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IMECE2003-43558

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Proceedings of IMECE’03
2003 ASME International Mechanical Engineering Congress
Washington, D.C.,Proceedings
November 15–21,
2003
of IMECE’03
2003 ASME International Mechanical Engineering Congress and RD&D EXPO
November 15-21, 2003, Washington, D.C. USA
IMECE2003-43558
IMECE2003-43558
INVESTIGATION OF PERFORMANCE OF ACTIVE MICROCAPSULE ACTUATION
Donald J. Leo∗
Honghui Tan
Center for Intelligent Materials and System Structures
Department of Mechanical Engineering
Virginia Tech
Blacksburg, Virginia 24061
Email: htan@vt.edu
Department of Mechanical Engineering
Virginia Tech
Blacksburg, Virginia 24061
Email: donleo@vt.edu
Taigyoo Park
Department of Chemistry
Virginia Tech
Blacksburg, Virginia 24061
Email: tgpark@vt.edu
Timothy E. Long
Department of Chemistry
Virginia Tech
Blacksburg, Virginia 24061
Email: telong@vt.edu
ABSTRACT
Microcapsules are micron-sized hollow particles that
can be synthesized with fluid encapsulated in the interior.
The microcapsules can be used as a potential actuation
technique by incorporating stimulus-responsive materials,
such as permselective, light-sensitive and electrically sensitive materials. The microcapsules range from 10 to 80
microns in diameter and wall thickness normalized to radius might range from 0.05 to 0.5. The actuation concept
is to control the size of the microcapsules by varying the interior fluid pressure using an external stimulus. This paper
presents efforts to model the performance and capabilities of
microcapsules as micro actuators. We assume the pressure
of the fluid inside of the microcapsules can be controlled by
certain technique, such as thermal, electro or optical stimulus to the fluid. This paper will focus at modeling the performance of microcapsules under known pressure variation
of fluid inside. First the paper compares a thin-wall model
to a thick-wall model and identifies that thin-wall theory
is not accurate enough for microcapsules. Simulation results show that energy density in the order of 3J/cm3 is
∗ Address
theoretically achievable for thick microspheres. Two type
of materials are studied as the materials encapsulated in
microcapsules. Their constitutive equations are then incorporated into the thick-wall model. Simulations show hydrocarbon solvents are much more efficient than ideal gas
in terms of actuation performance.
INTRODUCTION
Active materials, such as piezoelectric materials, shape
memory materials, and electroactive polymers, have been
studied widely through the past decade in the search for
high energy density actuation technologies. Although many
of these materials exhibit sufficient energy density, some
are limited by their small deformations (piezoelectric materials), slow response time (shape memory alloys), or low
stress output (electroactive polymers). Various of amplification technologies have been developed for a number of these
materials, such as piezoelectric unimorph and bimorph actators [1], inchworm motors [2] and repetitive piezohydraulic
pumps [3].
The last decade has seen a stride in the development
of microactuation technology. Most microactuation tech-
all correspondence to this author.
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polymer
matrix
nologies rely on some means of movement of fluid by surface tension. One technology of this kind is to utilize thermal control of surface tension by taking advantage of the
thermalcapillary effect. Micropumping [4] and microoptical
switch [5] have been developed based on this effect. Another
technology is to apply electrical excitation to control surface
tension of fluid, including elctrocapillary [6], electro-osmosis
[7] and electrowetting [8, 9]. These fluid flow systems require a complex seal of micro-ducts, which are difficult to
fabricate. The pressure this technology can produce is limited by the surface tension the fluid.
In this paper we investigate the use of active microcapsules for controllable actuation. Microcapsules are hollow
micron-sized spheres that consist of a polymer shell that encapsulates a fluid or a gas. We define an active microcapsule
as one in which the properties of the encapsulated material
can be controlled via an external stimulus. Our initial work
presented in this paper focuses on the use of bulk temperature change to cause an expansion and contraction of the
interior fluid or gas, thus causing an volume change in the
encapsulated polymer. Another method of actuation is to
control the transport of fluid through the microcapsule shell
via application of an external stimulus.
A description of the microcapsule is shown in Figure 1.
The materials studied in this work consist of a polymer matrix with embedded, hollow microcapsules. The weight and
volume percentage of the microcapsules range from approximately 5% to 30%. We denote an Active Microcapsule
Polymer (AMP) as a material in which the properties of
the interior fluid or gas can be controlled with an external
stimulus. This work will concentrate on the development of
a mechanics model of the active microcapsule polymer to
determine the stress-strain characteristics as a function of
temperature. Initial experimental results will also be presented to demonstrate the basic properties of the actuation
principle.
polymer
shell
active
microcapsule
Figure 1.
active
material
Microcapsules embedded in matrix.
