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Chabouh G, van Elburg B, Versluis M, Segers T, Quilliet C, Coupier G. Buckling of lipidic ultrasound contrast agents under quasi-static load. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220025. [PMID: 36774952 DOI: 10.1098/rsta.2022.0025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 11/10/2022] [Indexed: 06/18/2023]
Abstract
Collapse of lipidic ultrasound contrast agents under high-frequency compressive load has been historically interpreted by the vanishing of surface tension. By contrast, buckling of elastic shells is known to occur when costly compressible stress is released through bending. Through quasi-static compression experiments on lipidic shells, we analyse the buckling events in the framework of classical elastic buckling theory and deduce the mechanical characteristics of these shells. They are then compared with that obtained through acoustic characterization. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.
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Affiliation(s)
- Georges Chabouh
- Université Grenoble Alpes, CNRS, LIPhy, Grenoble 38000, France
| | - Benjamin van Elburg
- Physics of Fluids Group, Technical Medical (TechMed) Center and MESA+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, The Netherlands
| | - Michel Versluis
- Physics of Fluids Group, Technical Medical (TechMed) Center and MESA+ Institute for Nanotechnology, University of Twente, Enschede 7500 AE, The Netherlands
| | - Tim Segers
- BIOS/Lab-on-a-Chip Group, Max Planck Center Twente for Complex Fluid Dynamics, MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands
| | | | - Gwennou Coupier
- Université Grenoble Alpes, CNRS, LIPhy, Grenoble 38000, France
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2
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Alam SB, Soligno G, Yang J, Bustillo KC, Ercius P, Zheng H, Whitelam S, Chan EM. Dynamics of Polymer Nanocapsule Buckling and Collapse Revealed by In Situ Liquid-Phase TEM. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:7168-7178. [PMID: 35621188 DOI: 10.1021/acs.langmuir.2c00432] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Nanocapsules are hollow nanoscale shells that have applications in drug delivery, batteries, self-healing materials, and as model systems for naturally occurring shell geometries. In many applications, nanocapsules are designed to release their cargo as they buckle and collapse, but the details of this transient buckling process have not been directly observed. Here, we use in situ liquid-phase transmission electron microscopy to record the electron-irradiation-induced buckling in spherical 60-187 nm polymer capsules with ∼3.5 nm walls. We observe in real time the release of aqueous cargo from these nanocapsules and their buckling into morphologies with single or multiple indentations. The in situ buckling of nanoscale capsules is compared to ex situ measurements of collapsed and micrometer-sized capsules and to Monte Carlo (MC) simulations. The shape and dynamics of the collapsing nanocapsules are consistent with MC simulations, which reveal that the excessive wrinkling of nanocapsules with ultrathin walls results from their large Föppl-von Kármán numbers around 105. Our experiments suggest design rules for nanocapsules with the desired buckling response based on parameters such as capsule radius, wall thickness, and collapse rate.
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Affiliation(s)
- Sardar B Alam
- The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Giuseppe Soligno
- The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Debye Institute for Nanomaterials Science, Utrecht University, Utrecht 3584 CC, The Netherlands
| | - Jiwoong Yang
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Karen C Bustillo
- The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Peter Ercius
- The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Haimei Zheng
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720, United States
| | - Stephen Whitelam
- The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Emory M Chan
- The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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3
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Fierling J, John A, Delorme B, Torzynski A, Blanchard GB, Lye CM, Popkova A, Malandain G, Sanson B, Étienne J, Marmottant P, Quilliet C, Rauzi M. Embryo-scale epithelial buckling forms a propagating furrow that initiates gastrulation. Nat Commun 2022; 13:3348. [PMID: 35688832 PMCID: PMC9187723 DOI: 10.1038/s41467-022-30493-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2021] [Accepted: 05/04/2022] [Indexed: 11/26/2022] Open
Abstract
Cell apical constriction driven by actomyosin contraction forces is a conserved mechanism during tissue folding in embryo development. While much is now understood of the molecular mechanism responsible for apical constriction and of the tissue-scale integration of the ensuing in-plane deformations, it is still not clear if apical actomyosin contraction forces are necessary or sufficient per se to drive tissue folding. To tackle this question, we use the Drosophila embryo model system that forms a furrow on the ventral side, initiating mesoderm internalization. Past computational models support the idea that cell apical contraction forces may not be sufficient and that active or passive cell apico-basal forces may be necessary to drive cell wedging leading to tissue furrowing. By using 3D computational modelling and in toto embryo image analysis and manipulation, we now challenge this idea and show that embryo-scale force balance at the tissue surface, rather than cell-autonomous shape changes, is necessary and sufficient to drive a buckling of the epithelial surface forming a furrow which propagates and initiates embryo gastrulation. Drosophila mesoderm invagination begins with the formation of a furrow. Here they show that a long-range mechanism, powered by actomyosin contraction between the embryo polar caps, works like a ‘cheese-cutter wire’ indenting the tissue surface and folding it into a propagating furrow.
