1
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Cochard T, Svetlizky I, Albertini G, Viesca RC, Rubinstein SM, Spaepen F, Yuan C, Denolle M, Song YQ, Xiao L, Weitz DA. Propagation of extended fractures by local nucleation and rapid transverse expansion of crack-front distortion. Nat Phys 2024; 20:660-665. [PMID: 38638457 PMCID: PMC11021187 DOI: 10.1038/s41567-023-02365-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 11/30/2023] [Indexed: 04/20/2024]
Abstract
Fractures are ubiquitous and can lead to the catastrophic material failure of materials. Although fracturing in a two-dimensional plane is well understood, all fractures are extended in and propagate through three-dimensional space. Moreover, their behaviour is complex. Here we show that the forward propagation of a fracture front occurs through an initial rupture, nucleated at some localized position, followed by a very rapid transverse expansion at velocities as high as the Rayleigh-wave speed. We study fracturing in a circular geometry that achieves an uninterrupted extended fracture front and use a fluid to control the loading conditions that determine the amplitude of the forward jump. We find that this amplitude correlates with the transverse velocity. Dynamic rupture simulations capture the observations for only a high transverse velocity. These results highlight the importance of transverse dynamics in the forward propagation of an extended fracture.
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Affiliation(s)
- T. Cochard
- National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing, China
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
| | - I. Svetlizky
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
| | - G. Albertini
- Faculty of Engineering, University of Nottingham, Nottingham, UK
| | - R. C. Viesca
- Department of Civil and Environmental Engineering, Tufts University, Medford, MA USA
| | - S. M. Rubinstein
- The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, Israel
| | - F. Spaepen
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
| | - C. Yuan
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA USA
| | - M. Denolle
- Earth and Space Sciences, University of Washington, Seattle, WA USA
| | - Y-Q. Song
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA USA
| | - L. Xiao
- National Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing, China
| | - D. A. Weitz
- School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA USA
- Department of Physics, Harvard University, Cambridge, MA USA
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA USA
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2
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Abstract
We introduce dynamic speckle holography, a new technique that combines imaging and scattering to measure three-dimensional maps of displacements as small as ten nanometers over several centimeters, greatly extending the capabilities of traditional imaging systems. We attain this sensitivity by imaging speckle patterns of light collected at three scattering angles and measuring the decay in the temporal correlation due to local motion. We use dynamic speckle holography to measure the strain field of a colloidal gel undergoing fracture and establish the surprising role of internal tension in driving the fracture.
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Affiliation(s)
- S Aime
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Molecular, Macromolecular Chemistry, and Materials, ESPCI Paris, CNRS, PSL University, 10 Rue Vauquelin, 75005 Paris, France
| | - M Sabato
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA
| | - L Xiao
- State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China
| | - D A Weitz
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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3
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Tiribocchi A, Montessori A, Lauricella M, Bonaccorso F, Succi S, Aime S, Milani M, Weitz DA. The vortex-driven dynamics of droplets within droplets. Nat Commun 2021; 12:82. [PMID: 33398018 PMCID: PMC7782531 DOI: 10.1038/s41467-020-20364-0] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 11/20/2020] [Indexed: 01/29/2023] Open
Abstract
Understanding the fluid-structure interaction is crucial for an optimal design and manufacturing of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in bio-technology, such as drug-delivery, tissue engineering and regenerative medicine. Here, we study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equilibrium states (NES), whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. The observed dynamic regimes range from long-lived NES at low core-area fraction, characterised by a planetary-like motion of the internal drops, to short-lived ones at high core-area fraction, in which a pre-chaotic motion results from multi-body collisions of inner drops, as combined with self-consistent hydrodynamic interactions. The onset of pre-chaotic behavior is marked by transitions of the cores from one vortex to another, a process that we interpret as manifestations of the system to maximize its entropy by filling voids, as they arise dynamically within the capsule.
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Affiliation(s)
- A. Tiribocchi
- grid.25786.3e0000 0004 1764 2907Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, Roma, 00161 Italy ,grid.5326.20000 0001 1940 4177Istituto per le Applicazioni del Calcolo CNR, via dei Taurini 19, Rome, 00185 Italy
| | - A. Montessori
- grid.5326.20000 0001 1940 4177Istituto per le Applicazioni del Calcolo CNR, via dei Taurini 19, Rome, 00185 Italy
| | - M. Lauricella
- grid.5326.20000 0001 1940 4177Istituto per le Applicazioni del Calcolo CNR, via dei Taurini 19, Rome, 00185 Italy
| | - F. Bonaccorso
- grid.25786.3e0000 0004 1764 2907Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, Roma, 00161 Italy ,grid.5326.20000 0001 1940 4177Istituto per le Applicazioni del Calcolo CNR, via dei Taurini 19, Rome, 00185 Italy
| | - S. Succi
- grid.25786.3e0000 0004 1764 2907Center for Life Nano Science@La Sapienza, Istituto Italiano di Tecnologia, Roma, 00161 Italy ,grid.5326.20000 0001 1940 4177Istituto per le Applicazioni del Calcolo CNR, via dei Taurini 19, Rome, 00185 Italy ,grid.38142.3c000000041936754XInstitute for Applied Computational Science, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA
| | - S. Aime
- grid.38142.3c000000041936754XInstitute for Applied Computational Science, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA ,grid.15736.360000 0001 1882 0021Matiére Molle et Chimie, Ecole Supérieure de Physique et Chimie Industrielles, Paris, 75005 France
| | - M. Milani
- grid.4708.b0000 0004 1757 2822Universitá degli Studi di Milano, via Celoria 16, Milano, 20133 Italy
| | - D. A. Weitz
- grid.38142.3c000000041936754XInstitute for Applied Computational Science, John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA ,grid.38142.3c000000041936754XDepartment of Physics, Harvard University, Cambridge, MA 02138 USA
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4
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Abstract
We present local direct imaging of the progressive adsorption of colloidal particles inside a 3D model porous medium. By varying the interparticle electrostatic interactions, we observe a large range of particle deposition regimes, from a single layer of particles at the surface of the medium to multiple layers and eventually clogging of the system. We derive the complete deposition dynamics and show that colloid accumulation is a self-limited mechanism towards a deposited fraction associated with a balance between the particle interactions and the imposed flow rate. These trends are explained and predicted using a simple probability model considering the particle adsorption energy and the variation of the drag energy with evolving porosity. This constitutes a direct validation of speculated particle transport mechanisms, and a further understanding of accumulation mechanisms.
