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Alexandre A, Anderson L, Collin-Dufresne T, Guérin T, Dean DS. Self-phoretic oscillatory motion in a harmonic trap. Phys Rev E 2024; 109:064147. [PMID: 39020931 DOI: 10.1103/physreve.109.064147] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2024] [Accepted: 05/15/2024] [Indexed: 07/20/2024]
Abstract
We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations that take place along a circle or a straight line. Our results are confirmed by numerical simulations.
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Affiliation(s)
- Arthur Alexandre
- Laboratory of Computational Biology and Theoretical Biophysics, Institute of Bioengineering, School of Life Sciences, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | | | | | | | - David S Dean
- Université Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Université Bordeaux, F-33400 Talence, France
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2
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Nolin A, Licht A, Pierson K, Lo CY, Kayser LV, Dhong C. Predicting human touch sensitivity to single atom substitutions in surface monolayers for molecular control in tactile interfaces. SOFT MATTER 2021; 17:5050-5060. [PMID: 33929468 DOI: 10.1039/d1sm00451d] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The mechanical stimuli generated as a finger interrogates the physical and chemical features of an object form the basis of fine touch. Haptic devices, which are used to control touch, primarily focus on recreating physical features, but the chemical aspects of fine touch may be harnessed to create richer tactile interfaces and reveal fundamental aspects of tactile perception. To connect tactile perception with molecular structure, we systematically varied silane-derived monolayers deposited onto surfaces smoother than the limits of human perception. Through mechanical friction testing and cross-correlation analysis, we made predictions of which pairs of silanes might be distinguishable by humans. We predicted, and demonstrated, that humans can distinguish between two isosteric silanes which differ only by a single nitrogen-for-carbon substitution. The mechanism of tactile contrast originates from a difference in monolayer ordering, as quantified by the Hurst exponent, which was replicated in two alkylsilanes with a three-carbon difference in length. This approach may be generalizable to other materials and lead to new tactile sensations derived from materials chemistry.
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Affiliation(s)
- Abigail Nolin
- Department of Materials Science & Engineering, University of Delaware, Newark, DE, USA.
| | - Amanda Licht
- Department of Materials Science & Engineering, University of Delaware, Newark, DE, USA.
| | - Kelly Pierson
- Department of Materials Science & Engineering, University of Delaware, Newark, DE, USA.
| | - Chun-Yuan Lo
- Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, USA
| | - Laure V Kayser
- Department of Materials Science & Engineering, University of Delaware, Newark, DE, USA. and Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, USA
| | - Charles Dhong
- Department of Materials Science & Engineering, University of Delaware, Newark, DE, USA. and Department of Biomedical Engineering, University of Delaware, Newark, DE, USA
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3
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Lyashenko IA, Borysiuk VN, Popov VL. Stick-slip boundary friction mode as a second-order phase transition with an inhomogeneous distribution of elastic stress in the contact area. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2017; 8:1889-1896. [PMID: 29046836 PMCID: PMC5629396 DOI: 10.3762/bjnano.8.189] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2017] [Accepted: 08/16/2017] [Indexed: 06/02/2023]
Abstract
This article presents an investigation of the dynamical contact between two atomically flat surfaces separated by an ultrathin lubricant film. Using a thermodynamic approach we describe the second-order phase transition between two structural states of the lubricant which leads to the stick-slip mode of boundary friction. An analytical description and numerical simulation with radial distributions of the order parameter, stress and strain were performed to investigate the spatial inhomogeneity. It is shown that in the case when the driving device is connected to the upper part of the friction block through an elastic spring, the frequency of the melting/solidification phase transitions increases with time.