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Affiliation(s)
| | - Alphy John
- Université Côte d'Azur, CNRS, Inserm, iBV, Nice, France
| | | | | | - Guy B Blanchard
- Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge, Great-Britain, England
| | - Claire M Lye
- Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge, Great-Britain, England
| | - Anna Popkova
- Université Côte d'Azur, CNRS, Inserm, iBV, Nice, France
| | | | - Bénédicte Sanson
- Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge, Great-Britain, England
| | | | | | | | - Matteo Rauzi
- Université Côte d'Azur, CNRS, Inserm, iBV, Nice, France.
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4
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Mokbel M, Djellouli A, Quilliet C, Aland S, Coupier G. Post-buckling dynamics of spherical shells. Proc Math Phys Eng Sci 2021. [DOI: 10.1098/rspa.2021.0378] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We explore the intrinsic dynamics of spherical shells immersed in a fluid in the vicinity of their buckled state, through experiments and three-dimensional axisymmetric simulations. The results are supported by a theoretical model that accurately describes the buckled shell as a two-variable-only oscillator. We quantify the effective ‘softening’ of shells above the buckling threshold, as observed in recent experiments on interactions between encapsulated microbubbles and acoustic waves. The main dissipation mechanism in the neighbouring fluid is also evidenced.
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Affiliation(s)
- Marcel Mokbel
- University of Applied Sciences (HTW) Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany
- Technische Universität Bergakademie Freiberg, Akademiestrasse,609599 Freiberg, Germany
| | - Adel Djellouli
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
- School of Engineering and Applied Sciences Cambridge, Harvard University, Cambridge, MA 02138, USA
| | | | - Sebastian Aland
- University of Applied Sciences (HTW) Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany
- Technische Universität Bergakademie Freiberg, Akademiestrasse,609599 Freiberg, Germany
| | - Gwennou Coupier
- Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
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5
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Chemically controlled pattern formation in self-oscillating elastic shells. Proc Natl Acad Sci U S A 2021; 118:2025717118. [PMID: 33649242 DOI: 10.1073/pnas.2025717118] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
Patterns and morphology develop in living systems such as embryos in response to chemical signals. To understand and exploit the interplay of chemical reactions with mechanical transformations, chemomechanical polymer systems have been synthesized by attaching chemicals into hydrogels. In this work, we design autonomous responsive elastic shells that undergo morphological changes induced by chemical reactions. We couple the local mechanical response of the gel with the chemical processes on the shell. This causes swelling and deswelling of the gel, generating diverse morphological changes, including periodic oscillations. We further introduce a mechanical instability and observe buckling-unbuckling dynamics with a response time delay. Moreover, we investigate the mechanical feedback on the chemical reaction and demonstrate the dynamic patterns triggered by an initial deformation. We show the chemical characteristics that account for the shell morphology and discuss the future designs for autonomous responsive materials.
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6
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Chabouh G, Dollet B, Quilliet C, Coupier G. Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy. THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA 2021; 149:1240. [PMID: 33639825 DOI: 10.1121/10.0003500] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 01/21/2021] [Indexed: 06/12/2023]
Abstract
We introduce a model that describes spherical oscillations of encapsulated microbubbles in an unbounded surrounding fluid. A Rayleigh-Plesset-like equation is derived by coupling the Navier-Stokes equation that describes fluid dynamics with the Navier equation that describes solid dynamics via the internal/external boundary conditions. While previous models were restricted to incompressible isotropic shells, the solid shell is modeled here as a compressible viscoelastic isotropic material and then generalized to an anisotropic material. The exact value of the resonance frequency is calculated analytically, and the damping constant is computed in the approximation of weak damping. A correction of the widely used Church model for incompressible shells is evidenced, and the effects of shell compressibility and anisotropy are discussed.
