of such devices can be used to
maneuver the satellite anyway required.
1. Introduction:
The era and amazing interest of miniaturized
satellite started in 1990s mostly because of the low
cost and the low weight of the system, which can be
easily transported as secondary payloads [1]. These
kind of satellites are classified as small, micro, nano,
pico and femto satellites [2] [3]. The beginning
missions of these satellites included functions that
doesn’t required any attitude adjustment or
propulsion. They had a working life of few months
and at most a year [4]. After their mission is complete
these satellites were destined to form space junk,
which is a potential danger in itself. Adding a
propulsion system to these satellites not only make
them more capable systems but also reduces the risk
of space junk by enabling the system to self-destruct
via atmosphere re-entry on completion of mission.
The propulsion of such satellites is a new challenge
for engineers as it requires small thrusters
(microthrusters) with a very small profile and wet
weight.
MEMS community has addressed this design
problem very well by fabricating miniaturized
propulsion systems called microthrusters. These
systems use various methods to produce thrust, some
of the popular methods for example are vapourizing
liquid microthruster (VLM) that uses liquid
propellant [5] [6], solid propellants [7] [8] and
electrospray technology [9] and very famous,
electrospray propulsion [10].
The system we are going to discuss here is a VLM
based system. Which uses microheater embedded in
the bimorph beam, which also opens and closes the
nozzle inlet. The device consists of an enclosed
chamber to hold water (test liquid), a converging
diverging nozzle and thermal bimorph valve
actuator. Prime focus of this paper will be on the
design of the actuator and the nozzle. A brief
description for design of microfluidic channels for
propellant transport is also discussed. To my

2. knowledge this device is first of its kind which
operates valve while vaporizing the propellant or
producing thrust. This device is not only limited to
space application but also applicable to microfluidic
transport.
The actuator that controls the valve consists of
three layers consisting of heating element, a high
coefficient of expansion element and a low
coefficient of expansion element, which form a
differential heating composite beam. The nozzle with
converging section is anisotropically etched in
silicon while the diverging section is realized by ion
etching to control the half angle of diverging section.
Possibility of using other suitable alloys and
materials have also been discussed giving the readers
a good scope of possibilities.
MEMS actuators can be broadly classified by
magnetic, electrostatic and thermal actuators.
Magnetic actuation is very reliable and efficient for
macro scale but requires high input voltage and
generally does not scales well with miniaturization at
MEMS scale. Whereas electrostatic actuation is quite
popular because of its ease of fabrication and low
inputs (such as piezoelectric actuation in MEMS
resonators) [11]. Thermal actuator are another
attractive option because of their low power
consumption and high displacement (even bi-
directional [12]) and small response time in order of
milliseconds [13]. Also there is no possibility of pull-
in and parasitic capacitance when compared to
electrostatic actuation. Which further strengthens the
use of this principle in my design. The nozzle design
is unique and to my best knowledge never utilized
before. The design require use of both anisotropic
etching and ion beam etching for making the
converging and diverging section of the nozzle. To
validate this both analytical and Fluent (ANSYS)
simulations have been produced, with excerpts from
text as well. Detailed fabrication steps have been
illustrated in order to demonstrate the intricate steps
that are necessary to realize the complete working
principle of the device. Some of the parameters are
assumed for the sake of simplicity and inaccessibility
to tests. But various optimizing algorithms have been
used balance various parameters using MATLAB.
Detailed results have been provided to the reader at
the end. Finally an interesting test setup is also
provided which can be used for observing the nozzle
exhaust by using just some household items.
2. Designof the valve
The thermal bimorph must be able to bear high
temperature loads and high stress along with fast
response time for high frequency application or
instant thrust (in this paper). The first new design of
thermally driven microvalve for fluid control
(pneumatic control) was developed in 1994 by Lisec
et al., which used cross members that buckle under
thermal loading to open a port which was
anisotropically etched on the substrate [14]. After
which a lot of research have been carried out. Which
led to development of various types of materials for
constructing the beam and fabrication steps to
increase the life of thermal actuator which is
subjected to high thermal loading. These materials
include ceramics (zirconia) [15] and alloys [16]. TiAl
alloys have also shown potential as bimorph
actuators which show negligible deflection of 5µm
for a beam length of 500µm. It has been found out
that TiAl can reach up to 500° C without forming
hillocks and stress gradients when compared to
Aluminum, which is unstable at high temperatures
[16]. I am using Polysilicon as the top layer and
Aluminum for the bottom layer, the properties are
obtained from a Technical Report on material
properties of MEMS, and ANSYS Engineering
Materials for simulation. Since both bonded beam
have different thermal coefficient of expansion they
expand with different strain. This differential strain
results in a certain curvature in the composite beam.
This curvature is very important for our device
because it will define the distance of the heat source
from the nozzle inlet. Detailed calculations and
procedure are provided in the following steps.
Cross section of the device.