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Affiliation(s)
- Iakov A Lyashenko
- Technische Universität Berlin, 10623 Berlin, Germany
- Sumy State University, 40007 Sumy, Ukraine
| | - Vadym N Borysiuk
- Technische Universität Berlin, 10623 Berlin, Germany
- Sumy State University, 40007 Sumy, Ukraine
| | - Valentin L Popov
- Technische Universität Berlin, 10623 Berlin, Germany
- National Research Tomsk State University, 634050 Tomsk, Russia
- National Research Tomsk Polytechnic University, 634050 Tomsk, Russia
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4
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Lyashenko IA, Filippov AE, Popov M, Popov VL. Effect of stress nonhomogeneity on the shear melting of a thin boundary lubrication layer. Phys Rev E 2016; 94:053002. [PMID: 27967082 DOI: 10.1103/physreve.94.053002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2016] [Indexed: 11/07/2022]
Abstract
We consider the dynamical properties of boundary lubrication in contact between two atomically smooth solid surfaces separated by an ultrathin layer of lubricant. In contrast to previous works on this topic, we explicitly consider the heterogeneity of tangential stresses, which arises in a contact of elastic bodies that are moved tangentially relative to each other. To describe phase transitions between structural states of the lubricant we use an approach based on the field theory of phase transitions. It is assumed that the lubricant layer, when stressed, can undergo a shear-melting transition of first or second order. While solutions for the homogeneous system can be easily obtained analytically, the kinetics of the phase transitions in the spatially heterogeneous system can only be studied numerically. In our numerical experiments melting of the lubricant layer starts from the outer boundary of contact and propagates to its center. The melting wave is followed by a wave of solidification. This process repeats itself periodically, following the stick-slip pattern that is characteristic of such systems. Depending on the thermodynamic and kinetic parameters of the model, different modes of sliding with almost complete or only partial intermediate solidification are possible.
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Affiliation(s)
- Iakov A Lyashenko
- Berlin University of Technology, 10623 Berlin, Germany.,Sumy State University, 40007 Sumy, Ukraine
| | - Alexander E Filippov
- Berlin University of Technology, 10623 Berlin, Germany.,Donetsk Institute for Physics and Engineering, 83114 Donetsk, Ukraine
| | - Mikhail Popov
- Berlin University of Technology, 10623 Berlin, Germany.,National Research Tomsk Polytechnic University, 634050 Tomsk, Russia.,National Research Tomsk State University, 634050 Tomsk, Russia
| | - Valentin L Popov
- Berlin University of Technology, 10623 Berlin, Germany.,National Research Tomsk Polytechnic University, 634050 Tomsk, Russia.,National Research Tomsk State University, 634050 Tomsk, Russia
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5
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Guérin T, Prost J, Joanny JF. Dynamical behavior of molecular motor assemblies in the rigid and crossbridge models. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2011; 34:60. [PMID: 21706282 DOI: 10.1140/epje/i2011-11060-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2011] [Accepted: 05/09/2011] [Indexed: 05/31/2023]
Abstract
We present a detailed analysis of the dynamical instabilities appearing in two kinetic theories for the collective behavior of molecular motors: the rigid two-state model and the two-state crossbridge (or power-stroke) model with continuous binding sites. We calculate force-velocity relations, discuss their stability, plot a diagram that summarizes the oscillation regimes, identify the location of the Hopf bifurcation with a memory effect, discuss the oscillation frequency and make a link with single-molecule experiments. We show that the instabilities present in these models naturally translate into non-linearities in force-displacement relations, and at linear order give forces that are similar to the delayed stretch activation observed in oscillating muscles. We also find that instabilities can appear for both apparent load-decelerated and load-accelerated detachment rates in a 3-state crossbridge model.