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Affiliation(s)
- Georges Chabouh
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
| | - Benjamin Dollet
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
| | | | - Gwennou Coupier
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
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7
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Finn JR, Galvin JE, Hornbostel K. CFD investigation of CO2 absorption/desorption by a fluidized bed of micro-encapsulated solvents. CHEMICAL ENGINEERING SCIENCE: X 2020. [DOI: 10.1016/j.cesx.2019.100050] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022] Open
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8
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Finn JR, Galvin JE, Panday R, Ashfaq H. Deformation and water loss from solvent filled microcapsules under compressive loads. AIChE J 2020. [DOI: 10.1002/aic.16905] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Justin R. Finn
- National Energy Technology Laboratory Albany Oregon
- AECOM, Inc., National Energy Technology Laboratory Albany Oregon
| | | | - Rupen Panday
- National Energy Technology Laboratory Albany Oregon
- REM Engineering Services PLLC, National Energy Technology Laboratory Morgantown West Virginia
| | - Huda Ashfaq
- National Energy Technology Laboratory Albany Oregon
- ORISE Oak Ridge Tennessee
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9
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Coupier G, Djellouli A, Quilliet C. Let's deflate that beach ball. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:129. [PMID: 31571019 DOI: 10.1140/epje/i2019-11900-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Accepted: 08/27/2019] [Indexed: 06/10/2023]
Abstract
We investigate the relationship between pre-buckling and post-buckling states as a function of shell properties, within the deflation process of shells of an isotropic material. With an original and low-cost set-up that allows to measure simultaneously volume and pressure, elastic shells whose relative thicknesses span on a broad range are deflated until they buckle. We characterize the post-buckling state in the pressure-volume diagram, but also the relaxation toward this state. The main result is that before as well as after the buckling, the shells behave in a way compatible with predictions generated through thin shell assumption, and that this consistency persists for shells where the thickness reaches up to 0.3 the shell's midsurface radius.
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Affiliation(s)
| | - Adel Djellouli
- Univ. Grenoble Alpes, CNRS, LIPhy, 38000, Grenoble, France
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10
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Lei C, Li Q, Yang L, Deng F, Li J, Ye Z, Wang Y, Zhang Z. Controlled reversible buckling of polydopamine spherical microcapsules: revealing the hidden rich phenomena of post-buckling of spherical polymeric shells. SOFT MATTER 2019; 15:6504-6517. [PMID: 31343046 DOI: 10.1039/c9sm00705a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Under external pressure compression, various kinds of artificial microcapsules can undergo buckling induced deformation and catastrophic rupturing failure, which needs to be understood for their diverse practical applications. For this, many theories and numerical simulations have recently emerged, leading to some intriguing but often debatable predictions and scaling laws. However, experimental testing of these predictions is very limited, due to challenges in realizing prescribed buckling pathways and in situ monitoring of the buckling procedure. Herein, we report the buckling behaviors of well-defined spherical polydopamine (PDA) capsules with tunable sizes and homogeneous nanoscale shells. Simple but controlled solvent evaporation was implemented inside a home-made optical chamber to induce buckling of PDA capsules by following a prescribed pathway toward targeted shapes that are only dictated by the inherent material properties of the capsules. In addition, the buckling speed was slowed down to the timescale of minutes, which can prevent buckling from being trapped at some metastable intermediate states as well as facilitating in situ optical monitoring of the whole buckling procedure in slow motion. In this way, several classic buckling behaviors were clearly observed, including the sudden appearance of spinodal-like dimples above critical pressures, transition of the indentation rim from the axisymmetric to polygonal shape, and evolution of multi-indented buckling into single indented buckling following Ostwald ripening. These observations are qualitatively comparable with recent predictions from numerical results. Furthermore, some novel buckling phenomena have been reported for the first time, which might stimulate further theories and numerical simulations.