3. 2.1 Design of Cantilever Bimorph
In 1992 Doring et al. reported a high frequency (1ms)
thermal bimorph cantilever actuator which wascapable of
directing fluid duct at high switch rates [17]. Some of the
devices that have similar principles of the one discussed
here have also been designed such as high output valve to
amplify the actuation, thus the output [18]. The material
property set and the dimension considerations are given
in the table 1. A schematic diagram from Solidworks®
shows the realization of the cantilever beam in figure 1,
with complete dimensions of the cantilever (mm).
Fig 1: Schematic of composite beam.
Table 1: Material Properties.
Consider the following line diagram in figure 2.
Since the thermal coefficient of expansion of silicon
is smaller than Aluminum, aluminum expands more
compared to silicon which results in bending of the
composite beam. This bending may be assumed as a
segment of circle with radius r. s represents the arc
of composite beam. d is the total deflection of the
beam. This can be found out by following equations
given in the steps.
Fig 2: Line diagram showing the geometry of beam bending.
Assumptions:
1. Thickness of Silicon is double of Aluminum
2. Pressure inside the chamber 𝐩 𝒄= 3 Bar
3. Pressure at exit 𝐩 𝒆= 25 mBar
4. Temperature of aluminum = 227°C
Optimizing and finding beam dimensions:
 Optimization is required to find a valid
deflection such that it’s neither small nor
large, it should be within practical limits.
 Material 2 is the Silicon and Material 1 is
Aluminum.
 The design is initiated by assuming that
thickness of aluminum beam is half of silicon
beam, i.e. 𝒕 𝟏 =
𝟏
𝟐
𝒕 𝟐 , this is important to form
a relation between the thickness of material
(beam) and the maximum tip deflection, t2 vs
tip deflection.
 This is done using MATLAB and plotting the
relation between silicon beam thickness and
tip deflection, as shown in the figure 3.
 Analytical equation for beam bending is used
[19] and MATLAB code is provided in the
appendix.

𝟏
𝒓
=
𝟔× 𝒘 𝟏 𝒘 𝟐 𝑬 𝟏 𝑬 𝟐 𝒕 𝟏 𝒕 𝟐(𝒕 𝟏+𝒕 𝟐)(𝜶 𝟏−𝜶 𝟐 )×∆𝑻
(𝒘 𝟏 𝑬 𝟏 𝒕 𝟏
𝟐
) 𝟐+(𝒘 𝟐 𝑬 𝟐 𝒕 𝟐
𝟐
) 𝟐+𝟐×𝒘 𝟏 𝒘 𝟐 𝑬 𝟏 𝑬 𝟐 𝒕 𝟏 𝒕 𝟐×(𝟐𝒕 𝟏
𝟐
+𝟐𝒕 𝟐
𝟐
+𝟑𝒕 𝟏 𝒕 𝟐)
 𝒅 = 𝒓 − 𝒓𝒄𝒐𝒔𝜽
 The graph below shows design point which is
used to simulate the concept.
Material property Silicon Aluminum (Al
alloy in FEA)
Length (l) 100µm 100µm
Width (w) 50µm 50µm
Thickness (t) 30µm 15µm
Young’s Mod (E) 158Gpa 69Gpa
Thermal expansion
Coefficient (α)
2.9*10-6
ppm/°C
25*10-6
ppm/°C
Temperature(°C)dT 200°C -
Silicon
Aluminum