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Affiliation(s)
- T Guérin
- Physicochimie Curie (Institut Curie/CNRS-UMR168/UPMC), Institut Curie, Centre de Recherche, Paris Cedex, France,
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Daub EG, Carlson JM. Stick-slip instabilities and shear strain localization in amorphous materials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:066113. [PMID: 20365237 DOI: 10.1103/physreve.80.066113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2009] [Indexed: 05/29/2023]
Abstract
We study the impact of strain localization on the stability of frictional slipping in dense amorphous materials. We model the material using shear transformation zone (STZ) theory, a continuum approximation for plastic deformation in amorphous solids. In the STZ model, the internal state is quantified by an effective disorder temperature, and the effective temperature dynamics capture the spontaneous localization of strain. We study the effect of strain localization on stick-slip instabilities by coupling the STZ model to a noninertial spring slider system. We perform a linear stability analysis to generate a phase diagram that connects the small scale physics of strain localization to the macroscopic stability of sliding. Our calculations determine the values of spring stiffness and driving velocity where steady sliding becomes unstable and we confirm our results through numerical integration. We investigate both homogeneous deformation, where no shear band forms, and localized deformation, where a narrow shear band spontaneously forms and accommodates all of the deformation. Our results show that at a given velocity, strain localization leads to unstable frictional sliding at a much larger spring stiffness compared to homogeneous deformation, and that localized deformation cannot be approximated by a homogeneous model with a narrower material. We also find that strain localization provides a physical mechanism for irregular stick-slip cycles in certain parameter ranges. Our results quantitatively connect the internal physics of deformation in amorphous materials to the larger scale frictional dynamics of stick-slip.
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Affiliation(s)
- Eric G Daub
- Geophysics Group and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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7
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Takeshi O. Continuum theory of memory effect in crack patterns of drying pastes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061501. [PMID: 18643266 DOI: 10.1103/physreve.77.061501] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2007] [Indexed: 05/26/2023]
Abstract
A possible clarification of memory effect observed in crack patterns of drying pastes [A. Nakahara and Y. Matsuo, J. Phys. Soc. Jpn. 74, 1362 (2005)] is presented in terms of a macroscopic elastoplastic model of isotropic pastes. We study flows driven by steady gravitational force instead of external oscillation. The model predicts creation of residual tension in favor of cracks perpendicular to the flow direction, thus causing the same type of memory effect as that reported by Nakahara and Matsuo for oscillated CaCO3 pastes.
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Affiliation(s)
- Ooshida Takeshi
- Department of Applied Mathematics and Physics, Tottori University, Japan.
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8
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Yuu S, Umekage T, Kawasaki Y. Numerical simulation for the friction mechanism of a powder bed using two-dimensional distinct element method. ADV POWDER TECHNOL 2006. [DOI: 10.1163/156855206777213447] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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9
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Urbakh M, Klafter J, Gourdon D, Israelachvili J. The nonlinear nature of friction. Nature 2004; 430:525-8. [PMID: 15282597 DOI: 10.1038/nature02750] [Citation(s) in RCA: 247] [Impact Index Per Article: 12.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2003] [Accepted: 06/09/2004] [Indexed: 11/09/2022]
Abstract
Tribology is the study of adhesion, friction, lubrication and wear of surfaces in relative motion. It remains as important today as it was in ancient times, arising in the fields of physics, chemistry, geology, biology and engineering. The more we learn about tribology the more complex it appears. Nevertheless, recent experiments coupled to theoretical modelling have made great advances in unifying apparently diverse phenomena and revealed many subtle and often non-intuitive aspects of matter in motion, which stem from the nonlinear nature of the problem.
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Affiliation(s)
- Michael Urbakh
- School of Chemistry, Raymond and Beverley Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel.
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10
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Protopopescu V, Barhen J. Non-Lipschitzian control algorithms for extended mechanical systems. CHAOS (WOODBURY, N.Y.) 2004; 14:400-407. [PMID: 15189068 DOI: 10.1063/1.1721111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We derive the properties of a general control algorithm [Braiman et al., Phys. Rev. Lett. 90, 094301 (2003)] for quantities describing global features of nonlinear extended mechanical systems. The control algorithm is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that (i) certain average quantities of the controlled system can be driven-exactly or approximately-towards desired targets which become linearly stable attractors for the system's dynamics; (ii) the basins of attraction of these targets are reached in very short times; and (iii) while within reasonably broad ranges the time-scales of the control and of the intrinsic dynamics may be quite different, this disparity does not affect significantly the overall efficiency of the proposed scheme, up to natural fluctuations.