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Affiliation(s)
- G Gerber
- Université Paris-Est, Laboratoire Navier (ENPC-IFSTTAR-CNRS), Champs-sur-Marne 77420, France
- Experimental Soft Condensed Matter Group, School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Bensouda
- Université Paris-Est, Laboratoire Navier (ENPC-IFSTTAR-CNRS), Champs-sur-Marne 77420, France
| | - D A Weitz
- Experimental Soft Condensed Matter Group, School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - P Coussot
- Université Paris-Est, Laboratoire Navier (ENPC-IFSTTAR-CNRS), Champs-sur-Marne 77420, France
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5
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Mutafopulos K, Spink P, Lofstrom CD, Lu PJ, Lu H, Sharpe JC, Franke T, Weitz DA. Traveling surface acoustic wave (TSAW) microfluidic fluorescence activated cell sorter (μFACS). Lab Chip 2019; 19:2435-2443. [PMID: 31192328 DOI: 10.1039/c9lc00163h] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We report a microfluidic fluorescence activated cell-sorting (μFACS) device that employs traveling surface acoustic waves (TSAW) to sort cells at rates comparable to conventional jet-in-air FACS machines, with high purity and viability. The device combines inertial flow focusing and sheath flow to align and evenly space cells, improving the sorting accuracy and screening rate. We sort with an interdigital transducer (IDT) whose tapered geometry allows precise positioning of the TSAW for optimal cell sorting. We sort three different cell lines at several kHz, at cell velocities exceeding one meter per second, while maintaining both sorting purity and cell viability at around 90% simultaneously.
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Affiliation(s)
- K Mutafopulos
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
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6
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Ziblat R, Weaver JC, Arriaga LR, Chong S, Weitz DA. Determining the lipid specificity of insoluble protein transmembrane domains. Lab Chip 2018; 18:3561-3569. [PMID: 30406786 DOI: 10.1039/c8lc00311d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
While the specificity of protein-lipid interactions is a key feature in the function of biological membranes, studying the specifics of these interactions is challenging because most membrane proteins are insoluble in water due to the hydrophobic nature of their transmembrane domains (TMDs). Here, we introduce a method that overcomes this solubility limitation and identifies the affinity profile of protein TMDs to specific lipid formulations. Using 5 human TMDs as a sample group, our results demonstrate that TMDs are highly selective and that these specific lipid-TMD interactions can involve either a single lipid, or the combination of multiple lipid species.
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Affiliation(s)
- R Ziblat
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
| | - J C Weaver
- Wyss Institute for Biologically Inspired Engineering, Harvard University, Cambridge, MA 02138, USA
| | - L R Arriaga
- Department of Physical Chemistry, Universidad Complutense, Madrid, 28040, Spain
| | - S Chong
- New England Biolabs, Inc., 240 County Road, Ipswich, MA 01938, USA
| | - D A Weitz
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA. and Department of Physics, Harvard University, Cambridge, MA02138, USA
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7
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Ung WL, Mutafopulos K, Spink P, Rambach RW, Franke T, Weitz DA. Enhanced surface acoustic wave cell sorting by 3D microfluidic-chip design. Lab Chip 2017; 17:4059-4069. [PMID: 28994439 DOI: 10.1039/c7lc00715a] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
We demonstrate an acoustic wave driven microfluidic cell sorter that combines advantages of multilayer device fabrication with planar surface acoustic wave excitation. We harness the strong vertical component of the refracted acoustic wave to enhance cell actuation by using an asymmetric flow field to increase cell deflection. Precise control of the 3-dimensional flow is realized by topographical structures implemented on the top of the microchannel. We experimentally quantify the effect of the structure dimensions and acoustic parameter. The design attains cell sorting rates and purities approaching those of state of the art fluorescence-activated cell sorters with all the advantages of microfluidic cell sorting.
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Affiliation(s)
- W L Ung
- School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
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8
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Chaudhuri M, Allahyarov E, Löwen H, Egelhaaf SU, Weitz DA. Triple Junction at the Triple Point Resolved on the Individual Particle Level. Phys Rev Lett 2017; 119:128001. [PMID: 29341657 DOI: 10.1103/physrevlett.119.128001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2017] [Indexed: 06/07/2023]
Abstract
At the triple point of a repulsive screened Coulomb system, a fcc crystal, a bcc crystal, and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single-particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.
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Affiliation(s)
- M Chaudhuri
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University, 40225 Düsseldorf, Germany
| | - E Allahyarov
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University, 40225 Düsseldorf, Germany
- Theoretical Department, Joint Institute for High Temperatures, Russian Academy of Sciences (IVTAN), Moscow 125412, Russia
| | - H Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich Heine University, 40225 Düsseldorf, Germany
| | - S U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, 40225 Düsseldorf, Germany
| | - D A Weitz
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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9
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Amstad E, Weitz DA. Reply to the 'Comment on "Robust scalable high throughput production of monodisperse drops"' by M. Nakajima, Lab Chip, 2017, 17, DOI: 10.1039/C7LC00181A. Lab Chip 2017; 17:2332-2333. [PMID: 28603796 DOI: 10.1039/c7lc00494j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
This reply to the comment by Nakajima on our article that appeared in Lab on a Chip (E. Amstad, M. Chemama, M. Eggersdorfer, L. R. Arriaga, M. Brenner and D. A. Weitz, Lab Chip, 2016, 16, 4163-4172) highlights the differences between the microchannel step emulsification devices developed by the Nakajima group and the millipede device reported by us in Lab on a Chip.
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Affiliation(s)
- E Amstad
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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10
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Haliburton JR, Kim SC, Clark IC, Sperling RA, Weitz DA, Abate AR. Efficient extraction of oil from droplet microfluidic emulsions. Biomicrofluidics 2017; 11:034111. [PMID: 28611871 PMCID: PMC5438281 DOI: 10.1063/1.4984035] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2017] [Accepted: 05/10/2017] [Indexed: 06/07/2023]
Abstract
Droplet microfluidic techniques can perform large numbers of single molecule and cell reactions but often require controlled, periodic flow to merge, split, and sort droplets. Here, we describe a simple method to convert aperiodic flows into periodic ones. Using an oil extraction module, we efficiently remove oil from emulsions to readjust the droplet volume fraction, velocity, and packing, producing periodic flows. The extractor acts as a universal adaptor to connect microfluidic modules that do not operate under identical flow conditions, such as droplet generators, incubators, and merger devices.
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Affiliation(s)
| | - S C Kim
- Department of Bioengineering and Therapeutic Sciences, California Institute for Quantitative Biosciences (QB3), University of California, San Francisco, California 94158, USA
| | - I C Clark
- Department of Bioengineering and Therapeutic Sciences, California Institute for Quantitative Biosciences (QB3), University of California, San Francisco, California 94158, USA
| | - R A Sperling
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D A Weitz
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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11
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Eggersdorfer ML, Zheng W, Nawar S, Mercandetti C, Ofner A, Leibacher I, Koehler S, Weitz DA. Tandem emulsification for high-throughput production of double emulsions. Lab Chip 2017; 17:936-942. [PMID: 28197593 DOI: 10.1039/c6lc01553k] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Core-shell double emulsions produced using microfluidic methods with controlled structural parameters exhibit great potential in a wide range of applications, but the low production rate of microfluidic methods hinders the exploitation of the capabilities of microfluidics to produce double emulsions with well-defined features. A major obstacle towards the scaled-up production of core-shell double emulsions is the difficulty of achieving robust spatially controlled wettability in integrated microfluidic devices. Here, we use tandem emulsification, a two-step process with microfluidic devices, to scale up the production. With this method, single emulsions are generated in a first device and are re-injected directly into a second device to form uniform double emulsions. We demonstrate the application of tandem emulsification for scalable core-shell emulsion production with both integrated flow focusing and millipede devices and obtain emulsions of which over 90% are single-core monodisperse double emulsion drops. With both mechanisms, the shell thickness can be controlled, so that shells as thin as 3 μm are obtained for emulsions 50 μm in radius.