4. Fig 3: Plot between Silicon beam thickness and tip deflection.
2.2 Design of Nozzle
Few parameters of nozzle is referred from a
research paper. Consider the following cross
sectional line diagram of the nozzle in figure 4.
Fig 4: Line diagram showing the geometry of nozzle.
Optimizing and finding beam dimensions:
 The nozzle that we are using is a converging-
diverging nozzle (cd-nozzle). The
converging nozzle has a fixed dimension in
the sense that the half angles are fixed by
anisotropic etching of the silicon, i.e. 54.7°.
 The divergent section’s profile is fixed,
which is conical. If we make it by anisotropic
etching, flow separation will occur near the
walls. For optimum performance of conical
diffuser the half angle at exit should be
designed between 12° and 18° [20]. We can
save weight by increasing the half angle
which decreases the nozzle length but at the
cost of performance.
 Now if the steam escaping the nozzle is
saturated, it will not expand faster and also
freezes at exit creating icing problems. To
avoid this the steam must be superheated or
expansion ratio (area at exit/ area at
throat) should be decreased. Since the
temperature is fixed for the
aluminum=227°C (dT=200°C) we will
design the expansion ratio accordingly.
 Formulas to consider:
Thrust, 𝐅 = 𝐦̇ 𝐯𝒆 + (𝐩 𝒆 − 𝐩 𝒂 )𝐀 𝒆 = 𝐂 𝑭 𝐩 𝒄 𝐀𝒕
𝑀𝑎𝑠𝑠 𝐹𝑙𝑜𝑤 𝑟𝑎𝑡𝑒, 𝐦̇ =
𝐅
𝑰 𝒔𝒑
=
𝐩 𝒄 𝐀 𝒕
𝒄̇
=
𝐯𝒆
𝐠
𝐶ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦, 𝒄̇ =
√ 𝐑𝐓
𝛙
𝐂 𝑭 = 𝛙√ 𝟐𝜸
𝜸 − 𝟏
[𝟏 − (
𝐩 𝒆
𝐩 𝒄
)
𝜸−𝟏
𝜸
+
𝐀 𝒆
𝐀 𝒕
𝐩 𝒆 − 𝐩 𝒂
𝐩 𝒄
𝛙 = √ 𝜸 (
𝟐
𝜸 + 𝟏
)
𝜸+𝟏
𝜸−𝟏
Where 𝐯𝒆 is the nozzle exit velocity (m s−1), P
total pressure (Pa), 𝐩 𝒆 nozzle exit pressure (Pa),
𝐩 𝒂 ambient pressure (Pa), 𝐩 𝒄 chamber pressure
(pa), 𝐀 𝒕 nozzle throat area, 𝑰 𝒔𝒑 specific impulse
(s), T temperature (K), 𝐀 𝒆 nozzle exit area, 𝐀 𝒓
area ratio=
𝐀 𝒆
𝐀𝒕
, V volume of the chamber, R gas
constant (J Kg−1
K) and γ specific heat ratio.
 Calculations
γ= 1.32
ψ=0.671
𝒄̇ = 𝟕𝟏𝟓.𝟗
 Optimizing Cf and Ar we ge t following graph:
Fig 5: Plot between Area Ratio and Coefficient of Thrust.
Our Design Point
Our Design Point

5. We can observe that Cf increases with area ratio. But
in our design we have to optimize out throat area
considering:
1. Thickness of wafer.
2. Area of cantilever covering the nozzle inlet
3. Anisotropic etching pattern of converging
section.
4. Length of Converging nozzle = 40µm.
5. Area ratio = 3 , which give Cf = 1.622
The thinnest wafer present is of 275 µm [21]. If we
consider etching the chamber uses 185µm (may be not
possible in practical) this leaves total nozzle length =
90µm.Figure 6 showsthe complete diagram of the nozzle
with dimensional consideration.
Fig 6: Line diagram showing the geometry of nozzle.
Now consider figure 7. In this we can find the
dimension of throat. For this we need the distance
between the inlet and the throat section which is by
design equal to = 40µm.
Fig 7: Line diagram showing the converging section and
diverging section.
For converging section length = 40µm
Inlet area = 2500 µm2
(dictated by width of beam)
The throat area At = (27.18)2
µm2
=738.74 µm2
Therefore Ae= 2216.22 µm2
= 47 µm
Which gives diverging half angle of 12° (approx., 11.25°
actual) for a diverging section length of 50µm, which is
exactly we need. Now consider figure 8. The divergent
section hasa length of 50µm. And we know the area ratio.
This gives us complete dimensions of the divergent
section. All these dimensions will be used in the
simulation in ANSYS.
3. Results and Calculation
Firstly we will calculate the power required for the
microheater to convert water at27°C into steamat 227°C.
Assumptions:
1. Pressure inside the chamber=3bar
2. Volume of chamber=5 time volume of composite
beam.
Volume of the entire beam is given by:
𝑳 × 𝒘 × ( 𝒕𝟏 + 𝒕𝟐) = 𝟐𝟎𝟎 × 𝟓𝟎 × ( 𝟑𝟎 + 𝟏𝟓)µ𝒎 𝟑
= 𝟒. 𝟓 × 𝟏𝟎 𝟓µ𝒎 𝟑 =. 𝟒𝟓× 𝟏𝟎−𝟏𝟐 𝒎 𝟑
Taking density of water to be 1000kg/m3
and volume of
chamber=volume of water, we get mass of water m inside
the chamber:
𝒎 = 𝟓 ×. 𝟒𝟓× 𝟏𝟎−𝟏𝟐 × 𝟏𝟎𝟎𝟎 = 𝟐. 𝟐𝟓𝒏𝒌𝒈
Enthalpy of water at 27°C, 1Bar=113.19 kJ/kg [22] [23]
Enthalpy of water at 27°C, 3Bar=113.47 kJ/kg
Enthalpy of steam at 227°C, 3Bar=2921.15kJ/kg
So, the heat required = 2921.15-113.19=2807.96kJ/kg
For 2.25 nkg, heat required=6.32 mW (per second flow)
Now we have
At = (27.18)2
µm2
=738.74 µm2
𝐩 𝒄= 3 Bar
Cf = 1.622, Therefore
𝐅 = 𝐂 𝑭 𝐩 𝒄 𝐀 𝒕 = 𝟏. 𝟔𝟐𝟐 × 𝟑 × 𝟏𝟎 𝟓 × 𝟕𝟑𝟖. 𝟕𝟒×
𝟏𝟎−𝟏𝟐 = 𝟎. 𝟑𝟔𝒎𝑵 , Also
𝐦̇ =
𝐩 𝒄 𝐀𝒕
𝒄̇
=
𝟑×𝟏𝟎 𝟓×𝟕𝟑𝟖.𝟕𝟒×𝟏𝟎−𝟏𝟐
𝟕𝟏𝟓.𝟗
= 𝟎. 𝟑𝟏µ
𝒌𝒈
𝒔
* Which is comparable to otherlab tested devices [5].