Defining a spherical coordinate system (r, θ, φ) with origin
at the center of sphere as shown in Figure 2, the geometry
boundary of the deformed sphere satisfies a < r < b. φ is
the angular position in the plane normal to the (r, θ) plane.
a
E
A0
B0
r
θ
Pi
b
Po
No applied pressure
LINEAR ELASTICITY MODEL
The actuation analysis will be based on a linear elasticity model of the microcapsule. We assume that the microcapsule is made of hyper elastic material, which means the
stress is only dependent on the current strain. The material
is also assumed to be isotropic and has a constant elastic
modulus E. The deformation of the microsphere under internal and external pressure is shown in Figure 2. At zero
pressure, the sphere has boundary conditions A0 < ρ < B0 ,
where ρ is the radius of any point of the hollow sphere.
Pressures are applied to the sphere, which changes the inner
radius and outer radius respectively to be a and b. Because
the applied pressure Pi and Po are uniform, the shape of microcapsule after deformation maintains its spherical shape.
Figure 2.
Under pressure
Deformation of a microsphere under pressure
THIN WALL THEORY
Thin-wall theory normally limits the thickness ratio to
be around 0.1. Although the microcapsules generally have a
large thickness range (from very small to 0.5 of the capsule
radius), it is still interesting to look at a thin-wall model
because of its simplicity. For the microcapsule shown in
Figure 2, if we assume the wall of the hollow sphere is thin
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enough to satisfy t = b − a << r, the stress of the microcapsule under zero external pressure and uniform internal
pressure in spherical coordinates can be computed by[10]
σr = −Pi
σθ = σφ =
Pi r
,
2t
where σij and εij is the {i, j} component of stress tensor
and strain tensor, respectively. The variable εkk is defined
as the summation of strains in three normal directions εkk =
εrr + εθθ + εφφ . µ and λ are Lamé constants, which are
related to elastic modulus E and Poisson’s ratio ν as
(1)
λ=
where Pi is the internal pressure. Because the symmetry of
sphere, there is no difference between θ and φ directions,
which means the strain and stress in these two directions
should be equal. For convenience, we denote the stress and
strain in θ or φ direction by using a subscript t , which means
the direction is tangent to the surface. The strain in the
tangent direction can be calculated as in [10]
εt = εθ =
1
(σθ − νσφ − νσr ),
E
2π(r + dr) − 2πr
dr
=
2πr
r
εrθ = εrφ = εθφ = 0
σrθ = σrφ = σθφ = 0.
(2)
(9)
Applying the strain-displacement relationship in spherical
coordinates yields
εrr = u (r)
εθθ = εφφ =
u(r)
.
r
(10)
Applying Equation (7) for i = r, j = r yields
(3)
σrr = 2µεrr + λ(εrr + εθθ + εφφ ).
Substituting Equation (1) and (2) into (3) and differentiating yields
1 r
dr
= [ (1 − ν) + ν]dPi .
r
E 2t
E
1 1−ν
ln( +
) + Const.
ν
r
2tν
(4)
σrr = (2µ + λ)u (r) + 2λ
u(r)
.
r
(5)
Substituting initial conditions (Pi0 , r0 ) into the above equations yields
1
+ 1−ν
E
2tν
.
ln 1r
ν r0 + 1−ν
2tν
u(r)
.
r
(13)
The equilibrium stress equations without body force in [11]
expressed in spherical coordinates is
(6)
∂σrr 1 ∂σrθ
1 ∂σrφ 1
+
+
+ (2σrr −σθθ −σφφ +σrθ cosθ) = 0
∂r
r ∂θ r sinθ ∂φ r
(14)
Substituting Equation (9), (12) and (13) into the above
equation and simplifying yields
THICK WALL THEORY
The stress-strain relationship of a isotropic material for
linearized elasticity theory can be found in [11]
σij = 2µεij + λεkk ,
(12)
In the same manner, applying Equation (7) for θ and φ
direction and substituting in Equation (10) yields
σθθ = σφφ = λu (r) + 2(µ + λ)
Pi = Pi0 −
(11)
Substituting Equation (10) into the above equation yields
Integrating the above equation yields
Pi = −
(8)
Because the symmetry of geometry and external force, the
deformation function u is only a function of radius r and
there is no shear deformation and shear stress
where ν is Poisson’s Ratio. If we consider the strain of the
whole sphere other than the shell, because the microcapsule
maitain spherical shape through deformation, the strain in
tangent direction is
εt =
Eν
E
,µ =
.