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Affiliation(s)
- Caifen Lei
- Key Laboratory of Functional Polymer Materials of Ministry of Education, Institute of Polymer Chemistry, College of Chemistry, Nankai University, 300071 Tianjin, China.
| | - Qiang Li
- Key Laboratory of Functional Polymer Materials of Ministry of Education, Institute of Polymer Chemistry, College of Chemistry, Nankai University, 300071 Tianjin, China.
| | - Lu Yang
- School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China
| | - Fei Deng
- Key Laboratory of Functional Polymer Materials of Ministry of Education, Institute of Polymer Chemistry, College of Chemistry, Nankai University, 300071 Tianjin, China.
| | - Jianyao Li
- School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China
| | - Zihan Ye
- Key Laboratory of Functional Polymer Materials of Ministry of Education, Institute of Polymer Chemistry, College of Chemistry, Nankai University, 300071 Tianjin, China.
| | - Ying Wang
- Key Laboratory of Functional Polymer Materials of Ministry of Education, Institute of Polymer Chemistry, College of Chemistry, Nankai University, 300071 Tianjin, China.
| | - Zhenkun Zhang
- Key Laboratory of Functional Polymer Materials of Ministry of Education, Institute of Polymer Chemistry, College of Chemistry, Nankai University, 300071 Tianjin, China.
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11
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Munglani G, Wittel FK, Vetter R, Bianchi F, Herrmann HJ. Collapse of Orthotropic Spherical Shells. PHYSICAL REVIEW LETTERS 2019; 123:058002. [PMID: 31491319 DOI: 10.1103/physrevlett.123.058002] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2019] [Revised: 06/24/2019] [Indexed: 06/10/2023]
Abstract
We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature's collapsed shells could be understood from the viewpoint of material orthotropy.
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Affiliation(s)
- Gautam Munglani
- Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, Stefano-Franscini-Platz 3, CH-8093 Zürich, Switzerland
- Institute of Plant and Microbial Biology, University of Zürich, Zollikerstrasse 107, CH-8008 Zürich, Switzerland
| | - Falk K Wittel
- Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, Stefano-Franscini-Platz 3, CH-8093 Zürich, Switzerland
| | - Roman Vetter
- Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, Stefano-Franscini-Platz 3, CH-8093 Zürich, Switzerland
| | - Filippo Bianchi
- Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, Stefano-Franscini-Platz 3, CH-8093 Zürich, Switzerland
| | - Hans J Herrmann
- Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, Stefano-Franscini-Platz 3, CH-8093 Zürich, Switzerland
- Physique et Mécanique des Milieux Hétérogènes (PMMH), ESPCI, 7 quai St. Bernard, 75005 Paris, France
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12
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Baumgarten L, Kierfeld J. Shallow shell theory of the buckling energy barrier: From the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure. Phys Rev E 2019; 99:022803. [PMID: 30934269 DOI: 10.1103/physreve.99.022803] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2018] [Indexed: 06/09/2023]
Abstract
We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure p to an additional point force. For a pressure p below the classical critical buckling pressure p_{c}, indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome. The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state. Starting from nonlinear shallow shell theory, we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques. We find a clear crossover between two regimes: For p/p_{c}≪1 the postbuckling barrier state is a mirror-inverted Pogorelov dimple, and for (1-p/p_{c})≪1 the barrier state is a shallow dimple with indentations smaller than shell thickness and exhibits extended oscillations, which are well described by linear response. We find systematic expansions of the nonlinear shallow shell equations about the Pogorelov mirror-inverted dimple for p/p_{c}≪1 and the linear response state for (1-p/p_{c})≪1, which enable us to derive asymptotic analytical results for the energy barrier landscape in both regimes. Upon approaching the buckling bifurcation at p_{c} from below, we find a softening of an ideal spherical shell. The stiffness for the linear response to point forces vanishes ∝(1-p/p_{c})^{1/2}; the buckling energy barrier vanishes ∝(1-p/p_{c})^{3/2}; and the shell indentation in the barrier state vanishes ∝(1-p/p_{c})^{1/2}. This makes shells sensitive to imperfections which can strongly reduce p_{c} in an avoided buckling bifurcation. We find the same softening scaling in the vicinity of the reduced critical buckling pressure also in the presence of imperfections. We can also show that the effect of axisymmetric imperfections on the buckling instability is identical to the effect of a point force that is preindenting the shell. In the Pogorelov limit, the energy barrier maximum diverges ∝(p/p_{c})^{-3} and the corresponding indentation diverges ∝(p/p_{c})^{-2}. Numerical prefactors for proportionalities both in the softening and the Pogorelov regime are calculated analytically. This also enables us to obtain results for the critical unbuckling pressure and the Maxwell pressure.
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Affiliation(s)
- Lorenz Baumgarten
- Institute for Theoretical Physics, University of Bremen, 28359 Bremen, Germany
- Physics Department, TU Dortmund University, 44221 Dortmund, Germany
| | - Jan Kierfeld
- Physics Department, TU Dortmund University, 44221 Dortmund, Germany
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13
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Baumgarten L, Kierfeld J. Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing. Phys Rev E 2018; 97:052801. [PMID: 29906947 DOI: 10.1103/physreve.97.052801] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2018] [Indexed: 11/07/2022]
Abstract
We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017)2160-330810.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.