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Affiliation(s)
- V Protopopescu
- Center for Engineering Science Advanced Research, Computing and Computational Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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11
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Lemaître A, Carlson J. Boundary lubrication with a glassy interface. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061611. [PMID: 15244589 DOI: 10.1103/physreve.69.061611] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2003] [Revised: 03/16/2004] [Indexed: 05/24/2023]
Abstract
Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo nonaffine deformations in response to stress. The generalization we study phenomenologically incorporates the effects of aging and glassy relaxation. Under experimental conditions associated with typical transitions from stick-slip to steady sliding and stop-start tests, these effects can be dominant, although the full STZ description is necessary to account for more complex, chaotic transitions.
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Affiliation(s)
- Anaël Lemaître
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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12
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Volfson D, Tsimring LS, Aranson IS. Stick-slip dynamics of a granular layer under shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:031302. [PMID: 15089281 DOI: 10.1103/physreve.69.031302] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2003] [Indexed: 05/24/2023]
Abstract
Stick-slip regime of shear granular flows is studied theoretically and numerically. Numerical experiments are carried out for a thin Couette cell using soft-particle molecular dynamics code in two dimensions. We apply order parameter theory of partially fluidized granular flows and find a good agreement with simulations and experiments by Nasuno et al.
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Affiliation(s)
- Dmitri Volfson
- Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA
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13
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Khomenko AV, Yushchenko OV. Solid-liquid transition of ultrathin lubricant film. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:036110. [PMID: 14524835 DOI: 10.1103/physreve.68.036110] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2003] [Indexed: 11/07/2022]
Abstract
We represent a melting of ultrathin lubricant film by friction between atomically flat surfaces as a result of action of spontaneously appearing elastic field of stress shear component caused by the external supercritical heating. The kinetics of this solid-liquid transition is described by the Maxwell-type and Voigt-Kelvin equations for viscoelastic matter as well as by the relaxation equation for temperature. We show that these equations coincide formally with the synergetic Lorenz system, where the stress acts as the order parameter, the conjugate field is reduced to the elastic shear strain, and the temperature is the control parameter. Using the adiabatic approximation we find the steady-state values of these quantities. Taking into account the deformational defect of the shear modulus, we show that lubricant melting is realized according to mechanism of the first-order transition. The critical temperature of the friction surfaces increases with growth of the characteristic value of shear viscosity and decreases with growth of the shear modulus value linearly.
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Affiliation(s)
- Alexei V Khomenko
- Physical Electronics Department, Sumy State University, 40007 Sumy, Ukraine.
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14
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Gourdon D, Israelachvili JN. Transitions between smooth and complex stick-slip sliding of surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:021602. [PMID: 14524981 DOI: 10.1103/physreve.68.021602] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2003] [Indexed: 05/24/2023]
Abstract
Shear measurements were performed on mica surfaces with molecularly thin films of squalane (C30H62) confined between them. Squalane is a branched hydrocarbon liquid that can be in the liquid, glassy, or liquid-crystalline state under confinement. The friction forces, especially the transitions between smooth and intermittent (e.g., stick-slip) sliding, were measured over a wider range of applied loads (pressures), sliding velocities (shear rates), and temperatures than in previous studies. The results reveal that, depending on the conditions, qualitatively different behavior can arise in the same system. These include both abrupt and continuous transitions, both upper and lower critical transition temperatures, short and very long transient effects, and chaotic, sawtooth, or sinusoidal stick-slip that can slowly decay with time or distance sheared. The differences between these branched and simpler, e.g., spherical, unbranched molecules are compared, as well as with unlubricated (dry) surfaces and macroscopic (geological) systems.
