In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.
The decay of a small homogeneous perturbation of the temperature of a dilute granular gas in the steady uniform shear flow state is investigated. Using kinetic theory based on the inelastic Boltzmann equation, a closed equation for the decay of the perturbation is derived. The equation involves the generalized shear viscosity of the gas in the time-dependent shear flow state, and therefore it predicts relevant rheological effects beyond the quasi-elastic limit. A good agreement is found when comparing the theory with molecular dynamics simulation results. Moreover, the Onsager postulate on the…
Numerical simulations of vesicle suspensions are performed in two dimensions to study their dynamical and rheological properties. An hybrid method is adopted, which combines a mesoscopic approach for the solvent with a curvature-elasticity model for the membrane. Shear flow is induced by two counter-sliding parallel walls, which generate a linear flow profile. The flow behavior is studied for various vesicle concentrations and viscosity ratios between the internal and the external fluid. Both the intrinsic viscosity and the thickness of depletion layers near the walls are found to increase wit…
Different from previous modelings of self-propelled particles, we develop a method to propel the particles with a constant average velocity instead of a constant force. This constant propulsion velocity (CPV) approach is validated by its agreement with the conventional constant propulsion force (CPF) approach in the flowing regime. However, the CPV approach shows its advantage of accessing quasistatic flows of yield stress fluids with a vanishing propulsion velocity, while the CPF approach is usually unable to because of finite system size. Taking this advantage, we realize the cyclic self-pro…
We analyze the electro-rheological effect in immiscible fluid mixtures with dielectric mismatch. By taking the electric field effect into account, which couples to the dynamics of domain morphology under flow, we propose a set of electro-rheological constitutive equations valid under the condition where the relative magnitude of the flow field is stronger than that of the electric field. Through the comparison with recent experiment, we point out a unique dynamical stress response inherent in situations, where the cross-coupling between different fields is essential.
A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice (CML) model for such complex spatio-temporal behaviour in a passively sheared nematic liquid crystal, using local maps constructed so as to accurately de…
The nonlinear rheological properties of dense suspensions are discussed within simplified models, suggested by a recent first principles approach to the model of Brownian particles in a constant-velocity-gradient solvent flow. Shear thinning of colloidal fluids and dynamical yielding of colloidal glasses arise from a competition between a slowing down of structural relaxation, because of particle interactions, and enhanced decorrelation of fluctuations, caused by the shear advection of density fluctuations. A mode coupling approach is developed to explore the shear-induced suppression of parti…
We investigate the dynamics and rheological properties of a circular colloidal cluster that is continuously sheared by magnetic and optical torques in a two-dimensional (2D) Taylor-Couette geometry. By varying the two driving fields, we obtain the system flow diagram and report the velocity profiles along the colloidal structure. We then use the inner magnetic trimer as a microrheometer, and observe continuous thinning of all particle layers followed by thickening of the third one above a threshold field. Experimental data are supported by Brownian dynamics simulations. Our approach gives a un…
We report on numerical simulations of simple models of athermal, bidisperse, soft-core, massive disks in two dimensions, as a function of packing fraction $ϕ$, inelasticity of collisions as measured by a parameter $Q$, and applied uniform shear strain rate $\dotγ$. Our particles have contact interactions consisting of normally directed elastic repulsion and viscous dissipation, as well as tangentially directed viscous dissipation, but no inter-particle Coulombic friction. Mapping the phase diagram in the $(ϕ,Q)$ plane for small $\dotγ$, we find a sharp first-order rheological phase transition …
We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that was generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements reviously published by Aussillous {\it et al.} (J. Fluid Mech., vol. 736, 2013, pp. 594-615). The highly-resolved simulation data allows to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phase, which is information needed to infer …
We investigate a rheological property of a dense granular material under shear. By a numerical experiment of the system with constant volume, we find a critical volume fraction at which the shear stress and the pressure behave as power-law functions of the shear strain rate. We also present a simple scaling argument that determines the power-law exponents. Using these results, we interpret a power-law behavior observed in the system under constant pressure.
