We perform detailed computational and experimental measurements of the driven dynamics of a dense, uniform suspension of sedimented microrollers driven by a magnetic field rotating around an axis parallel to the floor. We develop a lubrication-corrected Brownian Dynamics method for dense suspensions of driven colloids sedimented above a bottom wall. The numerical method adds lubrication friction between nearby pairs of particles, as well as particles and the bottom wall, to a minimally-resolved model of the far-field hydrodynamic interactions. Our experiments combine fluorescent labeling with particle tracking to trace the trajectories of individual particles in a dense suspension, and to measure their propulsion velocities. Previous computational studies [B. Sprinkle et al., J. Chem. Phys., 147, 244103, 2017] predicted that at sufficiently high densities a uniform suspension of microrollers separates into two layers, a slow monolayer right above the wall, and a fast layer on top of the bottom layer. Here we verify this prediction, showing good quantitative agreement between the bimodal distribution of particle velocities predicted by the lubrication-corrected Brownian Dynamics and those measured in the experiments. The computational method accurately predicts the rate at which particles are observed to switch between the slow and fast layers in the experiments. We also use our numerical method to demonstrate the important role that pairwise lubrication plays in motility-induced phase separation in dense monolayers of colloidal microrollers, as recently suggested for suspensions of Quincke rollers [D. Geyer et al., Physical Review X, 9(3), 031043, 2019].
We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model, consisting of two continuous lines of rotlets, exhibits a linear instability driven only by hydrodynamics interactions, and reproduces the lengthscale selection observed in large scale particle simulations and in experiments. By adjusting only one parameter, the distance between the two lines, our dispersion relation exhibits quantitative agreement with the simulations a…
We develop efficient numerical methods for performing many-body Brownian dynamics simulations of a recently-observed fingering instability in an active suspension of colloidal rollers sedimented above a wall [M. Driscoll, B. Delmotte, M. Youssef, S. Sacanna, A. Donev and P. Chaikin, Nature Physics, 2016, doi:10.1038/nphys3970]. We present a stochastic Adams-Bashforth integrator for the equations of Brownian dynamics, which has the same cost as but is more accurate than the widely-used Euler-Maruyama scheme, and uses a random finite difference to capture the stochastic drift proportional to the…
We combine experiments, large scale simulations and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant in this system, leading to strong density-velocity coupling. We characterize a uniform suspension and show that density waves propagate freely in all directions in a dispersive fashion. When sharp density gradients are introduced in the suspension, we observe the formation of a shock. Unlike Burgers' shock-like structures observed in other active and driven …
Recent work has identified persistent cluster states which were shown to be assembled and held together by hydrodynamic interactions alone [Driscoll \textit{et al.} (2017) Nature Physics, 13(4), 375]. These states were seen in systems of colloidal microrollers; microrollers are colloidal particles which rotate about an axis parallel to the floor and generate strong, slowly decaying, advective flows. To understand these bound states, we study a simple, yet rich, model system of two microrollers. Here we show that pairs of microrollers can exhibit hydrodynamic bound states whose nature depends o…
We introduce methods for large scale Brownian Dynamics (BD) simulation of many rigid particles of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid multiblob method at a cost comparable to the cost of deterministic simulations. We demonstrate that we can efficiently generate deterministic and random displacements for many particles using preconditioned Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-Yamakawa (RPY) mobility matrix and it "square" root are available for the given boundary conditions. W…
We numerically study the impact-induced hardening in dense suspensions. We employ the lattice Boltzmann method and perform simulations of dense suspensions under impacts, which incorporate the contact between suspended particles with the free surface of the suspension. Our simulation for a free-falling impactor on a dense suspension reproduces experimental results, where rebound takes place for frictional particles at high-speed impact and high volume fraction shortly after the impact before subsequently sinking. We found that the shear stress of the suspension is not affected by the impact, w…
A first principles approach to the nonlinear flow of dense suspensions is presented which captures shear thinning of colloidal fluids and dynamical yielding of colloidal glasses. The advection of density fluctuations plays a central role, suppressing the caging of particles and speeding up structural relaxation. A mode coupling approach is developed to explore these effects.
