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, allowing access to rotational motion for all particles at the single-particle level. We reveal interparticle hydrodynamic rotational coupling in charged colloidal crystals. We also find that higher local crystallinity in denser crystals enhances rotational diffusivity, and that nearly arrested particles exhibit a stick-slip rotational motion due to frictional coupling. Our method sheds new light on the largely-unexplored local rotational dynamics of spherical particles in dense colloidal materials.
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…
Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress leve…
We probe the three dimensional flow structure and rheology of gravitational (non-density matched) suspensions for a range of driving rates in a split-bottom geometry. We establish that for sufficiently slow flows, the suspension flows as if it were a dry granular medium, and confirm recent theoretical modeling on the rheology of split-bottom flows. For faster driving, the flow behavior is shown to be consistent with the rheological behavior predicted by the recently developed "inertial number approaches for suspension flows.
Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits \textit{in situ} variation of particle packing fraction. Bulk, $B$, and shear, $G$, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio $G/B$ with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft parti…
This is a comment on the recent letter by Wang and Brady on "Constant stress and pressure rheology of colloidal suspensions", Phys. Rev. Lett. 115, 158301 (2015).
Equilibrium sedimentation density profiles of charged binary colloidal suspensions are calculated by computer simulations and density functional theory. For deionized samples, we predict a colloidal ``brazil nut'' effect: heavy colloidal particles sediment on top of the lighter ones provided that their mass per charge is smaller than that of the lighter ones. This effect is verifiable in settling experiments.
We study the rheological behavior of concentrated granular suspensions of simple spherical particles. Under controlled stress, the system exhibits an S-shaped flow curve (stress vs. shear rate) with a negative slope in between the low-viscosity Newtonian regime and the shear thickened regime. Under controlled shear rate, a discontinuous transition between the two states is observed. Stress visualization experiments with a novel fluorescent probe suggest that friction is at the origin of shear thickening. Stress visualization shows that the stress in the system remains homogeneous (no shear ban…
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.
We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the pos…
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 deviatoric stresses of colloidal suspensions are routinely calculated using the expression introduced by Batchelor [J. Fluid Mech. 83, 97--117 (1977)]. We show by example that the central feature in its derivation, the thermodynamic force driving particles down the density gradient, is inconsistent with the motion of the colloids. A new expression for the stress is proposed.
A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation.The critical shear stress of shear thickening in so…
Using a novel bi-axial confocal rheoscope, we investigate the structure and rheology of sheared colloidal suspensions under confinement. Consistent with previous work [X. Cheng \textit{et al., Proc. Natl. Acad. Sci. U. S. A.}, 2011, 109, 63], we observe a vorticity-aligned string phase in moderate concentrated colloidal suspensions under uniaxial shear. Using bi-axial shear protocols, we directly manipulate the orientation and morphology of the string structures. Simultaneously, we measure the suspension rheology along both the flow and vorticity directions with a bi-axial force measurement de…
In charge-stabilized colloidal suspensions, highly charged macroions, dressed by strongly correlated counterions, carry an effective charge that can be substantially reduced (renormalized) from the bare charge. Interactions between dressed macroions are screened by weakly correlated counterions and salt ions. Thermodynamic and structural properties of colloidal suspensions depend sensitively on the magnitudes of both the effective charge and the effective screening constant. Combining a charge renormalization theory of effective electrostatic interactions with Monte Carlo simulations of a one-…
We show that the shear-induced solidification of dilute charge-stabilized (DLVO) colloids is due to the interplay between the shear-induced formation and breakage of large non-Brownian clusters. While their size is limited by breakage, their number density increases with the shearing-time. Upon flow cessation, the dense packing of clusters interconnects into a rigid state by means of grainy bonds, each involving a large number of primary colloidal bonds. The emerging picture of shear-driven solidification in dilute colloidal suspensions combines the gelation of Brownian systems with the jammin…
Using Brownian dynamics simulations we perform a systematic investigation of the shear-induced migration of colloidal particles subject to Poiseuille flow in both cylindrical and planar geometry. We find that adding an attractive component to the interparticle interaction enhances the migration effect, consistent with recent simulation studies of platelet suspensions. Monodisperse, bidisperse and polydisperse systems are studied over a range of shear rates, considering both steady states and the transient dynamics arising from the onset of flow. For bidisperse and polydisperse systems size seg…
We study the fingering instability of the interface between two miscible fluids, a colloidal suspension and its own solvent. The temporal evolution of the interface in a Hele-Shaw cell is found to be governed by the competition between the non-linear viscosity of the suspension and an off-equilibrium, effective surface tension $Γ_e$. By studying suspensions in a wide range of volume fractions, $Φ_\mathrm{C}$, we show that $Γ_e \sim Φ_\mathrm{C}^2$, in agreement with Korteweg's theory for miscible fluids. The surface tension exhibits an anomalous increase with particle size, which we account fo…
Using grand-canonical Monte Carlo simulations we investigate the impact of charged walls on the crystallization properties of charged colloidal suspensions confined between these walls. The investigations are based on an effective model focussing on the colloids alone. Our results demonstrate that the fluid-wall interaction stemming from charged walls has a crucial impact on the fluid's high-density behavior as compared to the case of uncharged walls. In particular, based on an analysis of in-plane bond order parameters we find surface-charge-induced freezing and melting transitions.
