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. 1 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 2 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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) Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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. 4 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 6 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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. REFERENCES [1] Craig D. Near. Piezoelectric actuator technology. SPIE, 2717:246—258, 1996. [2] M. Bexell, A. L. Tiensuu, J. A. Schweitz, J. Soderkvist, and S. Johansson. Characterization of an inchworm prototype motor. Sensors and Actuators, A(43):322— 329, 1994. [3] Lisa Mauck and C. S. Lynch. Piezoelectric hydraulic pump. SPIE, 3668:844—852, 1999. [4] T. A. Sammarco and M. A. Burns. Thermocapillary pumping of discrete drops in microfabricated analysis devices. AI ChE Journal, 45(2):350—366, 1999. [5] M. Sata H. Togo and F. Shimokawa. Multi-element thermocapillary optical switch and sub-nanometer oil injection for its fabrication. In Proceedings of the IEEE MEMS’99, pages 418—423, 1999. [6] J. Lee and C. J. Kin. Surface tension driven microactuation based on continuous electrowetting (cew). Journal Microelectromechanical System, 9(2):171—180, 2000. [7] Scott T Brittain David C Duﬀy, Olivier J A Schueller and George M Whitesides. Rapid prototyping of microfluidic switches in poly(dimethyl siloxane) and their actuation by electro-osmotic flow. Micromechanics and Microengineering, 9:211—217, 1999. [8] R. B. Fair M. G. Pollack and A. D. Shenderov. Electrowetting-based on microactuation of liquid droplets for microfluidic applications. Applied Physics Letter, 77:1725, 2000. [9] J. A. M. Sondag-Huethorst and L. G. J. Fokkink. Electrical double layers on thiol-modified polycrystalline gold electrodes. Micromechanics and Microengineering, 367:49—57, 1994. [10] S. Timoshenko J. Goodier. Theory of Elasticity. McGraw-Hill, Inc., New York, 1970. [11] W. Slaughter. The Linearized Theory of Elasticity. Birkhauser, New York, 2002. [12] T. Sherwood R. Reid, J. Prausnitz. The properties of Gases and Liquids. McGraw-Hill, Inc., New York, 1977. 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 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright c 2003 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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