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(ϕ,F)$: at low $ϕ$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $ϕ$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy w…
Diverging correlation lengths on either side of the jamming transition are used to formulate a rheological model of granular shear flow, based on the propagation of stress through force chain networks. The model predicts three distinct flow regimes, characterized by the shear rate dependence of the stress tensor, that have been observed in both simulations and experiments. The boundaries separating the flow regimes are quantitatively determined and testable. In the limit of jammed granular solids, the model predicts the observed anomalous scaling of the shear modulus and a new relation for the…
We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent close to 0.5. Interestingly, the apparent viscosity can be related to a single relevant time scale $t_{rel}$, suggesting a strong connection between the local dynamics and the global mechanical behaviour. We propose a model based on the competition between the nucleation and the avalanche-like propagation of spatial strain heterogeneities. This model can explain…
We describe an optical fiber based interferometer to measure velocity profiles in sheared complex fluids using Dynamic Light Scattering (DLS). After a review of the theoretical problem of DLS under shear, a detailed description of the setup is given. We outline the various experimental difficulties induced by refraction when using a Couette cell. We also show that homodyne DLS is not well suited to measure quantitative velocity profiles in narrow-gap Couette geometries. On the other hand, the heterodyne technique allows us to determine the velocity field inside the gap of a Couette cell. All t…
A Landau theory is presented for the structural transition of electrically stabilized colloidal crystals under shear. The model suggests that a structural transition from an ordered layered colloidal crystal into a disordered structure occurs at a critical shear stress. The shear induced structural transition is related to a change of the rheological properties caused by the variation of the microstructure which can be verified by scattering experiments. The theory is used to establish the shape of the flow curves. A good qualitative agreement with experimental results can be achieved, while a…
The rheology of dense Brownian suspensions of hard spheres is investigated numerically beyond the low shear rate Newtonian regime. We analyze an athermal analogue of these suspensions, with an effective logarithmic repulsive potential representing the vibrational entropic forces. We show that both systems present the same rheology without adjustable parameters. Moreover, all rheological responses display similar Herschel-Bulkley relations once the shear stress and the shear rate are respectively rescaled by a characteristic stress scale and by a microscopic reorganization time-scale, both rela…
The microscopic deformation mechanism of charged colloidal glasses with extended-range interactions under shear is investigated by in-situ small-angle neutron scattering, and a dynamically correlated region (DCR) is identified. This short-lived region provides the resistance to the configurational rearrangement imposed by the external deformation, as evidenced by the evolution of the size of DCR in the shear thinning regime and the quantitative agreement between the local stress sustained by DCR and the macroscopic stress from rheological measurements at low and mediate shear rates. This findi…
We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless, disks at fixed packing fraction $ϕ$ in two dimensions. We use these distributions to address the question of how pressure increases as $ϕ$ increases above the jamming point $ϕ_J$, $p\sim |ϕ- ϕ_J|^y$. For statically jammed ensembles, our results are consistent with the exponent $y$ being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of $y$ is consistent wit…
The first normal stress difference (${\mathcal N}_1$) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in {\it dilute} granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behaviour in the {\it dense} limit. As in the elastic hard-sphere fluids, ${\mathcal N}_1$ remains {\it positive} (if the stress is define…
We present an experimental study of the flow dynamics of a lamellar phase sheared in the Couette geometry. High-frequency ultrasonic pulses at 36 MHz are used to measure time-resolved velocity profiles. Oscillations of the viscosity occur in the vicinity of a shear-induced transition between a high-viscosity disordered fluid and a low-viscosity ordered fluid. The phase coexistence shows up as shear bands on the velocity profiles. We show that the dynamics of the rheological data result from two different processes: (i) fluctuations of slip velocities at the two walls and (ii) flow dynamics in …
We develop computational methods that incorporate shear into fluctuating hydrodynamics methods. We are motivated by the rheological responses of complex fluids and soft materials. Our approach is based on continuum stochastic hydrodynamic equations that are subject to shear boundary conditions on the unit periodic cell in a manner similar to the Lees-Edwards conditions of molecular dynamics. Our methods take into account consistently the microstructure elastic mechanics, fluid-structure hydrodynamic coupling, and thermal fluctuations. For practical simulations, we develop numerical methods for…
Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies and variability under different loading conditions have not been fully explored. Here, we use a non-equilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as presence and absence of acoustic vibrations. Our results suggest that at low and inte…
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.…
The rheology of non-colloidal suspensions under cyclic shear is studied numerically. The main findings are a strain amplitude ($γ_0$) dependent response in the shear stress and second normal stress difference ($N_2$). Specifically, we find a reduced viscosity, an enhanced intracycle shear thinning, the onset of a finite $N_2$ and its frequency doubling, all near a critical strain amplitude $γ_c$ that scales with the volume fraction $ϕ$ as $γ_c \sim ϕ^{-2}$. These rheological changes also signify a reversible-irreversible transition (RIT), dividing stroboscopic particle dynamics into a reversib…
Dissipation and microstructure in sheared active suspensions of squirmers
