Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (F. Graner, B. Dollet, C. Raufaste, and P. Marmottant, this issue, 25 (2008) DOI 10.1140/epje/i2007-10298-8), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions.     

Calculation of the Viscosity of Polymer Melts Based on Measurements of the Recovered Rubber-Like Deformation

On the basis of a model of polymer flow, considering the forces of entropic elasticity of extended macromolecules within the Eyring's concept, the relationships between the shear rate, shear stress, viscosity, and recovered rubber-like deformation were derived. The reduction of activation energy of the flow, by an amount proportional to the recovered rubber-like deformation, leads to an exponential decrease of viscosity with increasing shear rates; this nonlinear dependence of viscosity on shear rate (and shear stress) is defined as the viscosity anomaly of polymers. The measurement of deformation recovery after the cessation of polymer flow in the mode of constant shear rate or shear stress on a rotational viscometer confirmed the validity of the theoretical dependences.     

Non-linear rheology of lamellar liquid crystals

We measure the non-linear relation between the shear stress and shear rate in the lyotropic lamellar phase of C₁₂E₅ /water system. The measured shear thinning exponent changes with the surfactant concentration. A simple rheology theory of a lamellar or smectic phase is proposed with a prediction ∼ σ^3/2 , where is the shear rate and σ is the shear stress. We consider that the shear flow passed through the defect structure causes the main dissipation. As the defect line density varies with the shear rate, the shear thinning arises. The defect density is estimated by the dynamic balance between the production and annihilation processes. The defect production is caused by the shear-induced layer undulation instability. The annihilation occurs through the shear-induced defect collision process. Further flow visualization experiment shows that the defect texture correlates strongly with the shear thinning exponent.     

Viscosity of a dusty plasma liquid

We present the results of our experimental study of the flow of a dusty plasma liquid produced by macroparticles in an argon plasma. The dependences of shear viscosity for such a liquid on the magnitude of the external force inducing the dusty plasma liquid flow and on the plasma-generating gas pressure are analyzed. We have established that the viscosity of a dusty plasma medium decreases with increasing shear stress in it, while the viscosity of such a liquid increases with buffer gas pressure. The flow of a dusty plasma liquid under the action of an external force has been found to resemble the plastic deformation of a Bingham body. We suggest that the formation of crystal-like dusty plasma clusters in a “liquid” phase can be responsible for the non-Newtonian behavior of the dusty plasma liquid flow.     

Towards local rheology of emulsions under Couette flow using Dynamic Light Scattering

We present local velocity measurements in emulsions under shear using heterodyne Dynamic Light Scattering. Two emulsions are studied: a dilute system of volume fraction φ = 20% and a concentrated system with φ = 75%. Velocity profiles in both systems clearly show the presence of wall slip. We investigate the evolution of slip velocities as a function of shear stress and discuss the validity of the corrections for wall slip classically used in rheology. Focussing on the bulk flow, we show that the dilute system is Newtonian and that the concentrated emulsion is shear-thinning. In the latter case, the curvature of the velocity profiles is compatible with a shear-thinning exponent of 0.4 consistent with global rheological data. However, even if individual profiles can be accounted for by a power law fluid (with or without a yield stress), we could not find a fixed set of parameters that would fit the whole range of applied shear rates. Our data, thus, raise the question of the definition of a global flow curve for such a concentrated system. These results show that local measurements are a crucial complement to standard rheological tools. They are discussed in the light of recent works on soft glassy materials. Received 1 November 2002 and Received in final form 8 January 2003 / Published online: 1 April 2003 RID="a" ID="a"e-mail: salmon@crpp.u-bordeaux.fr     

Spatial correlation of irreversible displacement in oscillatory-sheared metallic glasses

We report computer simulations on the oscillatory of CuZr metallic glasses at zero temperature with different shear amplitudes. In small system a homogenous shear deformation is found, while in large system an inhomogeneous shear deformation is found with a shear band formed. Concomitantly, spatial correlation of irreversible displacement exhibits an isotropic and exponential decay in the case of homogeneous deformation, whereas a mixed power-law and exponential decay in the case of anisotropic and inhomogeneous deformation. By projecting the azimuthal-dependent correlation function onto the spherical harmonics, we found a strong polar symmetry that accounts for the emerged shear band, and a weaker quadrupolar symmetry that accounts for the elastic filed generated by Eshelby inclusions. By this, we conclude that the anisotropy and decaying formula of the plastic correlation are dominated by the homogeneity or inhomogeneity for the deformation in the metallic glasses.     