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Affiliation(s)
- M L Eggersdorfer
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - W Zheng
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
| | - S Nawar
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - C Mercandetti
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - A Ofner
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - I Leibacher
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - S Koehler
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - D A Weitz
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA. and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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12
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Amstad E, Chemama M, Eggersdorfer M, Arriaga LR, Brenner MP, Weitz DA. Robust scalable high throughput production of monodisperse drops. Lab Chip 2016; 16:4163-4172. [PMID: 27714028 DOI: 10.1039/c6lc01075j] [Citation(s) in RCA: 124] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Monodisperse drops with diameters between 20 μm and 200 μm can be used to produce particles or capsules for many applications such as for cosmetics, food, and biotechnology. Drops composed of low viscosity fluids can be conveniently made using microfluidic devices. However, the throughput of microfluidic devices is limited and scale-up, achieved by increasing the number of devices run in parallel, can compromise the narrow drop-size distribution. In this paper, we present a microfluidic device, the millipede device, which forms drops through a static instability such that the fluid volume that is pinched off is the same every time a drop forms. As a result, the drops are highly monodisperse because their size is solely determined by the device geometry. This makes the operation of the device very robust. Therefore, the device can be scaled to a large number of nozzles operating simultaneously on the same chip; we demonstrate the operation of more than 500 nozzles on a single chip that produces up to 150 mL h-1 of highly monodisperse drops.
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Affiliation(s)
- E Amstad
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA. and Institute of Materials, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland
| | - M Chemama
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - M Eggersdorfer
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - L R Arriaga
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - M P Brenner
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
| | - D A Weitz
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA. and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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13
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Cowan ML, Page JH, Norisuye T, Weitz DA. Dynamic sound scattering: Field fluctuation spectroscopy with singly scattered ultrasound in the near and far fields. J Acoust Soc Am 2016; 140:1992. [PMID: 27914438 DOI: 10.1121/1.4962556] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Dynamic sound scattering (DSS) is a powerful acoustic technique for investigating the motion of particles or other inclusions inside an evolving medium. In DSS, this dynamic information is obtained by measuring the field autocorrelation function of the temporal fluctuations of singly scattered acoustic waves. The technique was initially introduced 15 years ago, but its technical aspects were not adequately discussed then. This paper addresses the need for a more complete account of the method by describing in detail two different implementations of this sound scattering technique, one of which is specifically adapted to a common experimental situation in ultrasonics. The technique is illustrated by the application of DSS to measure the mean square velocity fluctuations of particles in fluidized suspensions, as well as the dynamic velocity correlation length. By explaining the experimental and analytical methods involved in realizing the DSS technique in practice, the use of DSS will be facilitated for future studies of particulate suspension dynamics and particle properties over a wide range of particle sizes and concentrations, from millimeters down to nanometers, where the use of optical techniques is often limited by the opacity of the medium.
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Affiliation(s)
- M L Cowan
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
| | - J H Page
- Department of Physics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
| | - T Norisuye
- Department of Macromolecular Science and Engineering, Graduate School of Science and Technology, Kyoto Institute of Technology, Kyoto 606-8585, Japan
| | - D A Weitz
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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14
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Keita E, Kodger TE, Faure P, Rodts S, Weitz DA, Coussot P. Water retention against drying with soft-particle suspensions in porous media. Phys Rev E 2016; 94:033104. [PMID: 27739845 DOI: 10.1103/physreve.94.033104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2016] [Indexed: 06/06/2023]
Abstract
Polymers suspended in granular packings have a significant impact on water retention, which is important for soil irrigation and the curing of building materials. Whereas the drying rate remains constant during a long period for pure water due to capillary flow providing liquid water to the evaporating surface, we show that it is not the case for a suspension made of soft polymeric particles called microgels: The drying rate decreases immediately and significantly. By measuring the spatial water saturation and concentration of suspended particles with magnetic resonance imaging, we can explain these original trends and model the process. In low-viscosity fluids, the accumulation of particles at the free surface induces a recession of the air-liquid interface. A simple model, assuming particle transport and accumulation below the sample free surface, is able to reproduce our observations without any fitting parameters. The high viscosity of the microgel suspension inhibits flow towards the free surface and a drying front appears. We show that water vapor diffusion over a defined and increasing length sets the drying rate. These results and model allow for better controlling the drying and water retention in granular porous materials.
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Affiliation(s)
- E Keita
- Experimental Soft Matter Group, Harvard University, Cambridge, Massachusetts 02138, USA
- Université Paris-Est, Laboratoire Navier, ENPC-IFSTTAR-CNRS, Champs-sur-Marne, France
| | - T E Kodger
- Experimental Soft Matter Group, Harvard University, Cambridge, Massachusetts 02138, USA
| | - P Faure
- Université Paris-Est, Laboratoire Navier, ENPC-IFSTTAR-CNRS, Champs-sur-Marne, France
| | - S Rodts
- Université Paris-Est, Laboratoire Navier, ENPC-IFSTTAR-CNRS, Champs-sur-Marne, France
| | - D A Weitz
- Experimental Soft Matter Group, Harvard University, Cambridge, Massachusetts 02138, USA
| | - P Coussot
- Université Paris-Est, Laboratoire Navier, ENPC-IFSTTAR-CNRS, Champs-sur-Marne, France
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15
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Arriaga LR, Amstad E, Weitz DA. Scalable single-step microfluidic production of single-core double emulsions with ultra-thin shells. Lab Chip 2015; 15:3335-3340. [PMID: 26152396 DOI: 10.1039/c5lc00631g] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report a versatile and robust device for the continuous production of double emulsion drops with very thin shell thicknesses, of about 5% of the radius: for emulsions 50 μm in radius the shells can be as thin as a few micrometers. Importantly, the viscosity of the oil shell can be varied from that of water up to 70 times that of water without compromising device operation. Furthermore, this device can be easily scaled-up as it is made through soft lithography; this may enable the production of industrial quantities of double emulsion drops with ultra-thin shells, which may serve as templates to form capsules with homogeneous shell thicknesses, useful beyond scientific applications.
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Affiliation(s)
- L R Arriaga
- School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge, MA 02138, USA.