In a recent Nature Materials article, Brown et al. reported a generality of shear thickening in dense suspensions and demonstrated that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased to below a threshold. However, the generality of the shear thickening reported in the article may not be necessary true when a high electric/magnetic field is applied on an ER/MR fluid. Shear thickening of ER fluid and MR fluid under high electric/magnetic fields at low shear rates, indicating an obvious phase change inside the dense suspensions has been ob…
Shear thickening of particle suspensions is characterized by a transition between lubricated and frictional contacts between the particles. Using 3D numerical simulations, we study how the inter-particle friction coefficient influences the effective macroscopic friction coefficient and hence the microstructure and rheology of dense shear thickening suspensions. We propose expressions for effective friction coefficient in terms of distance to jamming for varying shear stresses and particle friction coefficient values. We find effective friction coefficient to be rather insensitive to interparti…
We introduce a novel approach to reveal ordering fluctuations in sheared dense suspensions, using line scanning in a combined rheometer and laser scanning confocal microscope. We validate the technique with a moderately dense suspension, observing modest shear-induced ordering and a nearly linear flow profile. At high concentration ($ϕ= 0.55$) and applied stress just below shear thickening, we report ordering fluctuations with high temporal resolution, and directly measure a decrease in order with distance from the suspension's bottom boundary as well as a direct correlation between order and …
Shear-Induced Collective Shape Oscillations in Dense Soft Suspensions
Rudolf Peierls Centre for Theoretical Physics, University of Oxford（鲁道夫·皮尔斯理论物理中心，牛津大学）；Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（理论与计算物理中心，理学院，里斯本大学）；Departamento de Física, Faculdade de Ciências, Universidade de Lisboa（物理系，理学院，里斯本大学）
Using Brownian dynamics computer simulations we show that a two-dimensional suspension of self-propelled ("active") colloidal particles crystallizes at sufficiently high densities. Compared to the equilibrium freezing of passive particles the freezing density is both significantly shifted and depends on the structural or dynamical criterion employed. In non-equilibrium the transition is accompanied by pronounced structural heterogeneities. This leads to a transition region between liquid and solid in which the suspension is globally ordered but unordered liquid-like "bubbles" still persist.
When a solid projectile is dropped onto a dense non-Brownian-particle suspension, the action of an extremely large resistance force on the projectile results in its drastic deceleration, followed by a rebound. In this study, we perform a set of simple experiments of dropping a solid-projectile impact onto a dense potato-starch suspension. From the kinematic data of the projectile motion, the restitution coefficient and timescale of the rebound are measured. By assuming linear viscoelasticity, the effective transient elasticity and viscosity can be estimated. We additionally estimate the Stokes…
Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient fl…
Shear viscosity and wall slip of dense suspensions of a silicone polymer incorporated with polydisperse particles were investigated. Three types of particles with low aspect ratios were used to achieve a relatively high maximum packing fraction of 0.86. Such a high maximum packing fraction allowed the preparation of suspensions with a wide range of solid volume fractions in the range of 0.62 to 0.82. The wall slip velocities of the suspensions in steady torsional and capillary flows were characterized and determined to be fully consistent with the mechanism of apparent slip layer formation at …
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…
Unlike dry granular materials, a dense granular suspension like cornstarch in water can strongly resist extensional flows. At low extension rates, such a suspension behaves like a viscous liquid, but rapid extension results in a response where stresses far exceed the predictions of lubrication hydrodynamics and capillarity. To understand this remarkable mechanical response, we experimentally measure the normal force imparted by a large bulk of the suspension on a plate moving vertically upward at a controlled velocity. We observe that above a velocity threshold, the peak force increases by ord…
A remarkable property of dense suspensions is that they can transform from liquid-like at rest to solid-like under sudden impact. Previous work showed that this impact-induced solidification involves rapidly moving jamming fronts; however, details of this process have remained unresolved. Here we use high-speed ultrasound imaging to probe non-invasively how the interior of a dense suspension responds to impact. Measuring the speed of sound we demonstrate that the solidification proceeds without a detectable increase in packing fraction, and imaging the evolving flow field we find that the shea…
Oscillatory shear has been widely used to study the rheological properties of suspensions under unsteady shear. Furthermore, recent works have shown that oscillatory flows can improve the flowability of dense suspensions. While most studies have been done under constant volume we here study oscillatory shear flows of a two-dimensional suspensions using a normal pressure-controlled set-up. To characterise the rheology, we introduce both a complex macroscopic friction coefficient $μ^{*}$, following the convention of the complex viscosity $η^{*}$, and a shear-rate averaged viscous number $J'$. Th…