(1 + ν)(1 − 2ν)
2(1 + ν)
r2 u (r) + 2ru (r) − 2u(r) = 0,
(7)
3
(15)
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COMPARISON OF THIN WALL AND THICK WALL
THEORY
In all simulations, we assume elastic modulus of the microcapsule material E = 30 MPa and outside radius R = 10
µm for all the simulations. The pressure inside and outside
of the microcapsule is assumed to be normal atmosphere
pressure 105 P a.
The deformation of a microcapsule versus internal pressure is shown in Figure 3 while assuming the external pressure is zero. In both plots, the pressure is normalized by the
elastic modulus and deformation is normalized by the initial
outer radius. It is noted for thickness 0.1 as in Figure 3(a)
that the thin-wall and thick-wall results are in good agreement for strain less than 4%. For 0.02 thickness, the two
models show considerable differences for even small strain.
The thin-wall model is thus only good for thickness ratio
less than 0.1 under small strains. We attribute these differences to the fact that the thick-wall theory takes into
account the wall-thinning effect as shown in Figure 4(b) at
large strain which the thin-wall theory does not consider.
The typical thick-wall results are shown in Figure 4.
The external pressure is set to be zero in order to identify the major features of the results. The deformation
and thickness of the sphere is simulated for a sphere with
normalized initial pressure P
E = 0.2 and normalized initial
thickness of rt00 = 0.1. Figure 4(a) shows the deformation of
outer radius up to 100% strain (from 1.0 to 2.0) when varying the internal pressure. Figure 4(b) shows the change of
wall-thickness for different internal pressures. Figure 4(a)
shows there is a maximum internal pressure when the outer
radius increases to be around 1.5 times initial value. When
the sphere deforms further, the capacity of the sphere to
hold pressure actually drops, which indicates that there is a
maximum pressure for the sphere to hold. When the pressure becomes larger than the maximum value, the sphere
will deform to plastic deformation stage and rupture. We
believe a possible explanation maybe that the effect of wallthinning effect reduces the strength of the structure considerably at large strain. It is also noted that when developing the thick-wall model a linearized elasticity model is
assumed, which might suggest this maximum pressure point
might be only due to the assumption of a linear model and
is no longer valid at large strains.
which has solution of displacement fields as following
u(r) = C1 r +
C2
r2
(16)
where C1 and C2 are integration constants which are to
be determined by boundary conditions. Substitute Equation (16) into Equation (12) yields
σrr = (2µ + 3λ)C1 −
4µ
C2 .
r3
(17)
Applying boundary conditions at r = a and r = b yields
4µ
C2 = Pi
a3
4µ
= (2µ + 3λ)C1 − 3 C2 = Po .
b
σrr |r=a = (2µ + 3λ)C1 −
σrr |r=b
(18)
Solve for the constants C1 and C2 and substitute into Equation (12) to determine the displacement fields as function
of the boundary conditions:
u(r) =
a3 Pi − b3 Po
a3 b3 Pi − Po
r
+
.
2µ + 3λ b3 − a3
4µr2 b3 − a3
(19)
The following equations holds according to the definition of
displacement field:
A0 = a − u(a), B0 = b − u(b),
(20)
where A0 and B0 is the inner radius and outer radius at
zero pressure. Given initial pressures at inner and outer
surface to be Pi0 and Po0 and geometry conditions a0 and
b0 , displacement field u0 can be calculated by Equation (19).
Then A0 and B0 can be computed as following
A0 = a0 − u0 (a0 ), B0 = b0 − u0 (b0 ).
(21)
Combining Equations (19),(20) and (21) yields
a3 b3 Pi − Po
a
a3 Pi − b3 Po
+
= A0
2µ + 3λ b3 − a3
4µr2 b3 − a3
b
a3 b3 Pi − Po
a3 Pi − b3 Po
b−
+
= B0 . (22)
2µ + 3λ b3 − a3
4µr2 b3 − a3
a−
SIMULATION OF PERFORMANCE
The work output of a microcapsule can be estimated as
a micro-pump that works in a cyclic fashion. The operation diagram is show in Figure 5. The microcapsule starts
with initial states in (a). The fluid is heated and expanded,
which results in the expansion of shell as in (b). Then the
shell becomes porous and fluid is pumped out of the shell
If internal and external pressure is given, the inner radius
a and outer radius b can be solved simultaneously by the
above equation.