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16
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Jensen KE, Weitz DA, Spaepen F. Local shear transformations in deformed and quiescent hard-sphere colloidal glasses. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:042305. [PMID: 25375492 DOI: 10.1103/physreve.90.042305] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2014] [Indexed: 06/04/2023]
Abstract
We perform a series of deformation experiments on a monodisperse, hard-sphere colloidal glass while simultaneously following the three-dimensional trajectories of roughly 50,000 individual particles with a confocal microscope. In each experiment, we deform the glass in pure shear at a constant strain rate [(1-5)×10(-5) s(-1)] to maximum macroscopic strains (5%-10%) and then reverse the deformation at the same rate to return to zero macroscopic strain. We also measure three-dimensional particle trajectories in an identically prepared quiescent glass in which the macroscopic strain is always zero. We find that shear transformation zones exist and are active in both sheared and quiescent colloidal glasses, revealed by a distinctive fourfold signature in spatial autocorrelations of the local shear strain. With increasing shear, the population of local shear transformations develops more quickly than in a quiescent glass and many of these transformations are irreversible. When the macroscopic strain is reversed, we observe partial elastic recovery, followed by plastic deformation of the opposite sign, required to compensate for the irreversibly transformed regions. The average diameter of the shear transformation zones in both strained and quiescent glasses is slightly more than two particle diameters.
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Affiliation(s)
- K E Jensen
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - D A Weitz
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - F Spaepen
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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17
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Cohen SIA, Rajah L, Yoon CH, Buell AK, White DA, Sperling RA, Vendruscolo M, Terentjev EM, Dobson CM, Weitz DA, Knowles TPJ. Spatial propagation of protein polymerization. Phys Rev Lett 2014; 112:098101. [PMID: 24655282 DOI: 10.1103/physrevlett.112.098101] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2013] [Indexed: 06/03/2023]
Abstract
We consider the spatial dependence of filamentous protein self-assembly. Through studying the cases where the spreading of aggregated material is dominated either by diffusion or by growth, we derive analytical results for the spatial evolution of filamentous protein aggregation, which we validate against Monte Carlo simulations. Moreover, we compare the predictions of our theory with experimental measurements of two systems for which we identify the propagation as either growth or diffusion controlled. Our results connect the macroscopic observables that characterize the spatial propagation of protein self-assembly with the underlying microscopic processes and provide physical limits on spatial propagation and prionlike behavior associated with protein aggregation.
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Affiliation(s)
- S I A Cohen
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - L Rajah
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - C H Yoon
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - A K Buell
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D A White
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - R A Sperling
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Vendruscolo
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - E M Terentjev
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - C M Dobson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D A Weitz
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - T P J Knowles
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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18
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Abstract
We present a microfluidic device that enables high throughput production of relatively monodisperse emulsion drops while controlling the average size. The device consists of a two-dimensional array of regularly-spaced posts. Large drops of a highly polydisperse crude emulsion are input into the device and are successively split by the posts, ultimately yielding a finer emulsion consisting of smaller, and much more monodisperse drops. The size distribution of the resultant emulsion depends only weakly on the viscosities of the input fluids and allows fluids of very high viscosities to be used. The average size and polydispersity of the drops depend strongly on the device geometry enabling both control and optimization. We use this device to produce drops of a highly viscous monomer solution and subsequently solidify them into polymeric microparticles. The production rate of these devices is similar to that achieved by membrane emulsification techniques, yet the control over the drop size is superior; thus these post-array microfluidic devices are potentially useful for industrial applications.
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Affiliation(s)
- E Amstad
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, USA.
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19
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Münster S, Jawerth LM, Fabry B, Weitz DA. Structure and mechanics of fibrin clots formed under mechanical perturbation. J Thromb Haemost 2013; 11:557-60. [PMID: 23489915 DOI: 10.1111/jth.12123] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2012] [Accepted: 12/23/2012] [Indexed: 11/30/2022]
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20
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Abstract
Modern confocal microscopes enable high-precision measurement in three dimensions by collecting stacks of 2D (x-y) images that can be assembled digitally into a 3D image. It is difficult, however, to ensure position accuracy, particularly along the optical (z) axis where scanning is performed by a different physical mechanism than in x-y. We describe a simple device to calibrate simultaneously the x, y, and z pixel-to-micrometer conversion factors for a confocal microscope. By taking a known 2D pattern and positioning it at a precise angle with respect to the microscope axes, we created a 3D reference standard. The device is straightforward to construct and easy to use.
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Affiliation(s)
- K E Jensen
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
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21
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Muluneh M, Sprakel J, Wyss HM, Mattsson J, Weitz DA. Direct visualization of pH-dependent evolution of structure and dynamics in microgel suspensions. J Phys Condens Matter 2011; 23:505101. [PMID: 22040676 DOI: 10.1088/0953-8984/23/50/505101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We use 3D confocal microscopy combined with image analysis and particle tracking techniques to study the structure and dynamics of aqueous suspensions of fluorescently labelled p(NIPAm-co-AAc) microgel particles. By adjusting the pH we can tune the interactions between the microgel particles from purely repulsive near neutral pH, to weakly attractive at low pH. This change in the interaction potential has a pronounced effect on the manner in which the suspensions solidify. We directly follow the evolution of the system after a quench from the liquid state to obtain detailed information on the route to kinetic arrest. At low pH and low concentration, dynamic arrest results mainly from crystallization driven by the attraction between particles; crystal nucleation occurs homogeneously throughout the sample and does not appear to be localized to geometric boundaries. Moreover, the growth of crystals is characterized by nucleation-limited kinetics where a rapid growth of crystal domains takes place after a long concentration-dependent lag time. At low pH and high concentration, relaxation of the suspension is constrained and it evolves only slightly, resulting in a disordered solid. At neutral pH, the dynamics are a function of the particle number concentration only; a high concentration leads to the formation of a disordered soft glassy solid.