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Affiliation(s)
- Delphine Gourdon
- Department of Chemical Engineering, University of California at Santa Barbara, Santa Barbara, California 93106, USA
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16
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Drummond C, Israelachvili J, Richetti P. Friction between two weakly adhering boundary lubricated surfaces in water. ACTA ACUST UNITED AC 2003; 67:066110. [PMID: 16241307 DOI: 10.1103/physreve.67.066110] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2002] [Indexed: 11/07/2022]
Abstract
The sliding of adhesive surfactant-bearing surfaces was studied with a surface forces apparatus nanotribometer. When the surfaces are fully immersed in an aqueous solution, the dynamic behavior is drastically different and more varied than under dry conditions. In solution, the shear stress exhibits at least five different velocity regimes. In particular, the sliding may proceed by an "inverted" stick-slip over a large range of driving velocities, this regime being bounded by smooth (kinetic) sliding at both lower and higher driving velocities. The general behavior of the system was studied in detail, i.e., over a large range of experimental conditions, and theoretically accounted for in terms of a general model based on the kinetics of formation and rupture of adhesive links (bonds) between the two shearing surfaces with an additional viscous term.
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Affiliation(s)
- C Drummond
- Centre de Recherche Paul Pascal, CNRS-Université de Bordeaux 1, Pessac Cedex, France
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Braiman Y, Barhen J, Protopopescu V. Control of friction at the nanoscale. PHYSICAL REVIEW LETTERS 2003; 90:094301. [PMID: 12689223 DOI: 10.1103/physrevlett.90.094301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2002] [Indexed: 05/24/2023]
Abstract
We propose a new algorithm to control frictional dynamics of a small array of particles towards preassigned values of the average sliding velocity. The control is based on the concepts of non-Lipschitzian dynamics and terminal attractor. Extensive numerical simulations illustrate the robustness, efficiency, and convenience of the algorithm.
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Affiliation(s)
- Y Braiman
- Center for Engineering Science Advanced Research, Computing and Computational Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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18
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Hartley RR, Behringer RP. Logarithmic rate dependence of force networks in sheared granular materials. Nature 2003; 421:928-31. [PMID: 12606996 DOI: 10.1038/nature01394] [Citation(s) in RCA: 157] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2002] [Accepted: 12/30/2002] [Indexed: 11/09/2022]
Abstract
Many models of slow, dense granular flows assume that the internal stresses are independent of the shearing rate. In contrast, logarithmic rate dependence is found in solid-on-solid friction, geological settings and elsewhere. Here we investigate the rate dependence of stress in a slowly sheared two-dimensional system of photoelastic disks, in which we are able to determine forces on the granular scale. We find that the mean (time-averaged) stress displays a logarithmic dependence on the shear rate for plastic (irreversible) deformations. However, there is no perceivable dependence on the driving rate for elastic (reversible) deformations, such as those that occur under moderate repetitive compression. Increasing the shearing rate leads to an increase in the strength of the force network and stress fluctuations. Qualitatively, this behaviour resembles the changes associated with an increase in density. Increases in the shearing rate also lead to qualitative changes in the distributions of stress build-up and relaxation events. If shearing is suddenly stopped, stress relaxations occur with a logarithmic functional form over long timescales. This slow collective relaxation of the stress network provides a mechanism for rate-dependent strengthening.
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Affiliation(s)
- R R Hartley
- Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Durham, North Carolina 27708-0305, USA
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Lemaître A. Rearrangements and dilatancy for sheared dense materials. PHYSICAL REVIEW LETTERS 2002; 89:195503. [PMID: 12443123 DOI: 10.1103/physrevlett.89.195503] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2001] [Indexed: 05/24/2023]
Abstract
Constitutive equations are proposed for dense materials, based on the identification of two types of free-volume activated rearrangements associated with shear and compaction. Two situations are studied: the case of an amorphous solid in a stress-strain test, and the case of a lubricant in tribology test. Varying parameters, strain softening, shear thinning, and stick-slip motion can be observed.
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Affiliation(s)
- Anaël Lemaître
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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20
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Aranson IS, Tsimring LS. Continuum theory of partially fluidized granular flows. PHYSICAL REVIEW E 2002; 65:061303. [PMID: 12188712 DOI: 10.1103/physreve.65.061303] [Citation(s) in RCA: 127] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2001] [Revised: 01/18/2002] [Indexed: 11/07/2022]
Abstract
A continuum theory of partially fluidized granular flows is developed. The theory is based on a combination of the equations for the flow velocity and shear stresses coupled with the order-parameter equation which describes the transition between the flowing and static components of the granular system. We apply this theory to several important granular problems: avalanche flow in deep and shallow inclined layers, rotating drums, and shear granular flows between two plates. We carry out quantitative comparisons between the theory and experiment.