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Affiliation(s)
| | - Jan Kierfeld
- Physics Department, TU Dortmund University, 44221 Dortmund, Germany
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14
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Djellouli A, Marmottant P, Djeridi H, Quilliet C, Coupier G. Buckling Instability Causes Inertial Thrust for Spherical Swimmers at All Scales. PHYSICAL REVIEW LETTERS 2017; 119:224501. [PMID: 29286796 DOI: 10.1103/physrevlett.119.224501] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Indexed: 06/07/2023]
Abstract
Microswimmers, and among them aspirant microrobots, generally have to cope with flows where viscous forces are dominant, characterized by a low Reynolds number (Re). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities. Here, we propose a swimming mechanism which uses the buckling instability triggered by pressure waves to propel a spherical, hollow shell. With a macroscopic experimental model, we show that a net displacement is produced at all Re regimes. An optimal displacement caused by nontrivial history effects is reached at intermediate Re. We show that, due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high-frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1 cm/s for a remote-controlled microrobot, a suitable value for biological applications such as drug delivery.
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Affiliation(s)
- Adel Djellouli
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
| | | | - Henda Djeridi
- Université Grenoble Alpes, Grenoble INP, CNRS, LEGI, F-38000 Grenoble, France
| | | | - Gwennou Coupier
- Université Grenoble Alpes, CNRS, LIPhy, F-38000 Grenoble, France
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15
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Abstract
The buckling mechanism in droplets stabilized by solid particles (armored droplets) is tackled at a mesoscopic level using dissipative particle dynamics simulations. We consider one spherical water droplet in a decane solvent coated with nanoparticle monolayers of two different types: Janus (particles whose surface shows two regions with different wetting properties) and homogeneous. The chosen particles yield comparable initial three-phase contact angles, selected to maximize the adsorption energy at the interface. We study the interplay between the evolution of droplet shape, layering of the particles, and their distribution at the interface when the volume of the droplets is reduced. We show that Janus particles affect strongly the shape of the droplet with the formation of a crater-like depression. This evolution is actively controlled by a close-packed particle monolayer at the curved interface. In contrast, homogeneous particles follow passively the volume reduction of the droplet, whose shape does not deviate too much from spherical, even when a nanoparticle monolayer/bilayer transition is detected at the interface. We discuss how these buckled armored droplets might be of relevance in various applications including potential drug delivery systems and biomimetic design of functional surfaces.
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Affiliation(s)
- François Sicard
- Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK.
| | - Alberto Striolo
- Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, UK.
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16
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Hutchinson JW, Thompson JMT. Nonlinear buckling behaviour of spherical shells: barriers and symmetry-breaking dimples. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0154. [PMID: 28373377 DOI: 10.1098/rsta.2016.0154] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/01/2016] [Indexed: 06/07/2023]
Abstract
The nonlinear axisymmetric post-buckling behaviour of perfect, thin, elastic spherical shells subject to external pressure and their asymmetric bifurcations are characterized, providing results for a structure/loading combination with an exceptionally nonlinear buckling response. Immediately after the onset of buckling, the buckling mode localizes into a dimple at the poles. The relations among the pressure, the dimple amplitude and the change in volume of the shell are determined over a large range of pole deflections. These results allow accurate evaluation of criteria such as the Maxwell condition for which the energies in the unbuckled and buckled states are the same and evaluation of the influences of pressure versus volume-controlled loadings. Non-axisymmetric bifurcation from the axisymmetric state, which occurs deep into the post-buckling regime in the form of multi-lobed dimples, is also established and discussed.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
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Affiliation(s)
- John W Hutchinson
- School of Engineering and Applied Sciences, Harvard University, Cambridge 02138, MA, USA
| | - J Michael T Thompson
- Department of Applied Maths and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
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17
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Salmon AR, Parker RM, Groombridge AS, Maestro A, Coulston RJ, Hegemann J, Kierfeld J, Scherman OA, Abell C. Microcapsule Buckling Triggered by Compression-Induced Interfacial Phase Change. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:10987-10994. [PMID: 27700114 DOI: 10.1021/acs.langmuir.6b03011] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
There is an emerging trend toward the fabrication of microcapsules at liquid interfaces. In order to control the parameters of such capsules, the interfacial processes governing their formation must be understood. Here, poly(vinyl alcohol) films are assembled at the interface of water-in-oil microfluidic droplets. The polymer is cross-linked using cucurbit[8]uril ternary supramolecular complexes. It is shown that compression-induced phase change causes the onset of buckling in the interfacial film. On evaporative compression, the interfacial film both increases in density and thickens, until it reaches a critical density and a phase change occurs. We show that this increase in density can be simply related to the film Poisson ratio and area compression. This description captures fundamentals of many compressive interfacial phase changes and can also explain the observation of a fixed thickness-to-radius ratio at buckling, [Formula: see text].