Recent studies have highlighted that oscillatory and time-dependent shear flows might help increase flowability of dense suspensions. While most focus has been on cross-flows we here study a simple two-dimensional suspensions where we apply simultaneously oscillatory and stationary shear along the same direction. We first show that the viscosities in this set-up significantly decrease with an increasing magnitude of the oscillations, contrary to previous claims. The decrease can be attributed to the large decrease in the number of contacts and an altered microstructure as the magnitude of the …
We study relaxation and rheology of dense athermal suspensions of frictionless particles close below the jamming density. Our key quantity, the relaxation time---determined from the exponential decay of the energy after the shearing has suddenly been switched off---is argued to be a determining factor behind the algebraic divergence of various quantities as the jamming density is approached from below. We also define and measure the ``dissipation time'', which is obtained directly in shearing simulations and find that it behaves similarly to the relaxation time. Comparing shear viscosity with …
We propose a unifying rheological framework for dense suspensions of non-Brownian spheres, predicting the onsets of particle friction and particle inertia as distinct shear thickening mechanisms, while capturing quasistatic and soft particle rheology at high volume fractions and shear rates respectively. Discrete element method simulations that take suitable account of hydrodynamic and particle-contact interactions corroborate the model predictions, demonstrating both mechanisms of shear thickening, and showing that they can occur concurrently with carefully selected particle surface propertie…
Non-Brownian suspensions present a transition from Newtonian behavior in the zero-shear limit to a shear thickening behaviour at a large shear rate, none of which is clearly understood so far. Here, we carry out numerical simulations of such an athermal dense suspension under shear, at an imposed confining pressure. This set-up is conceptually identical to the recent experiments of Boyer and co-workers [Phys. Rev. Lett. 107,188301 (2011)]. Varying the interstitial fluid viscosities, we recover the Newtonian and Bagnoldian regimes and show that they correspond to a dissipation dominated by visc…
Hypothesis: While the mechanical disruption of microscopic structures in complex fluids by large shear flows has been studied extensively, the effects of applied strains on the dielectric properties of macromolecular aggregates has received far less attention. Simultaneous rheology and dielectric experiments can be employed to study the dynamics of sheared colloidal suspensions over spatiotemporal scales spanning several decades. Experiments: Using a precision impedance analyzer, we study the dielectric behavior of strongly sheared aqueous suspensions of thermoreversible hydrogel poly(N-isopro…
Drying of bacterial suspensions is frequently encountered in a plethora of natural and engineering processes. However, the evaporation-driven mechanical instabilities of dense consolidating bacterial suspensions have not been explored heretofore. Here, we report the formation of two different crack patterns of drying suspensions of \textit{Escherichia coli} (\textit{E. coli}) with distinct motile behaviors. Circular cracks are observed for wild-type \textit{E. coli} with active swimming, whereas spiral-like cracks form for immotile bacteria. Using the elastic fracture mechanics and the poroela…
Cleaner analytic technique for quantifying compounds in dense suspension is needed for wastewater and environment analysis, chemical or bio-conversion process monitoring, biomedical diagnostics, food quality control among others. In this work, we introduce a green, fast, one-step method called nanoextraction for extraction and detection of target analytes from sub-milliliter dense suspensions using surface nanodroplets without toxic solvents and pre-removal of the solid contents. With nanoextraction, we achieve a limit of detection (LOD) of 10^(-9) M for a fluorescent model analyte obtained fr…
In Al2O3 suspensions, depending on the experimental conditions very different microstructures can be found, comprising fluid like suspensions, a repulsive structure, and a clustered microstructure. For technical processing in ceramics, the knowledge of the microstructure is of importance, since it essentially determines the stability of a workpiece to be produced. To enlighten this topic, we investigate these suspensions under shear by means of simulations. We observe cluster formation on two different length scales: the distance of nearest neighbors and on the length scale of the system size.…
Many dense particulate suspensions show a stress induced transformation from a liquid-like state to a solid-like shear jammed (SJ) state. However, the underlying particle-scale dynamics leading to such striking, reversible transition of the bulk remains unknown. Here, we study transient stress relaxation behaviour of SJ states formed by a well-characterized dense suspension under a step strain perturbation. We observe a strongly non-exponential relaxation that develops a sharp discontinuous stress drop at short time for high enough peak-stress values. High resolution boundary imaging and norma…
We present a first-principles theory for the active nonlinear microrheology of colloidal model systems: for constant external force on a spherical probe particle embedded in a dense host dispersion, neglecting hydrodynamic interactions, we derive an exact expression for the friction. Within mode-coupling theory (MCT), we discuss the threshold external force needed to delocalize the probe from a host glass, and its relation to strong nonlinear velocity-force curves in a host fluid. Experimental microrheology data and simulations, which we performed, are explained with a simplified model.