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Affiliation(s)
- Igor S Aranson
- Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA
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Metcalfe G, Tennakoon SGK, Kondic L, Schaeffer DG, Behringer RP. Granular friction, Coulomb failure, and the fluid-solid transition for horizontally shaken granular materials. PHYSICAL REVIEW E 2002; 65:031302. [PMID: 11909041 DOI: 10.1103/physreve.65.031302] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2000] [Revised: 11/07/2001] [Indexed: 11/07/2022]
Abstract
We present the results of an extensive series of experiments, molecular dynamics simulations, and models that address horizontal shaking of a layer of granular material. The goal of this work was to better understand the transition between the "fluid" and "solid" states of granular materials. In the experiments, the material-consisting of glass spheres, smooth and rough sand-was contained in a container of rectangular cross section, and subjected to horizontal shaking of the form x=A sin(omega(t)). The base of the container was porous, so that it was possible to reduce the effective weight of the sample by means of a vertical gas flow. The acceleration of the shaking could be precisely controlled by means of an accelerometer mounted onboard the shaker, plus feedback control and lockin detection. The relevant control parameter for this system was the dimensionless acceleration, Gamma=Aomega(2)/g, where g was the acceleration of gravity. As Gamma was varied, the layer underwent a backward bifurcation between a solidlike state that was stationary in the frame of the shaker and a fluidlike state that typically consisted of a sloshing layer of maximum depth H riding on top of a solid layer. That is, with increasing Gamma, the solid state made a transition to the fluid state at Gamma(cu) and once the system was in the fluid state, a decrease in Gamma left the system in the fluidized state until Gamma reached Gamma(cd)<Gamma(cu). In the fluidized state, the flow consisted of back and forth sloshing at the shaker frequency, plus a slower convective flow along the shaking direction and additionally in the horizontal direction transverse to the shaking direction. Molecular dynamics simulations show that the last of these flows is associated with shear and dilation at the vertical sidewalls. For Gamma<Gamma(cu) and in the solid state, there was a "gas" of free particles sliding on the surface of the material. These constituted much less than one layer's worth of particles in all cases. If these "sliders" were suppressed by placing a thin strip of plastic on the surface, the hysteresis was removed, and the transition to fluidization occurred at a slightly lower value than Gamma(cd) for the free surface case. The hysteresis was also suppressed if a vertical gas flow from the base was sufficient to support roughly 40% of the weight of the sample. Both the transition to the fluid state from the solid and the reverse transition from the fluid to the solid were characterized by similar divergent time scales. If Gamma was increased above Gamma(cu) by a fractional amount epsilon=(Gamma-Gamma(cu))/Gamma(cu), where epsilon was small, there was a characteristic time tau=Aepsilon(-beta) for the transition from solid to fluid to occur, where beta is 1.00+/-0.06. Similarly, if Gamma was decreased below Gamma(cd) in the fluidized state by an amount epsilon=(Gamma-Gamma(cd))/Gamma(cd), there was also a transient time tau=Bepsilon(-beta), where beta is again indistinguishable from 1.00. In addition, the amplitudes A and B are essentially identical. By placing a small "impurity" on top of the layer, consisting of a heavier particle, we found that the exponent beta varied as the impurity mass squared and changed by a factor of 3. A simple Coulomb friction model with friction coefficients mu(k)<mu(s) for the fluid and solid states predicts a reversible rather than hysteretic transition to the fluid state, similar to what we observe with the addition of the small overload from a plastic strip. In an improved model, we provide a relaxational mechanism that allows the friction coefficient to change continuously between the low and high values. This model produces the hysteresis seen in experiments.
