Networks and dense suspensions frequently reside near a boundary between soft (or fluid-like) and rigid (or solid-like) regimes. Transitions between these regimes can be driven by changes in structure, density, or applied stress or strain. In general, near the onset or loss of rigidity in these systems, dissipation-limiting heterogeneous nonaffine rearrangements dominate the macroscopic viscoelastic response, giving rise to diverging relaxation times and power-law rheology. Here, we describe a simple quantitative relationship between nonaffinity and the excess viscosity. We test this nonaffinity-viscosity relationship computationally and demonstrate its rheological consequences in simulations of strained filament networks and dense suspensions. We also predict critical signatures in the rheology of semiflexible and stiff biopolymer networks near the strain stiffening transition.
We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping magnitude $ζ$ in the low-temperature limit, we identify two well defined flow regimes, separated by a thin (temperature-dependent) crossover region. In the overdamped regime, the athermal rheology is governed by the competition between elastic forces and viscous forces, whose ratio gives the Weissenberg number $Wi= ζ\dotγ$ (up to elastic parameters); the macroscopic stress $Σ$ follows the frequently encountered Herschel-Bulkley law $Σ=…
We study the dynamical rheology of spring networks with a percolation model constructed by bond dilution in a two-dimensional triangular lattice. Hydrodynamic interactions are implemented by a Stokesian viscous coupling between the network nodes and a uniformly deforming liquid. Our simulations show that in a critical connectivity regime, these systems display weak power law rheology in which the complex shear modulus scales with frequency as G^* ~ (i * omega)^Delta where Delta = 0.41, in discord with a mean field prediction of Delta = 1/2. The weak power law rheology in the critical regime ca…
We report a transition from a disordered state to an ordered state in the flow of nearly mono-disperse granular matter flowing in an inclined channel with a bumpy base, in discrete element method simulations. For low particle-sidewall friction coefficients, the particles are disordered and the Bagnold velocity profile is obtained. However, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cro…
We discuss the linear and non-linear rheology of concentrated (sub)microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from…
We investigate the nonlinear rheological behavior of colloidal suspensions of Laponite, a synthetic clay, driven by a steady and homogeneous shear strain. We show that the external drive leads to a drastic slowing down of the aging dynamics or even, in some cases, in the rejuvenation of the system. Under shear, after a surprisingly long time, the spontaneous aging process observed at rest is suppressed. The system then reaches a non-equilibrium stationary state, characterised by a complex viscosity depending on the applied shear rate. In addition, the glass exhibits a non-Newtonian shear-thinn…
A fundamental challenge for disordered solids is predicting macroscopic yield from the microscopic arrangements of constituent particles. Yield is accompanied by a sudden and large increase in energy dissipation due to the onset of plastic rearrangements. This suggests that one path to understanding bulk rheology is to map particle configurations to their mode of deformation. Here, we perform laboratory experiments and numerical simulations that are designed to do just that: 2D dense colloidal systems are subjected to oscillatory shear, and particle trajectories and bulk rheology are measured.…
Soft cellular systems, such as foams or biological tissues, exhibit highly complex rheological properties, even in the quasistatic regime, that numerical modeling can help to apprehend. We present a numerical implementation of quasistatic strain within the widely used cellular Potts model. The accuracy of the method is tested by simulating the quasistatic strain 2D dry foams, both ordered and disordered. The implementation of quasistatic strain in CPM allows the investigation of sophisticated interplays between stress-strain relationship and structural changes that take place in cellular syste…
A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached both with thermal quenches and small perturbations of the system. The scaling of this relaxati…
In the last decade many research efforts have been focused on understanding the rheology of disordered materials, and several theoretical predictions have been put forward regarding their yielding behavior. Nevertheless, not many experiments nor molecular dynamics simulations were dedicated to testing those theoretical predictions. Here we use computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics, and self-propelled, dense active systems. In the active systems a yielding transition is observed as expected, when the self-propul…
In recent years, the paradigm of `soft glassy matter' has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting `soft glassy rheology' (SGR) model treats the shear stress in isolation, effectively `scalarizing' the stress and strain rate tensors. Here we offer generalizations of the SGR model that combine its nontrivial aging and yield properties with a tensorial structure that can be specifically adapted, for example, to the description of fluid film assemblies or disordered foams.