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Affiliation(s)
- Andrew R Salmon
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Richard M Parker
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Alexander S Groombridge
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Armando Maestro
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Roger J Coulston
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jonas Hegemann
- Physics Department, TU Dortmund University , Otto-Hahn-Str 4, Dortmund 44221, Germany
| | - Jan Kierfeld
- Physics Department, TU Dortmund University , Otto-Hahn-Str 4, Dortmund 44221, Germany
| | - Oren A Scherman
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Chris Abell
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
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18
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Quilliet C, Farutin A, Marmottant P. Effect of Gaussian curvature modulus on the shape of deformed hollow spherical objects. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:58. [PMID: 27255647 DOI: 10.1140/epje/i2016-16058-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2016] [Accepted: 04/28/2016] [Indexed: 06/05/2023]
Abstract
A popular description of soft membranes uses the surface curvature energy introduced by Helfrich, which includes a spontaneous curvature parameter. In this paper we show how the Helfrich formula can also be of interest for a wider class of spherical elastic surfaces, namely with shear elasticity, and likely to model other deformable hollow objects. The key point is that when a stress-free state with spherical symmetry exists before subsequent deformation, its straightforwardly determined curvature ("geometrical spontaneous curvature") differs most of the time from the Helfrich spontaneous curvature parameter that should be considered in order to have the model being correctly used. Using the geometrical curvature in a set of independent parameters unveils the role of the Gaussian curvature modulus, which appears to play on the shape of an elastic surface even though this latter is closed, contrary to what happens for surfaces without spontaneous curvature. In appendices, clues are given to apply this alternative and convenient formulation of the elastic surface model to the particular case of thin spherical shells of isotropic material (TSSIMs).
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Affiliation(s)
- C Quilliet
- CNRS, Université Grenoble Alpes, F-38000, Grenoble, France.
| | - A Farutin
- CNRS, Université Grenoble Alpes, F-38000, Grenoble, France
| | - P Marmottant
- CNRS, Université Grenoble Alpes, F-38000, Grenoble, France
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19
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Liu D, Peng X, Wu B, Zheng X, Chuong TT, Li J, Sun S, Stucky GD. Uniform Concave Polystyrene-Carbon Core–Shell Nanospheres by a Swelling Induced Buckling Process. J Am Chem Soc 2015. [DOI: 10.1021/jacs.5b05027] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Deyu Liu
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Xinxing Peng
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
- State
Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative
Innovation Center of Chemistry for Energy Materials and Department
of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Binghui Wu
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
- State
Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative
Innovation Center of Chemistry for Energy Materials and Department
of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Xueyun Zheng
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Tracy T Chuong
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Jialuo Li
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
| | - Shigang Sun
- State
Key Laboratory for Physical Chemistry of Solid Surfaces, Collaborative
Innovation Center of Chemistry for Energy Materials and Department
of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Galen D. Stucky
- Department
of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
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20
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Abstract
We study the buckling of elastic spherical shells under osmotic pressure with the osmolyte concentration of the exterior solution as a control parameter. We compare our results for the bifurcation behavior with results for buckling under mechanical pressure control, that is, with an empty capsule interior. We find striking differences for the buckling states between osmotic and mechanical buckling. Mechanical pressure control always leads to fully collapsed states with opposite sides in contact, whereas uncollapsed states with a single finite dimple are generic for osmotic pressure control. For sufficiently large interior osmolyte concentrations, osmotic pressure control is qualitatively similar to buckling under volume control with the volume prescribed by the osmolyte concentrations inside and outside the shell. We present a quantitative theory which also captures the influence of shell elasticity on the relationship between osmotic pressure and volume. These findings are relevant for the control of buckled shapes in applications. We show how the osmolyte concentration can be used to control the volume of buckled shells. An accurate analytical formula is derived for the relationship between the osmotic pressure, the elastic moduli and the volume of buckled capsules. This also allows use of elastic capsules as osmotic pressure sensors or deduction of elastic properties and the internal osmolyte concentration from shape changes in response to osmotic pressure changes. We apply our findings to published experimental data on polyelectrolyte capsules.
