Heterogeneous shear in hard sphere glasses

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Rheology of colloidal and metallic glass formers

Colloidal hard-sphere suspensions are convenient experimental models to understand soft matter, and also by analogy the structural-relaxation behavior of atomic or small-molecular fluids. We discuss this analogy for the flow and deformation behavior close to the glass transition. Based on a mapping of temperature to effective hard-sphere packing, the stress–strain curves of typical bulk metallic glass formers can be quantitatively compared with those of hard-sphere suspensions. Experiments on colloids give access to the microscopic structure under deformation on a single-particle level, providing insight into the yielding mechanisms that are likely also relevant for metallic glasses. We discuss the influence of higher-order angular signals in connection with non-affine particle rearrangements close to yielding. The results are qualitatively explained on the basis of the mode-coupling theory. We further illustrate the analogy of pre-strain dependence of the linear-elastic moduli using data on PS-PNiPAM suspensions.

Probing the Degree of Heterogeneity within a Shear Band of a Model Glass

Recent experiments provide evidence for density variations along shear bands in metallic glasses with a length scale of a few hundred nanometers. Via molecular dynamics simulations of a generic binary glass model, here we show that this is strongly correlated with variations of composition, coordination number, viscosity, and heat generation. Individual shear events along the shear band path show a mean distance of a few nanometers, comparable to recent experimental findings on medium range order. The aforementioned variations result from these localized perturbations, mediated by elasticity.

Shear-density coupling for a compressible single-component yield-stress fluid

Flow behavior of a single-component yield stress fluid is addressed on the hydrodynamic level. A basic ingredient of the model is a coupling between fluctuations of density and velocity gradient via a Herschel-Bulkley-type constitutive model. Focusing on the limit of low shear rates and high densities, the model approximates well-but is not limited to-gently sheared hard sphere colloidal glasses, where solvent effects are negligible. A detailed analysis of the linearized hydrodynamic equations for fluctuations and the resulting cubic dispersion relation reveals the existence of a range of densities and shear rates with growing flow heterogeneity. In this regime, after an initial transient, the velocity and density fields monotonically reach a spatially inhomogeneous stationary profile, where regions of high shear rate and low density coexist with regions of low shear rate and high density. The steady state is thus maintained by a competition between shear-induced enhancement of density inhomogeneities and relaxation via overdamped sound waves. An analysis of the mechanical equilibrium condition provides a criterion for the existence of steady state solutions. The dynamical evolution of the system is discussed in detail for various boundary conditions, imposing either a constant velocity, shear rate, or stress at the walls.

Stress-structure relation in dense colloidal melts under forward and instantaneous reversal of the shear

A dense supercooled colloidal melt in forward shear from a quiescent state shows overshoot in the shear stress at 10% strain with an unchanged fluid structure at equal stress before and after overshoot. In addition, we find an overshoot in the normal stress with a monotonic increase in the osmotic pressure at an identical strain. The first and second normal stresses become comparable in magnitude and opposite in sign. A functional dependence of the steady state stress and osmotic pressure with the Péclet number demonstrates the signature of crossover between Newtonian and nearly-Newtonian regimes. Moreover, instantaneous shear reversal from a steady state exhibiting the Bauschinger effect, where a strong history dependence is observed depending on the time of the flow reversal. The distribution of the particulate stress and osmotic pressure at the point of the flow reversal is shown to be a signature of the subsequent response. We link the history dependence of the stress-strain curves to changes in the fluid structure measured through the angular components of the radial distribution function. A uniform compression in the transition from forward to reversed flowing states is found.