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t0
=0.1
r0
2
Thick Wall
1.8
1.6
R
R0
Thin Wall
(a)
1.4
1.2
1
0.02
0.025
0.03
0.035
P
E
0.04
0.045
0.05
0.055
(a)
t0
=0.1
r0
0.1
Thick Wall
0.09
Thin Wall
t
R0
0.08
(b)
0.07
0.06
0.02
0.025
0.03
0.035
P
E
0.04
0.045
0.05
0.055
(b)
Figure 3. Comparison of deformation versus pressure for thin-wall
model and thick-wall model for normalized thickness 0.1 (a) and 0.2
(b).
Figure 4. Typical simulation results for thick-wall model for normalized thickness of 0.1 under zero external pressure: (a) deformation of
sphere due to internal pressure; (b) thickness change due to internal
pressure.
because the contraction of the microcapsule as shown in (c).
At the same time, the temperature of fluid in the microcapsules decreases and the pressure inside of the microcapsule
decrease further to some value below initial pressure. Then
the shell is made porous again and the fluid outside can
flow into the microcapsule as in (d). The microcapsules can
work in a cyclic operation in this manner.
It is noticed that the system only produces work in the
fluid exhaustion stage as shown in Figure 5(c) The work
output of the microcapsule can be calculated by the following equation:
W =
8
P dV ,
in Figure 4(a). Figure 6 shows a typical pressure-volume
diagram which can be used to calculate work. The microcapsule begins to contract from point 1 to point 2 which
corresponds to the load pressure P1 . If we can accurately
control the load pressure such that it is equal to the fluid
pressure inside the sphere through contraction, the total
output work can be maximized to be the total area below
P-V curve in Figure 6, which represents the upper limit of
work that can be extracted from the microcapsule in one
cycle. If we assume a constant load pressure P1 , the work
done in one cycle is equal to the grey area in the diagram.
Because a constant load pressure is of more engineering importance, output work under constant load pressure is then
analyzed. Figure 7 shows the energy density as a function
of strain for different shell thickness, which is calculated by
dividing the output work by the volume of microcapsule.
It is noted that energy density increases as shell thickness
increases. For normalized thickness t = 0.8, the volumetric
(23)
where P is pressure of fluid and V is the volume of fluid
pumped out, which is equal to volume change of the microcapule. The thick wall model developed in the previous
sections can be used to calculate the pressure as a function of radius of a microcapsules, which is already shown
5
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Elastic energy density
1
10
0.100
0.275
0.450
0.625
0.800
t=0.8
P
(a)
(b)
P1
(c)
t=0.45
t=0.275
-1
10
t=0.1
-2
10
(d)
-3
10
Figure 5. Diagram of operation in one cycle: (a) initial states; (b)
closed shell expansion; (c) fluid exhaustion; (d) fluid intake.
0
Figure 7.
0.01
0.02
0.03
0.04
0.05
Strain
0.06
0.07
0.08
0.09
0.1
Energy density for different normalized thickness.
IDEAL GAS
Ideal gases are usually gases with small molecular mass
which have boiling temperature as low as near absolute zero
temperature, such as oxygen and nitrogen. Equation (24)
shows the states equation of ideal gases
energy density can be as high as 3J/cm3 .
1
P
t=0.625
0
10
Energy Density (J/cm3)
P0
P V = R T,
(24)
2
where P is the pressure, V represents the volume and T
is temperature of gas. The variable R is a constant for all
ideal gases. For the gas encapsulated in a microcapsule as
in Figure 2, if we denote the initial conditions of ideal gas
as pressure Pi0 , volume of V0 and temperature at T0 , the
states of the same gases can be computed by
P1
P0
Pi0 V0
Pi V
.
=R=
T
T0
(25)
V
Figure 6.
For gas filled in the hollow sphere, the volume is related to
the inner radius as V = 43 π a3 . Substituting this expression
into Equation (25) yields
Work done in one cycle.
Pi a3
Pi0 a30
.
=
T
T0
TWO EXAMPLES OF ENCAPSULATED MATERIALS
The previous section presents a model to analyze the
deformation of a microsphere under internal pressure variation. In this section, we will incorporate the constitutive
equations of the encapsulated materials to enable us to simulate actuation performance for a microcapsule. We select
two kinds of materials, one of which is ideal gases and the
other kind is some common hydrocarbon solvents, because
these materials are very common and widely used in engineering applications.