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Affiliation(s)
- M Muluneh
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
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22
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Ehrlicher AJ, Nakamura F, Hartwig JH, Weitz DA, Stossel TP. Mechanical strain in actin networks regulates FilGAP and integrin binding to filamin A. Nature 2011; 478:260-3. [PMID: 21926999 PMCID: PMC3204864 DOI: 10.1038/nature10430] [Citation(s) in RCA: 265] [Impact Index Per Article: 20.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2011] [Accepted: 08/05/2011] [Indexed: 12/14/2022]
Affiliation(s)
- A J Ehrlicher
- Translational Medicine Division, Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts 02115, USA
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23
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Ramsteiner IB, Weitz DA, Spaepen F. Stiffness of the crystal-liquid interface in a hard-sphere colloidal system measured from capillary fluctuations. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:041603. [PMID: 21230283 DOI: 10.1103/physreve.82.041603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2010] [Indexed: 05/30/2023]
Abstract
Face-centered cubic single crystals of σ=1.55 μm diameter hard-sphere silica colloidal particles were prepared by sedimentation onto (100) and (110) oriented templates. The crystals had a wide interface with the overlaying liquid that was parallel to the template. The location of the interface was determined by confocal microscopic location of the particles, followed by identification of the crystalline and liquid phases by a bond-orientation order parameter. Fluctuations in the height of the interface about its average position were recorded for several hundred configurations. The interfacial stiffness γ was determined from the slope of the inverse squared Fourier components of the height profile vs the square of the wave number, according to the continuum capillary fluctuation method. The offset of the fit from the origin could quantitatively be accounted for by gravitational damping of the fluctuations. For the (100) interface, γ=(1.3±0.3)k(B)T/σ(2); for the (110) interface, γ=(1.0±0.2)k(B)T/σ(2). The interfacial stiffness of both interfaces was found to be isotropic in the plane. This is surprising for the (110), where crystallography predicts twofold symmetry. Sedimentation onto a (111) template yielded a randomly stacked hexagonal crystal with isotropic γ=0.66k(B)T/σ(2). This value, however, is less reliable than the two others due to imperfections in the crystal.
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Affiliation(s)
- I B Ramsteiner
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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24
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Abstract
We describe a novel microfluidic cell sorter which operates in continuous flow at high sorting rates. The device is based on a surface acoustic wave cell-sorting scheme and combines many advantages of fluorescence activated cell sorting (FACS) and fluorescence activated droplet sorting (FADS) in microfluidic channels. It is fully integrated on a PDMS device, and allows fast electronic control of cell diversion. We direct cells by acoustic streaming excited by a surface acoustic wave which deflects the fluid independently of the contrast in material properties of deflected objects and the continuous phase; thus the device underlying principle works without additional enhancement of the sorting by prior labelling of the cells with responsive markers such as magnetic or polarizable beads. Single cells are sorted directly from bulk media at rates as fast as several kHz without prior encapsulation into liquid droplet compartments as in traditional FACS. We have successfully directed HaCaT cells (human keratinocytes), fibroblasts from mice and MV3 melanoma cells. The low shear forces of this sorting method ensure that cells survive after sorting.
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Affiliation(s)
- T Franke
- Department of Physics and School of Engineering and Applied Science, Harvard University, Cambridge, USA
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25
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Lietor-Santos JJ, Kim C, Lynch ML, Fernandez-Nieves A, Weitz DA. The role of polymer polydispersity in phase separation and gelation in colloid-polymer mixtures. Langmuir 2010; 26:3174-3178. [PMID: 20175569 DOI: 10.1021/la903127a] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Mixtures of nonadsorbing polymer and colloidal particles exhibit a range of different morphologies depending on the particle and polymer concentrations and their relative size ratios. These can be very important for technological applications, where gelation can produce a weak solidlike structure that can help reduce phase separation, extending product shelf life. However, industrial products are typically formulated with polydisperse polymers, and the consequences of this on the phase behavior of the mixture are not known. We investigate the role of polymer polydispersity and show that a small amount of larger polymer in a distribution of nominally much smaller polymer can drastically modify the behavior. It can induce formation of a solidlike gel structure, abetted by the small polymer, but still allow further evolution of the phase separation process, as is seen with a monodisperse distribution of larger polymer. This coarsening ultimately leads to gravitational collapse. We describe the full phase behavior for polydisperse polymer mixtures and account for the origin of the behavior through measurements of the structure and dynamics and by comparing to the behavior with monodisperse polymers.
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Affiliation(s)
- J J Lietor-Santos
- School of Engineering and Applied Sciences and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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26
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Affiliation(s)
- A R Abate
- Department of Physics and School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
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27
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Kasza KE, Nakamura F, Hu S, Kollmannsberger P, Bonakdar N, Fabry B, Stossel TP, Wang N, Weitz DA. Filamin A is essential for active cell stiffening but not passive stiffening under external force. Biophys J 2009; 96:4326-35. [PMID: 19450503 DOI: 10.1016/j.bpj.2009.02.035] [Citation(s) in RCA: 82] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2008] [Revised: 01/27/2009] [Accepted: 02/18/2009] [Indexed: 10/20/2022] Open
Abstract
The material properties of a cell determine how mechanical forces are transmitted through and sensed by that cell. Some types of cells stiffen passively under large external forces, but they can also alter their own stiffness in response to the local mechanical environment or biochemical cues. Here we show that the actin-binding protein filamin A is essential for the active stiffening of cells plated on collagen-coated substrates. This appears to be due to a diminished capability to build up large internal contractile stresses in the absence of filamin A. To show this, we compare the material properties and contractility of two human melanoma cell lines that differ in filamin A expression. The filamin A-deficient M2 cells are softer than the filamin A-replete A7 cells, and exert much smaller contractile stresses on the substratum, even though the M2 cells have similar levels of phosphorylated myosin II light chain and only somewhat diminished adhesion strength. In contrast to A7 cells, the stiffness and contractility of M2 cells are insensitive to either myosin-inhibiting drugs or the stiffness of the substratum. Surprisingly, however, filamin A is not required for passive stiffening under large external forces.
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Affiliation(s)
- K E Kasza
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, USA
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28
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Abate AR, Poitzsch A, Hwang Y, Lee J, Czerwinska J, Weitz DA. Impact of inlet channel geometry on microfluidic drop formation. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 80:026310. [PMID: 19792252 DOI: 10.1103/physreve.80.026310] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2009] [Revised: 05/23/2009] [Indexed: 05/07/2023]
Abstract
We study the impact of inlet channel geometry on microfluidic drop formation. We show that drop makers with T-junction style inlets form monodisperse emulsions at low and moderate capillary numbers and those with Flow-Focus style inlets do so at moderate and high capillary numbers. At low and moderate capillary number, drop formation is dominated by interfacial forces and mediated by the confinement of the microchannels; drop size as a function of flow-rate ratio follows a simple functional form based on a blocking-squeezing mechanism. We summarize the stability of the drop makers with different inlet channel geometry in the form of a phase diagram as a function of capillary number and flow-rate ratio.
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Affiliation(s)
- A R Abate
- Department of Physics and SEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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29
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Guery J, Baudry J, Weitz DA, Chaikin PM, Bibette J. Diffusion through colloidal shells under stress. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:060402. [PMID: 19658462 DOI: 10.1103/physreve.79.060402] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2008] [Indexed: 05/28/2023]
Abstract
The permeability of solids has long been associated with a diffusive process involving activated mechanism as originally envisioned by Eyring. Tensile stress can affect the activation energy but definitive experiments of the diffusion rate of species through a stressed solid are lacking. Here we use core-shell (liquid core-solid shell) colloidal particles that are sensitive to osmotic pressure to follow the permeation of encapsulated probes at various stresses. We unambiguously show that the tensile stress applied on colloidal shells linearly reduces the local energy barrier for diffusion.