Flow instability due to coupling of shear-gradients with concentration: non-uniform flow of (hard-sphere) glasses

Flow-induced instabilities that lead to non-uniform stationary flow profiles have been observed in many different soft-matter systems. Two types of instabilities that lead to banded stationary states have been identified, which are commonly referred to as gradient- and vorticity-banding. The molecular origin of these instabilities is reasonably well understood. A third type of instability that has been proposed phenomenologically [Europhys. Lett., 1986, 2, 129 and Phys. Rev. E, 1995, 52, 4009] is largely unexplored. Essential to this "Shear-gradient Concentration Coupling" (SCC-) instability is a mass flux that is induced by spatial gradients of the shear rate. A possible reason that this instability has essentially been ignored is that the molecular origin of the postulated mass flux is not clear, and no explicit expressions for the shear-rate and concentration dependence of the corresponding transport coefficient exist. It is therefore not yet known what types of flow velocity- and concentration-profiles this instability gives rise to. In this paper, an expression for the transport coefficient corresponding to the shear-gradient induced mass flux is derived in terms of the shear-rate dependent pair-correlation function, and Brownian dynamics simulations for hard-spheres are presented that specify the shear-rate and concentration dependence of the pair-correlation function. This allows to explicitly formulate the coupled advection-diffusion equation and an equation of motion for the suspension flow velocity. The inclusion of a non-local contribution to the stress turns out to be essential to describe the SCC-banding transition. The coupled equations of motion are solved numerically, and flow- and concentration-profiles are discussed. It is shown that the SCC-instability occurs within the glass state at sufficiently small shear rates, leading to a banded flow-profile where one of the bands is non-flowing.

Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects

We study the shearing rheology of dense suspensions of elastic capsules, taking aggregation-free red blood cells as a physiologically relevant example. Particles are non-Brownian and interact only via hydrodynamics and short-range repulsive forces. An analysis of the different stress mechanisms in the suspension shows that the viscosity is governed by the shear elasticity of the capsules, whereas the repulsive forces are subdominant. Evidence for a dynamic yield stress above a critical volume fraction is provided and related to the elastic properties of the capsules. The shear stress is found to follow a critical jamming scenario and is rather insensitive to the tumbling-to-tank-treading transition. The particle pressure and normal stress differences display some sensitivity to the dynamical state of the cells and exhibit a characteristic scaling, following the behavior of a single particle, in the tank-treading regime. The behavior of the viscosity in the fluid phase is rationalized in terms of effective medium models. Furthermore, the role of confinement effects, which increase the overall magnitude and enhance the shear-thinning of the viscosity, is discussed.

Impact of attractive interactions on the rheology of dense athermal particles

Using numerical simulations, the rheological response of an athermal assembly of soft particles with tunable attractive interactions is studied in the vicinity of jamming. At small attractions, a fragile solid develops and a finite yield stress is measured. Moreover, the measured flow curves have unstable regimes, which lead to persistent shear banding. These features are rationalized by establishing a link between the rheology and the interparticle connectivity, which also provides a minimal model to describe the flow curves.

Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells

Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of transition, but rather follows a simple scaling law independent of volume fraction.

Single-particle fluctuations and directional correlations in driven hard-sphere glasses

Via event-driven molecular dynamics simulations and experiments, we study the packing-fraction and shear-rate dependence of single-particle fluctuations and dynamic correlations in hard-sphere glasses under shear. At packing fractions above the glass transition, correlations increase as shear rate decreases: the exponential tail in the distribution of single-particle jumps broadens and dynamic four-point correlations increase. Interestingly, however, upon decreasing the packing fraction, a broadening of the exponential tail is also observed, while dynamic heterogeneity is shown to decrease. An explanation for this behavior is proposed in terms of a competition between shear and thermal fluctuations. Building upon our previous studies [Chikkadi et al., Europhys. Lett. 100, 56001 (2012)], we further address the issue of anisotropy of the dynamic correlations.

Residual stresses in glasses

The history dependence of glasses formed from flow-melted steady states by a sudden cessation of the shear rate γ[over ˙] is studied in colloidal suspensions, by molecular dynamics simulations and by mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of γ[over ˙]t, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables but differing static properties.