(26)
Combining Equations (22) and (26), the new coupled equations have five variables (a, b, Pi , Po , T ) and three equations.
Numerical methods can be used to simulate the performance of the microcapsules.
Our preliminary experiment results show that the strain
of the materials is less than 10% under two hundred degree
temperature variation. On the other hand in order to minimize the possible errors resulted from linearization of elasticity, we will focus at deformation below 10% for the later
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analysis. Figure 8 shows the simulation results for ideal gas.
Figure 8(a) shows the simulation of internal pressure versus external pressure and deformation for a constant initial
thickness of 0.2. It shows the internal pressure needed for at
each constant strain increases linearly as external pressure
increases. For a fixed external pressure, the internal pressure increases for higher deformation. Figure 8(b) shows basically a 3-D plane plot for 0.2 wall thickness, which means
the temperature of gas varied with both the deformation
and external pressure linearly when the other one is fixed.
It is noted in the figure that in order to achieve 10% strain,
a minimum of 80000◦ C temperature is required, which is
a extremely high temperature. Figure 8(c) shows the temperature vs. different and thickness and deformation. It
is noted the temperature increases sharply when the thickness increases. When the thickness ratio increases to around
0.9, the temperature required increases to as high as 107◦ C,
which is far above the 104◦ C temperature range for thickness below. It indicates, for ideal gas, the performance is
sensitive to the thickness and large temperature variations
are needed to produce controllable actuation.
bining Equations (22) and (27), the new coupled equations
have a, b, Pi , Po , T five variables with three equations. Numerical methods can be used to simulate the performance
of the microcapsules.
Figure 9 shows the simulation results for a microsphere
whose elastic modulus E = 30M P a and initial internal
pressure is 20KP a. Compared with Figure 8(b) like a linear
plane shape, Figure 9(b) shows that for each constant external pressure line, the temperature first increases fast and
then it become flat as deformation increases. The temperature variation is around 200◦ C for 10% strain, which is also
much smaller than ideal gas. For higher external pressure,
the curve is flatter than for lower external pressure, which
indicates higher external pressure may actually favor better
performance. The results shows that hydrocarbon materials
such as isopatene might be a better choice of the encapsulated material in the microcapsule. As shown in Figure 9(c),
large thickness ratios require larger temperature variations.
Figure 10 shows the deformation versus temperature
plots for five materials. Neo-pentane has smallest requirement for temperature variations and it has the largest slope
at the most deformations among the five materials. It indicates system built with neo-pentane is more sensitive to
temperature change and can produce better performance.
Figure 11 shows the deformation versus temperature
plots for different normalized pre-pressures. At high prepressure of 0.05 the temperature variation for 10% strain is
at only 30◦ C, which is about half smaller than the 63◦ C for
the pre-pressure of 0.01 cases. Also noted is that the slope
of higher pre-pressure is larger, too. High pre-pressure is
effective to reduce the large temperature variation needed
when the system is actuated.
HYDROCARBON SOLVENT
In this section, to explore the performance of microcapsules, five hydrocarbon solvent materials will be studied.
The five materials are iso-pentane, n-pentane, neo-pentane,
n-Hexane and n-Heptane. The vaporization pressure as a
function of temperature can be estimated by Antoine Equation as follows:
lnP = A −
B
,
T +C
(27)
where A, B and C are constant dependent upon materials.
The units of pressure P is mmHg and units of temperature
T is ◦ K. Table 1 listed these parameters for the above five
hydrocarbon solvents from [12]. In the same manner, comTable 1.
Experimental Results
Preliminary tests have been performed with single microcapsules with iso-pentane encapsulated inside. The test
setup diagram is shown in Figure 12(a). The tested sample
is placed in a furnace which provide direct thermal excitation. A very small pressure of 0.01 atm is applied to the
sample through the quarts probe which also measures the
deformation of the microsphere. The applied pressure is
maintained to be constant by LVDT device whose pressure
can be linearly controlled by control voltage. Figure 12(b)
shows the plots of temperature in the furnace and strain
of the microcapsule versus time. The strain is calculated
by dividing the displacement of the quartz probe with the
initial diameter of the sphere. The regular curve is the
temperature which is controlled to ramp at a velocity of
5◦ C/min. The measured strain of the microsphere does not
show the same pattern as the temperature. The peak values
drop after each temperature variation cycle, which indicates
Parameters of Antonine equation.