School of Advanced Manufacturing Engineering, Nanjing University（南京大学高级制造工程学院）；Department of Mechanical Engineering and Institute of Applied Mathematics, University of British Columbia（不列颠哥伦比亚大学机械工程系与应用数学研究所）
We carry out constant volume simulations of steady-state, shear driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction $ϕ$ and a parameter $Q$ that measures the elasticity of binary particle collisions. We find a $Q^*(ϕ)$ that marks the clear crossover from a region characteristic of strongly inelastic collisions, $Q<Q^*$, to a region characteristic of weakly inela…
Muscle cells with sarcomeric structure exhibit highly nontrivial passive mechanical response. The difficulty of its continuum modeling is due to the presence of long-range interactions transmitted by extended protein skeleton. To build a rheological model for muscle 'material' we use a stochastic micromodel and derive a linear response theory for a half-sarcomere. Instead of the first order rheological equation, anticipated by A.V. Hill on the phenomenological grounds, we obtain a novel second order equation. We use the values of the microscopic parameters for frog muscles to show that the pro…
Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over $10^5$ particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for $Pe>1$, the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering …
We probe the flow of two dimensional foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate dependent and inhomogeneous (shear banded) velocity profiles, while monodisperse, ordered foams are also shear banded, but essentially rate independent. Second, we introduce a simple model based on balancing the averaged drag forces between the bubbles and the top plate and the averaged bubble-bubble drag forces. This model …
Although the notion of mechanical noise is expected to play a key role in the non-linear rheology of athermally sheared amorphous systems, its characterization has so far remained elusive. Here, we show using molecular dynamic simulations that in spite of the presence of strong spatio-temporal correlations in the system, the local stress exhibits normal diffusion under the effect of the mechanical noise in the finite driving regime. The diffusion constant appears to be proportional to the mean plastic activity. Our data suggests that the corresponding proportionality constant is density indepe…
We perform a detailed theoretical study of the edge fracture instability, which commonly destabilises the fluid-air interface during strong shear flows of entangled polymeric fluids, leading to unreliable rheological measurements. By means of direct nonlinear simulations, we map out phase diagrams showing the degree of edge fracture in the plane of the surface tension of the fluid-air interface and the imposed shear rate, within the Giesekus and Johnson-Segalman models, for different values of the nonlinear constitutive parameters that determine the dependencies on shear rate of the shear and …
We study theoretically the edge fracture instability in sheared complex fluids, by means of linear stability analysis and direct nonlinear simulations. We derive an exact analytical expression for the onset of edge fracture in terms of the shear-rate derivative of the fluid's second normal stress difference, the shear-rate derivative of the shear stress, the jump in shear stress across the interface between the fluid and the outside medium (usually air), the surface tension of that interface, and the rheometer gap size. We provide a full mechanistic understanding of the edge fracture instabili…
Oscillatory shear tests are widely used in rheology to characterize the linear and non-linear mechanical response of complex fluids, including the yielding transition. There is an increasing urge to acquire detailed knowledge of the deformation field that is effectively present across the sample during these tests; at the same time, there is mounting evidence that the macroscopic rheological response depends on the elusive microscopic behavior of the material constituents. Here we employ a strain-controlled shear-cell with transparent walls to visualize and quantify the dynamics of tracers emb…
Classical scaling relationships for rheological quantities such as the $μ(J)$-rheology have become increasingly popular for closures of two-phase flow modeling. However, these frameworks have been derived for monodisperse particles. We aim to extend these considerations to sediment transport modeling by using a more realistic sediment composition. We investigate the rheological behavior of sheared sediment beds composed of polydisperse spherical particles in a laminar Couette-type shear flow. The sediment beds consist of particles with a diameter size ratio of up to ten, which corresponds to g…
We undertake the investigation of sheared polymer chains grafted on flat surfaces to model liposomes covered with polyethylene glycol brushes as a case study for the mechanisms of efficient drug delivery in biologically relevant situations, for example, as carriers for topical treatments of illnesses in the human vasculature. For these applications, specific rheological properties are required, such as low viscosity at high shear rate to improve the transport of the liposomes. Therefore non - equilibrium, DPD simulations of polymer brushes of various length and shear rates are performed to obt…
Using non-equilibrium molecular dynamics simulations, we study the rheology of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres (DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is sheared with different shear rates using Lees-Edwards periodic boundary conditions. The steady-state rheological properties and the effect of the shear on the microstructure of the mixture are studied for different strengths of the dipolar coupling, $λ$, among the DSS. We find that at large shear rates, the mixture shows a shear-thinning behavior for all considered …
Pressure sensitivity in non-local flow behaviour of dense hydrogel particle suspensions
Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam（阿姆斯特丹大学范德瓦耳斯-泽曼研究所物理学院）；Physical Chemistry and Soft Matter, Wageningen University & Research（瓦赫宁根大学与研究物理化学与软物质系）；Institute of Process and Particle Engineering, Graz University of Technology（格拉茨工业大学工艺与颗粒工程研究所）；Department of Mechanical Engineering, Indian Institute of Technology Bombay（印度孟买理工学院机械工程系）；Institute of Physics, Otto von Guericke University Magdeburg（马格德堡奥托·冯·格里克大学物理研究所）；School of Engineering, Brown University（布朗大学工程学院）