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Affiliation(s)
- Guy Metcalfe
- CSIRO Thermal and Fluids Engineering, Melbourne, VIC 3190, Australia
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Filippov AE, Klafter J, Urbakh M. Confined molecules under shear: from a microscopic description to phenomenology. PHYSICAL REVIEW LETTERS 2001; 87:275506. [PMID: 11800895 DOI: 10.1103/physrevlett.87.275506] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2001] [Indexed: 05/23/2023]
Abstract
A coarse grained two-state model is derived starting from a molecular dynamics description of a molecular system under shear. This model captures the main features of the response of a confined system under shear, and generalizes the phenomenological Tomlinson model for the response of a driven system. The derivation is based on the solution of coupled microscopic equations using a mean field approximation. The two-state model agrees well with the direct numerical solution and offers a practical approach to investigate the response of sheared systems under a broad range of parameters.
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Affiliation(s)
- A E Filippov
- Donetsk Institute for Physics and Engineering of NASU, 83144, Donetsk, Ukraine
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Drummond C, Israelachvili J. Dynamic phase transitions in confined lubricant fluids under shear. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:041506. [PMID: 11308847 DOI: 10.1103/physreve.63.041506] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2000] [Indexed: 05/23/2023]
Abstract
A surface force apparatus was used to measure the transient and steady-state friction forces between molecularly smooth mica surfaces confining thin films of squalane, C30H62, a saturated, branched hydrocarbon liquid. The dynamic friction "phase diagram" was determined under different shearing conditions, especially the transitions between stick-slip and smooth sliding "states" that exhibited a chaotic stick-slip regime. The apparently very different friction traces exhibited by simple spherical, linear, and branched hydrocarbon films under shear are shown to be due to the much longer relaxation times and characteristic length scales associated with transitions from rest to steady-state sliding, and vice versa, in the case of branched liquids. The physical reasons and tribological implications for the different types of transitions observed with spherical, linear, and branched fluids are discussed.
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Affiliation(s)
- C Drummond
- Department of Chemical Engineering, Materials Department, and Materials Research Laboratory, University of California, Santa Barbara, CA 93106, USA
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Caroli C. Slip pulses at a sheared frictional viscoelastic/nondeformable interface. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:1729-37. [PMID: 11088634 DOI: 10.1103/physreve.62.1729] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2000] [Indexed: 11/07/2022]
Abstract
We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a nondeformable one, to slide under shear via a periodic set of "self-healing pulses," i.e., a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.
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Affiliation(s)
- C Caroli
- Groupe de Physique des Solides,* 2 Place Jussieu, 75251 Paris Cedex 05, France
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Langer JS. Viscoplasticity and the dynamics of brittle fracture. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:1351-1360. [PMID: 11088594 DOI: 10.1103/physreve.62.1351] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/1999] [Indexed: 05/23/2023]
Abstract
I propose a model of fracture in which the curvature of the crack tip is a relevant dynamical variable and crack advance is governed solely by plastic deformation of the material near the tip. This model is based on a rate-and-state theory of plasticity introduced in earlier papers by Falk, Lobkovsky, and myself. In the approximate analysis developed here, fracture is brittle whenever the plastic yield stress is nonzero. The tip curvature finds a stable steady-state value at all loading strengths, and the tip stress remains at or near the plastic yield stress. The crack speed grows linearly with the square of the effective stress intensity factor above a threshold that depends on the surface tension. This result provides a possible answer to the fundamental question of how breaking stresses are transmitted through plastic zones near crack tips.
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Affiliation(s)
- JS Langer
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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Hayakawa H. Slow viscous flows in micropolar fluids. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:5477-92. [PMID: 11031601 DOI: 10.1103/physreve.61.5477] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/1999] [Revised: 01/07/2000] [Indexed: 11/07/2022]
Abstract
A systematic calculation of micropolar fluid flows around a sphere and a cylinder is presented. The explicit velocity fields and the drag forces exerted by the fluid flow in both two and three dimensions are obtained. The solution of a steady micropolar fluid flow inside the cylinder is also obtained and is identical to the form observed in an experiment on granular vibrating beds.