Vorticity banding during the lamellar-to-onion transition in a lyotropic surfactant solution in shear flow

We report on the rheology of a lyotropic lamellar surfactant solution (SDS/dodecane/pentanol/ water), and identify a discontinuous transition between two shear thinning regimes which correspond to the low-stress lamellar phase and the more viscous shear-induced multilamellar vesicle, or “onion” phase. We study in detail the flow curve, stress as a function of shear rate, during the transition region, and present evidence that the region consists of a shear-banded phase where the material has macroscopically separated into bands of lamellae and onions stacked in the vorticity direction. We infer very slow and irregular transformations from lamellae to onions as the stress is increased through the two-phase region, and identify distinct events consistent with the nucleation of small fractions of onions that coexist with sheared lamellae.     

Effect of solid solution strengthening by iridium on the nucleation of dislocations in a molybdenum single crystal during nanoindentation

The nucleation of dislocations in single crystals of molybdenum and a Mo-1.5 at % Ir solid solution has been investigated by nanoindentation. In the curve of indentation of a Berkovich indenter into the single crystals, an abrupt transition from elastic to plastic deformation has been observed at a depth of 20–40 nm due to the nucleation of dislocations in the initially dislocation-free region under the contact. Alloying of molybdenum by iridium results in a twofold increase in shear stresses under which dislocations nucleated in the contact. Therefore, the solid solution impurity of iridium in molybdenum leads to an increase not only in the plastic strain resistance (to an increase in the hardness) but also in the elastic shear stresses under which dislocations are generated (homogeneously or heterogeneously) in the contact. The latter effect cannot be explained only by an increase in the elastic moduli because of its smallness; however, it is determined to a large extent by a higher degree of perfection of the solid solution crystal as compared to unalloyed molybdenum.     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Shape dynamics and rheology of soft elastic particles in a shear flow

The shape dynamics of soft, elastic particles in an unbounded simple shear flow is investigated theoretically under Stokes flow conditions. Three types of motion-steady-state, trembling, and tumbling-are predicted, depending on the shear rate, elastic shear modulus, and initial particle shape. The steady-state motion is found to be always stable. In addition, the existence of a trembling regime is documented for the first time in nonvesicle systems, and a complete phase diagram is developed. The rheological properties of dilute suspensions of such soft particles generally exhibit shear-thinning behavior and can even display negative intrinsic viscosity for sufficiently soft particles.     

Plastic response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain rate

We analyze in detail the atomistic response of a model amorphous material submitted to plastic shear in the athermal, quasi-static limit. After a linear stress-strain behavior, the system undergoes a noisy plastic flow. We show that the plastic flow is spatially heterogeneous. Two kinds of plastic events occur in the system: quadrupolar localized rearrangements, and shear bands. The analysis of the individual motion of a particle shows also two regimes: a hyper-diffusive regime followed by a diffusive regime, even at zero temperature.     

Molecular origin of shear thickening in transient polymer networks: A molecular dynamics study

This paper proposes a simple model of transient networks of telechelic associating polymers for molecular simulations and reports the main results obtained by molecular dynamics on the rheological properties of the transient networks. The steady shear viscosity obtained by the non-equilibrium molecular dynamics simulation exhibits shear thickening at moderate shear rates and shear thinning at larger shear rates. The behavior is similar to that observed in experiments of telechelic associating polymers. By analyzing the distribution function of the end-to-end vector of bridge chains as a function of the shear rate, we find that shear thickening is mainly caused by the stress from the bridge chains highly stretched by shear flow. We also find that fracture of the transient network occurs in the shear-thinning regime at high shear rates.     