6. 4. Fabrication steps
Fabrication steps are obtained by studying previous works in the field of microthruster and other MEMS devices as well,
which may not be the exact methods that can be applied.[5] [6] [24] [25]. Table 2 shows major fabrication steps of the
bottom half which will house the nozzle and the bimorph. We will be considering the fabrication of cantilever bimorph
operated valve only, as the C-C valve will have similar fabrication steps with one extra fixed support.
 Wafer cleaning by Piranha cleaning
process followed by thermal oxide
growth at 1100°C. Oxide thickness of
1.0µm to protect the mask#1 during
anisotropic etching of silicon.
 Photolithography and anisotropic
etching of silicon to open cavity for
fabricating cantilever and nozzle.
 Photoresist coating.
 Mask#2 positive photolithography, for
opening anchor point for the cantilever.
 Isotropic etching of silicon.
 Mask#3 positive photolithography, for
anisotropic etching of the silicon, for
making the converging part of the
nozzle.
 TMAH at temperature around 70°C
(etch rate @ 1.2min/µm).
 Removal of oxide layer by immersing
the wafer into Buffer HF, to selectively
remove SiO2.
 Photoresist deposit to cover the
converging nozzle for subsequent
Aluminum deposit.
 Mask#4 positive photolithography, for
opening the anchor.
 Deposition of Aluminum electrode (or
the lower member of the cantilever
beam). Vacuum evaporation of
Aluminum at substrate temperature of
140°C, followed by sintering at 450°C
(high vacuum, high temperature PVD
process).

7.  Electrical insulation required (SiO2,
CVD) to avoid conduction by silicon
layer (negligible).
 High rate deposition of microcrystalline
silicon using conventional plasma-
enhanced chemical vapor deposition.
[24] Since we need thicker material at
the top.
 Photoresist deposit.
 Mask#5 Negative photolithography for
forming the entire cantilever structure.
 Backside etching of diverging section of
the nozzle using RIE.
 12° to 18° half angle taper [24].
 This is very crucial for avoiding flow
separation in divergent section due to
larger angle (54.7°). [25]
 Photoresist removal.
 Packaging of the device. Anodic
bonding.
 Microfluidic channeling for liquid
propellant supply.
 *Image not to scale.
Table 2: Fabrication steps.