Inverse Patchy Colloids (IPCs) differ from conventional patchy particles because their patches repel (rather than attract) each other and attract (rather than repel) the part of the colloidal surface that is free of patches. These particular features occur, .e.g., in heterogeneously charged colloidal systems. Here we consider overall neutral IPCs carrying two, relatively small, polar patches. Previous studies of the same model under planar confinement have evidenced the formation of branched, disordered aggregates composed of ring-like structures. We investigate here the bulk behavior of the s…
In this work we develop a theoretical framework for the localization of flow in the steadily flowing regime of sheared disordered solids with inertial dynamics on a microscopic scale. To this aim we perform rheology studies at fixed shear rate on a 3D model of dense disordered solid. Our particle based simulations reveal the existence of heterogeneous shear-profiles in the stationary flow under homogeneous driving conditions. To rationalize this result, we propose a continuum model that couples the dynamics of the local flow to the evolution of a kinetic temperature field. A linear stability a…
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；College of Physics, Chengdu University of Technology（成都理工大学物理学院）；Med-X Research Institute and School of Biomedical Engineering, Shanghai Jiao Tong University（上海交通大学Med-X研究院与生物医学工程学院）；School of Physics, East China Normal University（华东师范大学物理系）；Jiangsu First-Imaging Medical Equipment Co., Ltd.（江苏首影医疗设备有限公司）；State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology（成都大学地质灾害防治与地质环境国家重点实验室）
The change in contact angles due to the injection of low salinity water or any other wettability altering agent in an oil-rich porous medium is modeled by a network model of disordered pores transporting two immiscible fluids. We introduce a dynamic wettability altering mechanism, where the time dependent wetting property of each pore is determined by the cumulative flow of water through it. Simulations are performed to reach steady-state for different possible alterations in the wetting angle ($θ$). We find that deviation from oil-wet conditions re-mobilizes the stuck clusters and increases t…
Collagen is the most abundant extracellular-matrix protein in mammals and the main structural and load-bearing element of connective tissues. Collagen networks show remarkable strain-stiffening properties which tune the mechanical functions of tissues and regulate cell behaviours. Linear and non-linear mechanical properties of in-vitro disordered collagen networks have been widely studied using rheology for a range of self-assembly conditions in recent years. However, a one to one correlation between the onset of macroscopic network failure and local deformations inside the sample is yet to be…
We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime - completely absent in the known vacuum response - exhibits coupled fluid flow and network deformation, with both components responding non-affinely. This regime contains an additional plateau (peak) in the frequency-dependent storage (loss) modulus - features which vanish without full hydrodynamic interactions. The mechanical response of immersed networks such as biopolymers and hydrogels is thus richer than previously established, a…
We report on the frictional properties of a single contact between a glassy polymer lens and a flat silica substrate covered either by a disordered or by a self-assembled alkylsilane monolayer. We find that, in contrast to common belief, the Amontons proportionality between frictional and normal stresses does not hold. Besides, we observe that the velocity dependence of the sliding stress is strongly sensitive to the structure of the silane layer. Analysis of the frictional rheology observed on both disordered and self-assembled monolayers suggests that dissipation is controlled by the plastic…
Collagen forms the structural scaffold of connective tissues in all mammals. Tissues are remarkably resistant against mechanical deformations because collagen molecules hierarchically self-assemble in fibrous networks that stiffen with increasing strain. Nevertheless, collagen networks do fracture when tissues are overloaded or subject to pathological conditions such as aneurysms. Prior studies of the role of collagen in tissue fracture have mainly focused on tendons, which contain highly aligned bundles of collagen. By contrast, little is known about fracture of the orientationally more disor…
A minimal model for studying the mechanical properties of amorphous solids is a disordered network of point masses connected by unbreakable springs. At a critical value of its mean connectivity, such a network becomes fragile: it undergoes a rigidity transition signaled by a vanishing shear modulus and transverse sound speed. We investigate analytically and numerically the linear and non-linear visco-elastic response of these fragile solids by probing how shear fronts propagate through them. Our approach, that we tentatively label shear front rheology, provides an alternative route to standard…
We investigate the nonequilibrium behavior of dense, plastic-crystalline suspensions of mildly anisotropic colloidal hard dumbbells under the action of an oscillatory shear field by employing Brownian dynamics computer simulations. In particular, we extend previous investigations, where we uncovered novel nonequilibrium phase transitions, to other aspect ratios and to a larger nonequilibrium parameter space, that is, a wider range of strains and shear frequencies. We compare and discuss selected results in the context of novel scattering and rheological experiments. Both simulations and experi…
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by executing a series of cell rearrangements, or T1 transitions. In a disordered 2D vertex model, the tissue fluidizes when the T1 energy barriers disappear as the target shape index approaches a critical value ($s^*_{0} \sim 3.81$), and the shear modulus describing the linear response also vanishes at this same critical point. However, the ordered ground states of…
Solid-to-solid transition in dense assemblies of elongated cells
Sun Yat-sen University（中山大学）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University（中山大学物理学院磁电物理与器件广东省重点实验室）；Interdisciplinary Research Center for Physical Mechanics in Complex Systems and Its Engineering Applications, School of Physics, Sun Yat-sen University（中山大学物理学院复杂系统力学及其工程应用交叉研究中心）；Aix Marseille Univ, CNRS and Turing Centre for Living Systems, CPT (UMR 7332)（艾克斯-马赛大学、法国国家科学研究中心及图灵生命系统中心，CPT（UMR 7332））；Aix Marseille Univ, Université de Toulon, CNRS, LAI (UMR 7333), Turing Centre for Living Systems（艾克斯-马赛大学、土伦大学、法国国家科学研究中心、LAI（UMR 7333）及图灵生命系统中心）
We study the rheological response of dense suspensions of elliptical particles, with an aspect ratio equal to 3, under oscillatory shear flows and imposed pressure by numerical simulations. Like for the isotropic particles, we find that the oscillatory shear flows respect the Cox-Merz rule at large oscillatory strains but differ at low strains, with a lower viscosity than the steady shear and higher shear jamming packing fractions. However, unlike the isotropic cases (i.e., discs and spheres), frictionless ellipses get dynamically arrested in their initial orientational configuration at small …