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Affiliation(s)
- J Guery
- Laboratoire Colloïdes et Matériaux divisés, ESPCI ParisTech, UPMC, CNRS UMR 7195, 10 rue Vauquelin, 75005 Paris, France
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30
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Kasza KE, Koenderink GH, Lin YC, Broedersz CP, Messner W, Nakamura F, Stossel TP, MacKintosh FC, Weitz DA. Nonlinear elasticity of stiff biopolymers connected by flexible linkers. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:041928. [PMID: 19518277 DOI: 10.1103/physreve.79.041928] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2007] [Revised: 02/13/2009] [Indexed: 05/27/2023]
Abstract
Networks of the biopolymer actin, cross-linked by the compliant protein filamin, form soft gels. They can, however, withstand large shear stresses due to their pronounced nonlinear elastic behavior. The nonlinear elasticity can be controlled by varying the number of cross-links per actin filament. We propose and test a model of rigid filaments decorated by multiple flexible linkers that is in quantitative agreement with experiment. This allows us to estimate loads on individual cross-links, which we find to be less than 10 pN.
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Affiliation(s)
- K E Kasza
- Department of Physics and SEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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31
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Liétor-Santos JJ, Kim C, Lu PJ, Fernández-Nieves A, Weitz DA. Gravitational compression of colloidal gels. Eur Phys J E Soft Matter 2009; 28:159-164. [PMID: 19018579 DOI: 10.1140/epje/i2008-10390-7] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2008] [Revised: 09/10/2008] [Indexed: 05/27/2023]
Abstract
We study the compression of depletion gels under the influence of a gravitational stress by monitoring the time evolution of the gel interface and the local volume fraction, φ, inside the gel. We find φ is not constant throughout the gel. Instead, there is a volume fraction gradient that develops and grows along the gel height as the compression process proceeds. Our results are correctly described by a non-linear poroelastic model that explicitly incorporates the φ-dependence of the gravitational, elastic and viscous stresses acting on the gel.
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Affiliation(s)
- J J Liétor-Santos
- Department of Physics and HSEAS, Harvard University, Pierce Hall, 29 Oxford Street, Cambridge, MA 02138, USA
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32
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Ramsteiner IB, Jensen KE, Weitz DA, Spaepen F. Experimental observation of the crystallization of hard-sphere colloidal particles by sedimentation onto flat and patterned surfaces. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 79:011403. [PMID: 19257031 DOI: 10.1103/physreve.79.011403] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2008] [Indexed: 05/27/2023]
Abstract
We present a confocal microscopy study of 1.55 microm monodisperse silica hard spheres as they sediment and crystallize at the bottom wall of a container. If the particles sediment onto a feature less flat wall, the two bottom layers crystallize simultaneously and layerwise growth follows. If the wall is replaced by a hexagonal template, only layerwise growth occurs. Our results complement earlier numerical simulations and experiments on other colloidal systems.
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Affiliation(s)
- I B Ramsteiner
- School of Engineering and Applied Sciences, Harvard University, 9 Oxford Street, Cambridge, Massachusetts 02138, USA
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33
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Holtze C, Rowat AC, Agresti JJ, Hutchison JB, Angilè FE, Schmitz CHJ, Köster S, Duan H, Humphry KJ, Scanga RA, Johnson JS, Pisignano D, Weitz DA. Biocompatible surfactants for water-in-fluorocarbon emulsions. Lab Chip 2008; 8:1632-9. [PMID: 18813384 DOI: 10.1039/b806706f] [Citation(s) in RCA: 480] [Impact Index Per Article: 30.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Drops of water-in-fluorocarbon emulsions have great potential for compartmentalizing both in vitro and in vivo biological systems; however, surfactants to stabilize such emulsions are scarce. Here we present a novel class of fluorosurfactants that we synthesize by coupling oligomeric perfluorinated polyethers (PFPE) with polyethyleneglycol (PEG). We demonstrate that these block copolymer surfactants stabilize water-in-fluorocarbon oil emulsions during all necessary steps of a drop-based experiment including drop formation, incubation, and reinjection into a second microfluidic device. Furthermore, we show that aqueous drops stabilized with these surfactants can be used for in vitro translation (IVT), as well as encapsulation and incubation of single cells. The compatability of this emulsion system with both biological systems and polydimethylsiloxane (PDMS) microfluidic devices makes these surfactants ideal for a broad range of high-throughput, drop-based applications.
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Affiliation(s)
- C Holtze
- Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, USA
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34
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Bailey AE, Poon WCK, Christianson RJ, Schofield AB, Gasser U, Prasad V, Manley S, Segre PN, Cipelletti L, Meyer WV, Doherty MP, Sankaran S, Jankovsky AL, Shiley WL, Bowen JP, Eggers JC, Kurta C, Lorik T, Pusey PN, Weitz DA. Spinodal decomposition in a model colloid-polymer mixture in microgravity. Phys Rev Lett 2007; 99:205701. [PMID: 18233160 DOI: 10.1103/physrevlett.99.205701] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2007] [Revised: 08/19/2007] [Indexed: 05/25/2023]
Abstract
We study phase separation in a deeply quenched colloid-polymer mixture in microgravity on the International Space Station using small-angle light scattering and direct imaging. We observe a clear crossover from early-stage spinodal decomposition to late-stage, interfacial-tension-driven coarsening. Data acquired over 5 orders of magnitude in time show more than 3 orders of magnitude increase in domain size, following nearly the same evolution as that in binary liquid mixtures. The late-stage growth approaches the expected linear growth rate quite slowly.
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Affiliation(s)
- A E Bailey
- Dept. of Physics & SEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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35
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Fernández-Nieves A, Vitelli V, Utada AS, Link DR, Márquez M, Nelson DR, Weitz DA. Novel defect structures in nematic liquid crystal shells. Phys Rev Lett 2007; 99:157801. [PMID: 17995213 DOI: 10.1103/physrevlett.99.157801] [Citation(s) in RCA: 124] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2007] [Indexed: 05/25/2023]
Abstract
We use double-emulsion drops to experimentally investigate the defect structures of spherical shells of nematic liquid crystals. We uncover a rich scenario of coexisting defect structures dictated by the unavoidable finite thickness of even the thinnest shell and by the thickness variation around the sphere. These structures are characterized by a varying number of disclination lines and pairs of surface point defects on the inner and outer surfaces of the nematic shell. In the limit of very thick shells the defect structure ultimately merges with that of a bulk nematic liquid crystal drop.
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Affiliation(s)
- A Fernández-Nieves
- Department of Physics and HSEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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36
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Liu J, Koenderink GH, Kasza KE, Mackintosh FC, Weitz DA. Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels. Phys Rev Lett 2007; 98:198304. [PMID: 17677669 DOI: 10.1103/physrevlett.98.198304] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2006] [Indexed: 05/16/2023]
Abstract
We image semiflexible polymer networks under shear at the micrometer scale. By tracking embedded probe particles, we determine the local strain field, and directly measure its uniformity, or degree of affineness, on scales of 2-100 microm. The degree of nonaffine strain depends upon the polymer length and cross-link density, consistent with theoretical predictions. We also find a direct correspondence between the uniformity of the microscale strain and the nonlinear elasticity of the networks in the bulk.