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Affiliation(s)
- H Hayakawa
- Graduate School of Human and Environmental Studies, Kyoto University, Japan
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Affiliation(s)
- Markus Porto
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Michael Urbakh
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
| | - Joseph Klafter
- School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel
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28
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Affiliation(s)
- Fereydoon Family
- Department of Physics, Emory University, Atlanta, Georgia 30322, and Center for Engineering Science Advanced Research, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
| | - H. G. E. Hentschel
- Department of Physics, Emory University, Atlanta, Georgia 30322, and Center for Engineering Science Advanced Research, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
| | - Y. Braiman
- Department of Physics, Emory University, Atlanta, Georgia 30322, and Center for Engineering Science Advanced Research, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
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29
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Nielsen SB, Carlson JM, Olsen KB. Influence of friction and fault geometry on earthquake rupture. ACTA ACUST UNITED AC 2000. [DOI: 10.1029/1999jb900350] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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30
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Persson BNJ. Friction dynamics for curved solid surfaces with long-range elasticity. J Chem Phys 2000. [DOI: 10.1063/1.1290025] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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31
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Langer JS, Lobkovsky AE. Rate-and-state theory of plastic deformation near a circular hole. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:6978-83. [PMID: 11970636 DOI: 10.1103/physreve.60.6978] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/1999] [Indexed: 04/18/2023]
Abstract
We show that a simple rate-and-state theory accounts for most features of both time-independent and time-dependent plasticity in a spatially inhomogeneous situation, specifically, a circular hole in a large stressed plate. Those features include linear viscoelastic flow at small applied stresses, strain hardening at larger stresses, and a dynamic transition to viscoplasticity at a yield stress. In the static limit, this theory predicts the existence of a plastic zone near the hole for some but not all ranges of parameters. The rate-and-state theory also predicts dynamic failure modes that we believe may be relevant to fracture mechanics.
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Affiliation(s)
- J S Langer
- Department of Physics, University of California, Santa Barbara, California 93106, USA
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Hayakawa H. Simple model for granular friction. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:4500-4. [PMID: 11970305 DOI: 10.1103/physreve.60.4500] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/1998] [Revised: 06/02/1999] [Indexed: 04/18/2023]
Abstract
We propose a simple phenomenological model to describe the motion of a plate on granular layers pushed at a constant speed. The model contains the order parameter characterizing the transition from a solidlike state to a liquidlike state. The model reproduces the hysteresis in frictional force and the universal profile of the slip velocity, which are observed in experiment. Our model predicts that the area of hysteresis loop depends on the pushing speed.
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Affiliation(s)
- H Hayakawa
- Graduate School of Human and Environmental Studies, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan
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Braiman Y, Hentschel HG, Family F, Mak C, Krim J. Tuning friction with noise and disorder. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:R4737-40. [PMID: 11969507 DOI: 10.1103/physreve.59.r4737] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/1999] [Indexed: 04/18/2023]
Abstract
We present numerical and experimental evidence which demonstrates that under certain conditions friction can be reduced by spatial disorder and/or thermal noise. We discuss possible mechanisms for this behavior.
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Affiliation(s)
- Y Braiman
- Center for Engineering Science Advanced Research, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
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Rozman MG, Urbakh M, Klafter J, Elmer FJ. Atomic Scale Friction and Different Phases of Motion of Embedded Molecular Systems. J Phys Chem B 1998. [DOI: 10.1021/jp981332h] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- M. G. Rozman
- Institut fur Polymere, ETH Zentrum, CH-8092 Zurich, Switzerland, and Institut of Physics, Tartu University, Riia 142, EE2400 Tartu, Estonia
| | - M. Urbakh
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - J. Klafter
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - F.-J. Elmer
- Institut für Physik, Universitat Basel, CH-4056 Basel, Switzerland
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35
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Affiliation(s)
- Jianping Gao
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430
| | - W. D. Luedtke
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430
| | - Uzi Landman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430
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Rozman MG, Urbakh M, Klafter J. Origin of stick-slip motion in a driven two-wave potential. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:6485-6494. [PMID: 9965870 DOI: 10.1103/physreve.54.6485] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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