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Affiliation(s)
- Sebastian Knoche
- TU Dortmund University, Department of Physics, 44221 Dortmund, Germany.
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21
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Knoche S, Kierfeld J. The secondary buckling transition: wrinkling of buckled spherical shells. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:18. [PMID: 25039007 DOI: 10.1140/epje/i2014-14062-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2014] [Revised: 05/13/2014] [Accepted: 06/17/2014] [Indexed: 06/03/2023]
Abstract
We theoretically explain the complete sequence of shapes of deflated spherical shells. Decreasing the volume, the shell remains spherical initially, then undergoes the classical buckling instability, where an axisymmetric dimple appears, and, finally, loses its axisymmetry by wrinkles developing in the vicinity of the dimple edge in a secondary buckling transition. We describe the first axisymmetric buckling transition by numerical integration of the complete set of shape equations and an approximate analytic model due to Pogorelov. In the buckled shape, both approaches exhibit a locally compressive hoop stress in a region where experiments and simulations show the development of polygonal wrinkles, along the dimple edge. In a simplified model based on the stability equations of shallow shells, a critical value for the compressive hoop stress is derived, for which the compressed circumferential fibres will buckle out of their circular shape in order to release the compression. By applying this wrinkling criterion to the solutions of the axisymmetric models, we can calculate the critical volume for the secondary buckling transition. Using the Pogorelov approach, we also obtain an analytical expression for the critical volume at the secondary buckling transition: The critical volume difference scales linearly with the bending stiffness, whereas the critical volume reduction at the classical axisymmetric buckling transition scales with the square root of the bending stiffness. These results are confirmed by another stability analysis in the framework of Donnel, Mushtari and Vlasov (DMV) shell theory, and by numerical simulations available in the literature.
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Affiliation(s)
- Sebastian Knoche
- Department of Physics, Technische Universität Dortmund, 44221, Dortmund, Germany,
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22
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Neubauer MP, Poehlmann M, Fery A. Microcapsule mechanics: from stability to function. Adv Colloid Interface Sci 2014; 207:65-80. [PMID: 24345731 DOI: 10.1016/j.cis.2013.11.016] [Citation(s) in RCA: 100] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2013] [Revised: 11/18/2013] [Accepted: 11/21/2013] [Indexed: 01/22/2023]
Abstract
Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.
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23
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Pocheau A, Roman B. Reversibility of crumpling on compressed thin sheets: reversibility of crumpling. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:28. [PMID: 24771237 DOI: 10.1140/epje/i2014-14028-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2013] [Revised: 02/25/2014] [Accepted: 03/24/2014] [Indexed: 06/03/2023]
Abstract
Compressing thin sheets usually yields the formation of singularities which focus curvature and stretching on points or lines. In particular, following the common experience of crumpled paper where a paper sheet is crushed in a paper ball, one might guess that elastic singularities should be the rule beyond some compression level. In contrast, we show here that, somewhat surprisingly, compressing a sheet between cylinders make singularities spontaneously disappear at large compression. This "stress defocusing" phenomenon is qualitatively explained from scale-invariance and further linked to a criterion based on a balance between stretching and curvature energies on defocused states. This criterion is made quantitative using the scalings relevant to sheet elasticity and compared to experiment. These results are synthesized in a phase diagram completed with plastic transitions and buckling saturation. They provide a renewed vision of elastic singularities as a thermodynamic condensed phase where stress is focused, in competition with a regular diluted phase where stress is defocused. The physical differences between phases is emphasized by determining experimentally the mechanical response when stress is focused or defocused and by recovering the corresponding scaling laws. In this phase diagram, different compression routes may be followed by constraining differently the two principal curvatures of a sheet. As evidenced here, this may provide an efficient way of compressing a sheet that avoids the occurrence of plastic damages by inducing a spontaneous regularization of geometry and stress.
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Affiliation(s)
- Alain Pocheau
- Centrale Marseille, IRPHE UMR 7342, Aix Marseille Université, CNRS, 13384, Marseille, France,
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