A consensus is emerging that discontinuous shear thickening (DST) in dense suspensions marks a transition from a flow state where particles remain well separated by lubrication layers, to one dominated by frictional contacts. We show here that reasonable assumptions about contact proliferation predict two distinct types of DST in the absence of inertia. The first occurs at densities above the jamming point of frictional particles; here the thickened state is completely jammed and (unless particles deform) cannot flow without inhomogeneity or fracture. The second regime shows strain- rate hyste…
Under an increasing applied shear stress ($σ$), viscosity of many dense particulate suspensions increases drastically beyond a stress onset ($σ_0$), a phenomenon known as discontinuous shear-thickening (DST). Recent studies point out that some suspensions can transform into a stress induced solid-like shear jammed (SJ) state at high particle volume fraction ($ϕ$). SJ state develops a finite yield stress and hence is distinct from a shear-thickened state. Here, we study the steady state shear-thickening behaviour of dense suspensions formed by dispersing colloidal polystyrene particles (PS) in …
We use 2D numerical simulations to study dense suspensions of non-Brownian hard particles using the Critical Load Model (CLM) under constant confining pressures. This simple model shows discontinuous shear thickening (DST) as the tangential forces get activated upon increased shear stresses. By parameterizing a simple binary system of frictional and non-frictional particles of different proportions we show that the jamming packing fraction, at which the viscosity diverges, is controlled by the fraction of frictional contacts. The viscosity of dense suspensions can thereby be expressed as a fun…
The shear rheology of dense colloidal and granular suspensions is strongly nonlinear, as these materials exhibit shear-thinning and shear-thickening, depending on multiple physical parameters. We numerically study the rheology of a simple model of soft repulsive particles at large densities, and show that nonlinear flow curves reminiscent of experiments on real suspensions can be obtained. By using dimensional analysis and basic elements of kinetic theory, we rationalize these multiple rheological regimes and disentangle the relative impact of thermal fluctuations, glass and jamming transition…
We investigate the flowing behavior of dense suspensions of non-colloidal particles, by coupling macroscopic rheometric experiments and local velocity and concentration measurements through MRI techniques. We find that the flow is localized at low velocities, and that the material is inhomogeneous; the local laws inferred from macroscopic rheometric observations must then be reinterpreted in the light of these local observations. We show that the short time response to a velocity step allows to characterize dense suspensions locally: they have a purely viscous behavior, without any observable …
We use shear reversal simulations to explore the rheology of dense, non-Brownian suspensions, resolving lubrication forces between neighbouring particles and modelling particle surface contacts. The transient stress response to an abrupt reversal of the direction of shear shows rate-independent, nonmonotonic behaviour, capturing the salient features of the corresponding classical experiments. Based on analyses of the hydrodynamic and particle contact stresses and related contact networks, we demonstrate distinct responses at small and large strains, associated with contact breakage and structu…
Dense particulate suspensions can not only increase their viscosity and shear thicken under external forcing, but also jam into a solid-like state that is fully reversible when the force is removed. An impact on the surface of a dense suspension can trigger this jamming process by generating a shear front that propagates into the bulk of the system. Tracking and visualizing such a front is difficult because suspensions are optically opaque and the front can propagate as fast as several meters per second. Recently, high-speed ultrasound imaging has been used to overcome this problem and extract…