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Affiliation(s)
- J Liu
- Department of Physics & SEAS, Harvard University, Cambridge, MA 02138, USA
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37
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Fernández-Nieves A, Link DR, Márquez M, Weitz DA. Topological changes in bipolar nematic droplets under flow. Phys Rev Lett 2007; 98:087801. [PMID: 17359128 DOI: 10.1103/physrevlett.98.087801] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2006] [Revised: 11/22/2006] [Indexed: 05/14/2023]
Abstract
Bipolar liquid crystal drops moving inside microchannels exhibit periodic director field transformations due to induced circulating flows inside them. These modifications are characterized by changes in the type of point surface disclinations; they periodically change from splay to bend disclinations, implying the drop changes between bipolar and escaped concentric configurations. Upon stopping the flow, this structure does not relax to the lower energy bipolar configuration; we argue this is due to drop flattening inside the channels.
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Affiliation(s)
- A Fernández-Nieves
- Department of Physics and HSEAS, Harvard University, Cambridge, MA 02138, USA
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38
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Dufresne ER, Stark DJ, Greenblatt NA, Cheng JX, Hutchinson JW, Mahadevan L, Weitz DA. Dynamics of fracture in drying suspensions. Langmuir 2006. [PMID: 16893207 DOI: 10.1021/la061251] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We investigate the dynamics of fracture in drying films of colloidal silica. Water loss quenches the nanoparticle dispersions to form a liquid-saturated elastic network of particles that relieves drying-induced strain by cracking. These cracks display intriguing intermittent motion originating from the deformation of arrested crack tips and aging of the elastic network. The dynamics of a single crack exhibits a universal evolution, described by a balance of the driving elastic power with the sum of interfacial power and the viscous dissipation rate of flowing interstitial fluid.
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Affiliation(s)
- E R Dufresne
- DEAS, Department of Physics, and Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
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39
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Dufresne ER, Stark DJ, Greenblatt NA, Cheng JX, Hutchinson JW, Mahadevan L, Weitz DA. Dynamics of fracture in drying suspensions. Langmuir 2006; 22:7144-7. [PMID: 16893207 DOI: 10.1021/la061251+] [Citation(s) in RCA: 83] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
We investigate the dynamics of fracture in drying films of colloidal silica. Water loss quenches the nanoparticle dispersions to form a liquid-saturated elastic network of particles that relieves drying-induced strain by cracking. These cracks display intriguing intermittent motion originating from the deformation of arrested crack tips and aging of the elastic network. The dynamics of a single crack exhibits a universal evolution, described by a balance of the driving elastic power with the sum of interfacial power and the viscous dissipation rate of flowing interstitial fluid.
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Affiliation(s)
- E R Dufresne
- DEAS, Department of Physics, and Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA.
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40
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Guery J, Bertrand E, Rouzeau C, Levitz P, Weitz DA, Bibette J. Irreversible shear-activated aggregation in non-Brownian suspensions. Phys Rev Lett 2006; 96:198301. [PMID: 16803145 DOI: 10.1103/physrevlett.96.198301] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2005] [Indexed: 05/10/2023]
Abstract
We have studied the effect of shear on the stability of suspensions made of non-Brownian solid particles. We demonstrate the existence of an irreversible transition where the solid particles aggregate at remarkably low volume fractions (phi approximately 0.1). This shear-induced aggregation is dramatic and exhibits a very sudden change in the viscosity, which increases sharply after a shear-dependent induction time. We show that this induction time is related exponentially to the shear rate, reflecting the importance of the hydrodynamic forces in reducing the repulsive energy barrier that prevents the particles from aggregating.
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Affiliation(s)
- J Guery
- ESPCI, UMR 7612, Laboratoire Colloïdes et Matériaux Divisés, ParisTech, France
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41
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Dinsmore AD, Prasad V, Wong IY, Weitz DA. Microscopic structure and elasticity of weakly aggregated colloidal gels. Phys Rev Lett 2006; 96:185502. [PMID: 16712371 DOI: 10.1103/physrevlett.96.185502] [Citation(s) in RCA: 56] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2005] [Indexed: 05/09/2023]
Abstract
We directly probe the microscopic structure, connectivity, and elasticity of colloidal gels using confocal microscopy. We show that the gel is a random network of one-dimensional chains of particles. By measuring thermal fluctuations, we determine the effective spring constant between pairs of particles as a function of separation; this is in agreement with the theory for fractal chains. Long-range attractions between particles lead to freely rotating bonds, and the gel is stabilized by multiple connections among the chains. By contrast, short-range attractions lead to bonds that resist bending, with dramatically suppressed formation of loops of particles.
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Affiliation(s)
- A D Dinsmore
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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42
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Liu J, Gardel ML, Kroy K, Frey E, Hoffman BD, Crocker JC, Bausch AR, Weitz DA. Microrheology probes length scale dependent rheology. Phys Rev Lett 2006; 96:118104. [PMID: 16605878 DOI: 10.1103/physrevlett.96.118104] [Citation(s) in RCA: 128] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2005] [Indexed: 05/08/2023]
Abstract
We exploit the power of microrheology to measure the viscoelasticity of entangled F-actin solutions at different length scales from 1 to 100 microm over a wide frequency range. We compare the behavior of single probe-particle motion to that of the correlated motion of two particles. By varying the average length of the filaments, we identify fluctuations that dissipate diffusively over the filament length. These provide an important relaxation mechanism of the elasticity between 0.1 and 30 rad/sec.
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Affiliation(s)
- J Liu
- Dept. of Physics & DEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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43
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Gardel ML, Nakamura F, Hartwig J, Crocker JC, Stossel TP, Weitz DA. Stress-dependent elasticity of composite actin networks as a model for cell behavior. Phys Rev Lett 2006; 96:088102. [PMID: 16606229 DOI: 10.1103/physrevlett.96.088102] [Citation(s) in RCA: 93] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2005] [Indexed: 05/08/2023]
Abstract
Networks of filamentous actin cross-linked with the actin-binding protein filamin A exhibit remarkable strain stiffening leading to an increase in differential elastic modulus by several orders of magnitude over the linear value. The variation of the frequency dependence of the differential elastic and loss moduli as a function of prestress is consistent with that observed in living cells, suggesting that cell elasticity is always measured in the nonlinear regime, and that prestress is an essential control parameter.
