Internal Stress in a Model Elastoplastic Fluid

Ooshida, Takeshi; Sekimoto, Ken

doi:10.1103/physrevlett.95.108301

Cited by 25 publications

(22 citation statements)

References 16 publications

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“…Models which take into account plastic deformation of elastic media under external fields can explain the memory effect of vibration. [26][27][28] Here, there is one big question about the other memory effect, namely the ''memory effect of flow'': some pastes remember the direction of vibration and flow, but others remember only the direction of vibration and cannot remember the flow direction. The emergence of the memory effect of flow depends on what kind of colloidal particles we use.…”

Section: Introductionmentioning

confidence: 99%

Effect of Interaction on the Formation of Memories in Paste

Matsuo

Nakahara

2012

J. Phys. Soc. Jpn.

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A densely packed colloidal suspension with plasticity, called paste, is known to remember directions of vibration and flow. These memories in paste can be visualized by the morphology of desiccation crack patterns. Here, we find that paste made of charged colloidal particles cannot remember flow direction. If we add sodium chloride into such paste to screen the Coulombic repulsive interaction between particles, the paste comes to remember flow direction. That is, one drop of salt water changes memory effect in the paste and thereby we can tune the morphology of desiccation crack patterns more precisely.

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Section: Introductionmentioning

confidence: 99%

Effect of Interaction on the Formation of Memories in Paste

Matsuo

Nakahara

2012

J. Phys. Soc. Jpn.

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“…In the realm of rheology, some Maxwelltype constitutive equations admit a rheological analogue of vorticity that becomes frozen in the limit of slow stress relaxation. 15) Such a frozen field can be explicitly constructed in some elastoplastic fluid models, 16,17) which gives a possible clarification of the memory effect in pastes found by Nakahara and Matsuo 18) in experimental studies of desiccation cracks. They found that, shaking a layer of wet paste for several tens of seconds and then leaving it still until it dries (typically for a few days), one can produce a strikingly anisotropic crack pattern.…”

Section: Introductionmentioning

confidence: 99%

Continuum Theory of Single-File Diffusion in Terms of Label Variable

et al. 2011

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The problem of one-dimensional diffusion is studied for Brownian particles with short-range repulsive interaction. The adoption of the continuous label variable as the spatial coordinate, inspired by the Lagrangian description in fluid mechanics, is shown to be effective in correct prediction of the anomalous diffusion, in which the mean square displacement of the particle grows in proportion to ffi ffi t p . The method is also applicable to the cases in which an external field is present. This suggests potential usefulness of the label variable formulation in describing the slow dynamics of glassy systems.

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“…This, or one of its variants, is often invoked in the analysis of bulk foams. However, as in the recent work of Takeshi and Sekimoto [15], we also include an elastic response, so that the model we propose has four key ingredients: elasticity up to a yield stress, plasticity, internal viscosity, and a viscous drag force.…”

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confidence: 99%

Two-Dimensional Foam Rheology with Viscous Drag

2006

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We formulate and apply a continuum model that incorporates elasticity, yield stress, plasticity, and viscous drag. It is motivated by the two-dimensional foam rheology experiments of Debregeas et al. [Phys. Rev. Lett. 87, 178305 (2001)] and Wang et al. [Phys. Rev. E 73, 031401 (2006)], and is successful in exhibiting their principal features, which are an exponentially decaying velocity profile and strain localization. Transient effects are also identified. DOI: 10.1103/PhysRevLett.97.038302 PACS numbers: 83.80.Iz, 82.70.Rr, 83.10.Ff While initially two-dimensional (2D) foams were introduced only as a simple model system for numerical and theoretical studies [1,2], recent years have also seen a variety of rheological experiments on so-called quasi-2D foams, i.e., foams consisting of a single layer of bubbles [3][4][5][6][7][8]. Using bubbles trapped between two glass plates (Hele-Shaw cell) in a cylindrical Couette geometry (the foam is contained between two concentric cylinders), Debrégeas et al. found that the flow of the foam localizes near the inner moving wall with an exponential velocity profile, forming shear bands [4]. While quasistatic cellular simulations [9,10] showed some agreement with the results, they continue to excite debate [7], especially in regard to the localization of shear and deformation [6], which is the salient feature of the experiment. Recently, Wang et al. have extended shear experiments to the simpler planar geometry [8]. While their experiments using bubbles between a liquid pool and a glass plate showed the formation of shear bands with an exponential velocity profile, a nearly linear velocity profile was obtained for a bubble floating on the liquid (bubble raft or Bragg raft). This has evidenced the crucial role played by the method used to confine the bubbles and indicates that the nonuniform stress imposed by the Couette geometry is not sufficient to explain the formation of shear bands with exponential decaying velocity.In this Letter, we introduce an elementary continuum model for the analysis of rheological properties of a twodimensional foam. It includes a viscous drag that has no counterpart in conventional 3D foam rheology. Our model is therefore closely related to the 2D viscous froth model [11] which was designed to enable dynamic simulations to be undertaken with the full cellular structure of the foam and included just such a viscous drag. Here the viscous drag will enter as a term in the continuum description, depending on a local average of the boundary velocity. Experiment and theory have already addressed this force as it arises in the flow of bubbles in cylindrical tubes and in narrow channels [5]. It is often associated with the name of Bretherton, who showed that the force varies with twothirds the power of velocity [12]. In some circumstances, a power law of one-half is suggested [13]. Nevertheless, as in the case of the 2D viscous froth, we adopt a linear form in order to keep the model and the analysis simple, in a search for a qualitative and semiquan...

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Internal Stress in a Model Elastoplastic Fluid

Cited by 25 publications

References 16 publications

Effect of Interaction on the Formation of Memories in Paste

Effect of Interaction on the Formation of Memories in Paste

Continuum Theory of Single-File Diffusion in Terms of Label Variable

Two-Dimensional Foam Rheology with Viscous Drag

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