类固态颗粒物质的剪切弹性行为测量

利用能以极慢变形率直接剪切颗粒固体的实验装置,测量了(玻璃珠)样品对大幅度循环剪切的力-位移曲线,以及一个循环周期后的塑性位移残留.发现随着循环频率的降低,样品会从有限塑性残留的弹塑行为转变到几乎没有塑性的纯弹性行为,同时伴随有率相关性.该转变在剪切力幅度高达样品破坏值的90%时依然存在,但需要极小的变形率(10~(-5)Hz)或惯性数(10~(-8)).这意味着无论是高频小幅度的声波扰动,还是极低频大幅度的直接剪切,静态颗粒固体都可做出纯弹性的力学响应.在足够慢的状态变化范围里,它仍是属于经典弹性理论范畴的一类材料.这个弹性区域一直未被报道和关注,可能是观测它时需要样品的变形率远比通常此类研究中所采用的慢变形还要小许多(大约两个数量级)的缘故.理论上本文测量结果支持描述颗粒固体宏观动力学的基本方程组,不能只有弹塑和率无关行为,它们必须在极慢变形极限下退化为经典弹性理论,并且在这个转变过程中表现出率相关特性.     

Dynamics of viscous vesicles in shear flow

The dynamics of giant lipid vesicles under shear flow is experimentally investigated. Consistent with previous theoretical and numerical studies, two flow regimes are identified depending on the viscosity ratio between the interior and the exterior of the vesicle, and its reduced volume or excess surface. At low viscosity ratios, a tank-treading motion of the membrane takes place, the vesicle assuming a constant orientation with respect to the flow direction. At higher viscosity ratios, a tumbling motion is observed in which the whole vesicle rotates with a periodically modulated velocity. When the shear rate increases, this tumbling motion becomes increasingly sensitive to vesicle deformation due to the elongational component of the flow and significant deviations from simpler models are observed. A good characterization of these various flow regimes is essential for the validation of analytical and numerical models, and to relate microscopic dynamics to macroscopic rheology of suspensions of deformable particles, such as blood.     

The mechanisms of plastic strain accommodation during the high strain rate collapse of corrugated Ni–Al laminate cylinders

The Thick-Walled Cylinder method was used on corrugated Ni–Al reactive laminates to examine how their mesostructures accommodate large strain, high strain rate plastic deformation and to examine the potential for intermetallic reaction initiation due to mechanical stimuli. Three main mesoscale mechanisms of large plastic strain accommodation were observed in addition to the bulk distributed uniform plastic flow: (a) the extrusion of wedge-shaped regions into the interior of the cylinder along planes of easy slip provided by angled layers, (b) the development of trans-layer shear bands in the layers with orientation close to radial and (c) the cooperative buckling of neighbouring layers perpendicular to the radius. These mesoscale mechanisms acted to block the development of periodic patterns of multiple, uniformly distributed, shear bands that have been observed in all previously examined solid homogeneous materials and granular materials. The high-strain plastic flow within the shear bands resulted in the dramatic elongation and fragmentation of Ni and Al layers. The quenched reaction between Al and Ni was observed inside these trans-layer shear bands and in a number of the interfacial extruded wedge-shaped regions. The reaction initiated in these spots did not ignite the bulk of the material, demonstrating that these mesostructured Ni-Al laminates are able to withstand high-strain, high-strain rate deformation without reaction. Numerical simulations of the explosively collapsed samples were performed using the digitized geometry of corrugated laminates and predictions of the final, deformed mesostructures agree with the observed deformation patterns.     

Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluids

With the eventual aim of describing flowing elasto-plastic materials, we focus here on the elementary process of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear strain. We characterize the effect of a nearby wall on this perturbation, and quantify the importance of finite-size effects. Although most of our explicit formulae refer to 2D situations, our statements hold for 3D situations as well.     

Acoustic heating produced in the thermoviscous flow of a Bingham plastic

This study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic’s viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation governing acoustic heating, and to retain those belonging to the thermal mode. The nonlinear terms of the final equation are a result of interaction between sounds and the thermal mode. In the field of intense sound, the resulting nonlinear acoustic terms form a driving force for the heating. The final governing dynamic equation of the thermal mode is valid in a weakly nonlinear flow. It is instantaneous, and does not imply that sounds be periodic. The equations governing the dynamics of both sounds and the thermal mode depend on sign of the shear rate. An example of the propagation of a bipolar initially acoustic pulse and the evolution of the heating induced by it is illustrated and discussed.