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Affiliation(s)
- M L Gardel
- Department of Physics and D.E.A.S., Harvard University, Cambridge, Massachusetts 02138, USA
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44
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Gardel ML, Nakamura F, Hartwig JH, Crocker JC, Stossel TP, Weitz DA. Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells. Proc Natl Acad Sci U S A 2006; 103:1762-7. [PMID: 16446458 PMCID: PMC1413620 DOI: 10.1073/pnas.0504777103] [Citation(s) in RCA: 266] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We show that actin filaments, shortened to physiological lengths by gelsolin and cross-linked with recombinant human filamins (FLNs), exhibit dynamic elastic properties similar to those reported for live cells. To achieve elasticity values of comparable magnitude to those of cells, the in vitro network must be subjected to external prestress, which directly controls network elasticity. A molecular requirement for the strain-related behavior at physiological conditions is a flexible hinge found in FLNa and some FLNb molecules. Basic physical properties of the in vitro filamin-F-actin network replicate the essential mechanical properties of living cells. This physical behavior could accommodate passive deformation and internal organelle trafficking at low strains yet resist externally or internally generated high shear forces.
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Affiliation(s)
- M. L. Gardel
- Department of Physics and Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138
| | - F. Nakamura
- Hematology Division, Brigham and Women’s Hospital, Department of Medicine, Harvard Medical School, Boston, MA 02115; and
| | - J. H. Hartwig
- Hematology Division, Brigham and Women’s Hospital, Department of Medicine, Harvard Medical School, Boston, MA 02115; and
| | - J. C. Crocker
- Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, PA 19104
| | - T. P. Stossel
- Hematology Division, Brigham and Women’s Hospital, Department of Medicine, Harvard Medical School, Boston, MA 02115; and
| | - D. A. Weitz
- Department of Physics and Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138
- To whom correspondence should be addressed at:
Department of Physics and Division of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA 02138. E-mail:
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45
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Manley S, Wyss HM, Miyazaki K, Conrad JC, Trappe V, Kaufman LJ, Reichman DR, Weitz DA. Glasslike arrest in spinodal decomposition as a route to colloidal gelation. Phys Rev Lett 2005; 95:238302. [PMID: 16384352 DOI: 10.1103/physrevlett.95.238302] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2004] [Indexed: 05/05/2023]
Abstract
Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich and colloid-poor regions. Gelation results when interconnected colloid-rich regions solidify. We show that this occurs when these regions undergo a glass transition, leading to dynamic arrest of the spinodal decomposition. The characteristic length scale of the gel decreases with increasing quench depth, and the nonergodicity parameter exhibits a pronounced dependence on scattering vector. Mode coupling theory gives a good description of the dynamics, provided we use the full static structure as input.
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Affiliation(s)
- S Manley
- Department of Physics & DEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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46
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Hashmi SM, Wickman HH, Weitz DA. Tetrahedral calcite crystals facilitate self-assembly at the air-water interface. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 72:041605. [PMID: 16383394 DOI: 10.1103/physreve.72.041605] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2005] [Indexed: 05/05/2023]
Abstract
Calcite crystals often nucleate and grow in solutions of calcium carbonate, and these crystallites can become trapped at the air water interface, where they form unusual structures. The most common is a fractal structure, which can extend over a large fraction of the interface, and whose origin is understood in terms of the aggregation of the particles. Much more rarely, a different and entirely unexpected structure is observed: the particles remain well separated on the interface, forming an ordered phase reminiscent of a two-dimensional colloidal crystal. The structure of the crystallites that form this ordered phase is always observed to be tetrahedral, in contrast to the much more common rhombohedral structure of the crystallites that form the fractal phase. We show that the interparticle interaction potential that leads to this ordered phase is a balance between a long-range attractive interaction and a long-range repulsive interaction. The attraction results from gravity-induced capillary forces, while the repulsion results from a dipole-dipole interaction due to the charged surface of the tetrahedral crystals. The interaction potential is estimated from the thermal motion of the particles, and fits to the theoretically expected values suggest that the effective surface charge on the tetrahedral crystals is sigma approximately 0.01 charges/nm2.
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Affiliation(s)
- S M Hashmi
- Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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47
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Abstract
Diblock copolymers are known to spontaneously organize into polymer vesicles. Typically, this is achieved through the techniques of film rehydration or electroformation. We present a new method for generating polymer vesicles from double emulsions. We generate precision water-in-oil-in-water double emulsions from the breakup of concentric fluid streams; the hydrophobic fluid is a volatile mixture of organic solvent that contains dissolved diblock copolymers. We collect the double emulsions and slowly evaporate the organic solvent, which ultimately directs the self-assembly of the dissolved diblock copolymers into vesicular structures. Independent control over all three fluid streams enables precision assembly of polymer vesicles and provides for highly efficient encapsulation of active ingredients within the polymerosomes. We also use double emulsions with several internal drops to form new polymerosome structures.
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Affiliation(s)
- Elise Lorenceau
- Department of Physics and Division of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
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48
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Manley S, Davidovitch B, Davies NR, Cipelletti L, Bailey AE, Christianson RJ, Gasser U, Prasad V, Segre PN, Doherty MP, Sankaran S, Jankovsky AL, Shiley B, Bowen J, Eggers J, Kurta C, Lorik T, Weitz DA. Time-dependent strength of colloidal gels. Phys Rev Lett 2005; 95:048302. [PMID: 16090846 DOI: 10.1103/physrevlett.95.048302] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2004] [Indexed: 05/03/2023]
Abstract
Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in local elasticity arising from bonding between neighboring colloidal particles can account for the strengthening of the network, while preserving network structure.
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Affiliation(s)
- S Manley
- Department of Physics & DEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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49
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Abstract
We perform experiments on two different dense colloidal suspensions with confocal microscopy to probe the relationship between local structure and dynamics near the glass transition. We calculate the Voronoi volume for our particles and show that this quantity is not a universal probe of glassy structure for all colloidal suspensions. We correlate the Voronoi volume to displacement and find that these quantities are only weakly correlated. We observe qualitatively similar results in a simulation of a polymer melt. These results suggest that the Voronoi volume does not predict dynamical behavior in experimental colloidal suspensions; a purely structural approach based on local single particle volume likely cannot describe the colloidal glass transition.
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Affiliation(s)
- J C Conrad
- Department of Physics and DEAS, Harvard University, 29 Oxford St, Cambridge, Massachusetts 02138, USA
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50
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Abstract
We present a unified framework for understanding the compaction of colloidal gels under their own weight. The dynamics of the collapse are determined by the value of the gravitational stress sigma(g), as compared to the yield stress sigma(Y) of the network. For sigma(g)<sigma(Y), gels collapse poroelastically, and their rate of compression decays exponentially in time. For sigma(g)>sigma(Y), the network eventually yields, leading to rapid settling. In both cases, the rate of collapse is backflow limited, while its overall magnitude is determined by a balance between gravitational stress and network elastic stress.
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Affiliation(s)
- S Manley
- Department of Physics and DEAS, Harvard University, Cambridge, Massachusetts 02138, USA
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