We study granular suspensions under a variety of extensional deformations and simple shear using numerical simulations. The viscosity and Trouton's ratio (the ratio of extensional to shear viscosity) are computed as functions of solids volume fraction $ϕ$ close to the limit of zero inertia. Suspensions of frictionless particles follow a Newtonian Trouton's ratio for $ϕ$ all the way up to $ϕ_0$, a universal jamming point that is independent of deformation type. In contrast, frictional particles lead to a deformation-type-dependent jamming fraction $ϕ_m$, which is largest for shear flows. Trouto…
Dense suspensions of hard particles in a liquid can exhibit strikingly counter-intuitive behavior, such as discontinuous shear thickening (DST) [1-8] and reversible shear jamming (SJ) into a state with finite yield stress [9-13]. Recent studies identified a stress-activated crossover from hydrodynamic interactions to frictional particle contacts to be key for these behaviors [2-4, 6-8, 10, 14]. However, many suspensions exhibit only DST and not SJ. Here we show that particle surface chemistry can play a central role in creating conditions that allow for SJ. We find the system's ability to form…
Dense suspension of particles in a liquid exhibit rich, non-Newtonian behaviors such as shear thickening and shear jamming. Shear thickening is known to be enhanced by increasing the particles' frictional interactions and also by making their shape more anisotropic. For shear jamming, however, only the role of interparticle friction has been investigated, while the effect of changing particle shape has so far not been studied systematically. To address this we here synthesize smooth silica particles and design the particle surface chemistry to generate strong frictional interactions such that …
We present a numerical study of dense colloidal suspensions in pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multi-particle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by L. Isa et al. [Phys. Rev. Lett. 102, 058302 (2009)]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With …
The rotational Brownian motion of colloidal spheres in dense suspensions reflects local hydrodynamics and friction, both key to non-linear rheological phenomena such as shear-thickening and jamming, and transport in crowded environments, including intracellular migration and blood flow. To fully elucidate the role of rotational dynamics experimentally, it is crucial to measure the translational and rotational motion of all spheres simultaneously. Here, we develop compositionally uniform colloidal spheres with an off-centre, fully embedded core with a different fluorophore to the particle body,…
We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient $μ_p$ and the viscous number $J$, we build a phase diagram that identifies three regimes of flow: Frictionless, Frictional Sliding, and Rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficient and small viscous numbers (below $J\sim 10^{-3}$) we show that the dominating dissipative mechanism is sliding of frict…
Shear flow of dense, non-Brownian suspensions is simulated using the discrete element method, taking particle contact and hydrodynamic lubrication into account. The resulting flow regimes are mapped in the parametric space of solid volume fraction, shear rate, fluid viscosity and particle stiffness. Below a critical volume fraction $ϕ_c$, the rheology is governed by the Stokes number, which distinguishes between viscous and inertial flow regimes. Above $ϕ_c$, a quasistatic regime exists for low and moderate shear rates. At very high shear rates, the $ϕ$ dependence is lost and soft particle rhe…
Acoustic transparency and absorption in dense granular suspensions
Institut Langevin, ESPCI Paris, Université PSL, CNRS（朗之万研究所，巴黎高等物理化工学院，巴黎文理研究大学，法国国家科学研究中心）；Laboratorio de Acústica Ultrasonora, Instituto de Física, Facultad de Ciencias, Universidad de la República（超声波声学实验室，物理研究所，理学院，共和国大学）
We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-indu…
We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [Stopper {\em et al.}, Phys. Rev. E {\bf 92}, 022151 (2015)] which amounts to using different free energy functionals for the self and distinct part of the van Hove function $G(r,t)$, we put forward a unified description employing a single functional for both components. To this end, interactions within the self part are removed via the zero-dimensional limit of the functional with a quenched self component. In addition, we m…
Acoustic modulation of shear thickening transition in dense adhesive suspensions
ENSL, CNRS, Laboratoire de Physique（法国国家科学研究中心里昂高等师范学院物理实验室）；Holcim Innovation Center（豪瑞创新中心）；Department of Polymer Engineering, IPC, University of Minho（米尼奥大学高分子工程系）