8. 5. ANSYS Simulation (Static Structural and Thermal Electric)
Figure 8 shows total deformation on application of thermal load of 227°C in Aluminum metal. Beambending is a complex
phenomenon, and hogging or sagging can’t be determined by just looking at it. Chenpeng Hsu and Wensyang Hsu state in
their FEM research that initial deflection may change the behavior of the beam [26]. So care should be taken to deposit
beam in such a way that it doesn’t sag from the beginning, to prevent it from bending downward and eventually rubbing in
the substrate without opening the valve.
We can see that analytical deflection of the tip (here red in color) was 2.2µm, and FEM simulation gives us value 2.5µm
which holds good considering the static structural model doesn’t allow flow of heat from Al to Si.
Fig 8: Total deformation in static structural simulation.
This figure 9 shows Thermal-Electrical stimulation. When 0.35V potential is applied across Aluminum a temperature
rise of 300°C approximately is observed. The purpose of this simulation is to show the spread of thermal gradient across
the entire composite beam. Mesh control was left to auto in this case.
Fig 9: Temperature distribution in the composite beam at 0.35V.
Close to
Analytical value

9. In figure 10 the Fluent (ANSYS) results were found as expected. The first contour shows pressure distribution in the
nozzle. The inlet (leftmost) haspressure input of 3Bar which is the high pressure side showed in red. Aswe move rightwards
the pressure reduces as velocity keeps on increasing in the converging section, further extending till final pressure at exit is
reached which has a numerical value of 25 mBar (lowest, blue region).
Fig 10: Static pressure (pa) contours, left to right- inlet, throat and exit.
This figure 11 shows velocity contour. The velocity is maximum at the exit which it should be. The exit velocity here is
544m/s. Since this conical nozzle is designed with nozzle exit half angle of 11.25° we can observe the flow is separating
near the exit walls. To avoid this we have to keep the nozzle exit half angle of diverging section in-between 12° to 18°,
stated previously in calculations.
Fig 11: Velocity contours.

10. This figure 12 shows contour for Mach number. The green region in the throat shown that the Mach number is nearly
‘1’ here. Which is very important in cd-nozzle design. If Mach number doesn’t reach ‘1’ at the throat, the gases will not
reach supersonic velocity at exit as the supersonic diffuser will fail to perform its function.
Fig 12: Mach number. Mach#=1 at throat.
6. Discussion
The results obtained and calculation done
considering theoretical models are well within limits.
This shows that design is quite possible to make.
Some of the important parameters to consider here
are temperature of operation, thrust produced, mass
flow rate of the gases, life of the device and form
factor. If made, this will be the smallest microthruster
that doesn’t uses solid propellant.
One important factor to consider here is the
temperature variation in the space. It’s reported that
temperature changes are quite harsh in space ranging
from -170°C to 123°C by Miracle Israel, Intern at
Astrome Technologies. Which should be considered
to avoid freezing and expansion of the propellant.
Also radiations at those levels are consideration to
prevent premature combustion.
Finally microfluidic channels that can be etched
to feed the microthruster should be able to keep the
device primed. When the bimorph heats up the
propellant near the nozzle the gases escaping it will
develop suction near the nozzle inlet, failing to
supply fuel at a constant rate may result into failure
of the bimorph due to overheating, as the fuel cools
the bimorph, also it will result in failure of thrust.
Here we didn’t discuss about the electrical
contacts. Proper doping of the substrate and choosing
the material will improve the performance of the
system. I recommend an insulation layer between the
aluminum electrode and the silicon electrode to
avoid conduction of silicon. If allowed, then
controlling the dimension is required.

11. 7. Testing OfNozzle Exhaust Characteristics.
7.1 Schlieren imaging [27] [28]
Schlieren imaging can be used for observing the exhaust.
In this method simple equipment are needed such as
tripod, a concave mirror, a point light source (LED) and a
camera. The setup is shown in the figure 13.
Fig 13: Schlieren imaging setup.
When the exhaust from the microthruster enters the light
field it changes the refractive index of the medium which
filled the view previously. This results in the refraction of
incoming light rays.Which canbe easily seenin the figure
14.
Fig 14: exhaust from microthruster [].
7.2 Sensitive cantilever setup [28] [6]
In this testing method a small cantilever made of foil is
place few millimeter below the microthruster nozzle exit.
A small silicon chip is placed on the beam and laser is
shown on the chip which acts as a mirror. A small
deflection in the cantilever displaces the mirror thus
deviating the incident laser light which is calibrated
according to the thrust. Aschematic from a researchpaper
shows the complete setup. The cantilever has to be heated
up to a certain temperature in order to evaporate the
condensate, if not done, the cantilever will bend due to
condensate mass.
Fig 15: Cantilever test setup.

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14. Appendix
1. Matlab code and plot 1

15. 2. Matlab code and plot2