Material
A
B
C
n-Pentane
15.8333
2477.07
-39.94
iso-pentane
15.6338
2348.67
-40.05
neo-pentane
15.2069
2034.15
-45.37
n-Hexane
15.8366
2697.55
-48.78
n-Heptane
15.8737
2911.32
-56.51
7
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DISTRIBUTION STATEMENT
This document has been approved for public release,
distribution unlimited.
that there is possibly some leakage of encapsulated material
through the shell. The average strain is around 5% for temperature variation from 100◦ C to 140◦ C. The simulated isopentane deformation as shown in Figure 10 is around 8% for
the same temperature range, which is considerably higher
than the experiment results. We think there are three major reasons that might contribute to the discrepancy. The
first is the simulated thickness ratio of the microsphere is
assumed to be 0.2, which can be different from actual value.
The second is that the elastic modulus of the material is actually dependent upon temperature, which is not considered
in the model. The third one is the different boundary conditions between the model and experimental setup. However,
the simulation results does predict the same order of performance as experiment shows. We expect better prediction to
be possible when we incorporate more accurate properties
into the model.
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SUMMARY AND FUTURE WORK
A linear elasticity model is presented to analyze the
deformation of microspheres under a controllable internal
pressure. Thin-wall model and thick-wall models are investigated and it was found that the thin-wall model is not
accurate when the thickness ratio is greater than 0.1. Simulation results show that the energy density of the expanding microcapsules is on the order of 3J/cm3 for thick microspheres. Two types of encapsulated materials are studied and the constitutive equations are incorporated into the
thick-wall model in order to analyze the performance of
the microcapsule. Major features, such as thickness and
pre-pressures, that re important to system performance are
identified. The hydrocarbon solvents can reduce the unrealistic temperature variations required by ideal gas. One
possible problem for the model is that the assumption of
linearization of elasticity might not be valid at large strain.
Nonlinear elasticity model will be required for accurate system analysis. Also, the physical method to achieve the temperature change of the materials is not addressed. Identifying an appropriate excitation source is crucial when designing the actuation system.
ACKNOWLEDGMENT
This work was supported by grant numbers NAG-103026 and NAG-1-03052. The program managers for this
effort are Dr. John Main (DARPA/DSO) and Dr. Garnett
Horner (NASA). The authors gratefully acknowledge the
support.
8
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Iso-Pentane
0.1
Internal Pressure
0.08
0.06
0.04
0.02
0
0.01
1.15
1.1
0.005
1.05
1
External Pressure
0
(a)
0.95
Deformation
(a)
Iso-Pentane
200
Tempreture (C)
150
100
50
0
-50
0.01
1.15
1.1
0.005
1.05
1
External Pressure
0
(b)
0.95
Deformation
(b)
Iso-Pentane
500
Tempreture (C)
400
300
200
100
0
-100
1
1.15
1.1
0.5
1.05
1
Thickness
0
0.95
Deformation
(c)
(c)
Figure 8. Simulation results for ideal gas for E=30(MPa) and initial
pressure Pi0 =20 (KPa): (a) internal pressure vs. external pressure
Figure 9. Simulation results for iso-pentane for E=30(MPa) and initial pressure Pi0 =20 (KPa): (a) internal pressure vs. external pressure
and deformation at t0 = 0.2; (b) temperature of gas vs. external pressure and deformation at t0 = 0.2; (c) temperature of gas vs. thickness
and deformation at 0 external pressure.
and deformation at t0 = 0.2; (b) temperature of gas vs. external pressure and deformation at t0 = 0.2; (c) temperature of gas vs. thickness
and deformation at zero external pressure.
9
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n-pentane
iso-pentane
neo-pentane
n-hextane
heptane
Figure 10.
Deformation vs. temperature for five materials.
P=0.01E
P=0.02E
P=0.05E
Figure 11. Deformation vs. temperature for different pre-pressure in
the microcapsule for 30 MPa elasticity modulus and initial normalized
thickness 0.1.
10
Temperature
Strain (% )
Quartz Probe
100
-5
80
-10
60
-15
sample
40
-20
20
-25
0
0
Furnace
20
40
60
80
time (min.)
(a) Test setup diagram
Figure 12.
ture.
140
120
0
Temperature (°C)
LVDT
160
%Strain
5
(b) Strain vs. temperature
Experiment test: (a) test setup; (b) strain vs. tempera-
10
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