The postulate of the existence of a jamming phase diagram (Liu and Nagel, Nature 396, 21 EP (1998aa)) provides a theoretical basis for the classification of a wide range of amorphous solids (colloidal, molecular and emulsion glasses, colloidal and polymer gels, foams and granular matter) on the basis of whether these materials are in the jammed or unjammed state. Whilst such simple classification is appealing, it fails to capture that the criterion of rigidity of such amorphous solids may be defined with respect to a particular deformation orientation or mode (i.e. shear, extrusion, consolidat…
We compute the electrostatic potential at the surface, or zeta potential $ζ$, of a charged particle embedded in a colloidal suspension using a hybrid mesoscopic model. We show that for weakly perturbing electric fields, the value of $ζ$ obtained at steady state during electrophoresis is statistically indistinguishable from $ζ$ in thermodynamic equilibrium. We quantify the effect of counterions concentration on $ζ$. We also evaluate the relevance of the lattice resolution for the calculation of $ζ$ and discuss how to identify the effective electrostatic radius.
Hypothesis: Aging in colloidal suspensions manifests as a reduction in kinetic freedom of the colloids. In aqueous suspensions of charged colloids, the role of inter-particle electrostatics interactions on the aging dynamics is well debated. Despite water being the dispersion medium, the influence of water structure on the physicochemical properties of aging colloids has never been considered before. Laponite, a model hectorite clay, could be used to evaluate the relative contributions of medium structure and electrostatics in determining the physicochemical properties of aging colloidal suspe…
A theory is presented for the onset of shear thickening in colloidal suspensions of particles, stabilized by an electrostatic repulsion. Based on an activation model a critical shear stress can be derived for the onset of shear thickening in dense suspensions for a constant potential and a constant charge approach of the spheres. Unlike previous models the total interaction potential is taken into account (sum of attraction and repulsion). The critical shear stress is related to the maximum of the total interaction potential scaled by the free volume per particle. A comparison with experimenta…
Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $ϕ$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $ϕ$. When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of s…
We present measurements of the thermal fluctuations of the free surface of an aging colloidal suspension, Laponite. The technique consists in measuring the fluctuations of the position of a laser beam that reflects from the free surface. Analysing the data statistics, we show that, as the fluid ages, the dynamics becomes intermittent. The intermittent events correspond to large changes in the local slope of the free surface over a few milliseconds. We show that those quakes are uncorrelated, although they are kept in memory by the surface over short time scales.
We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al., 2011. The friction coefficient and solid volume fraction are taken as functions of the dimensionless viscous number I defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive d…
Colloidal particles are often seen as big atoms that can be directly observed in real space. They are therefore playing an increasingly important role as model systems to study processes of interest in condensed matter physics such as melting, freezing and glass transitions. The solidification of colloidal suspensions has long been a puzzling phenomenon with many unexplained features. Here we demonstrate and rationalize the existence of instability and metastability domains in cellular solidification of colloidal suspensions, by direct in situ high-resolution X-ray radiography and tomography o…
We present a Lattice-Boltzmann method for simulating self-propelling (active) colloidal particles in two-dimensions. Active particles with symmetric and asymmetric force distribution on its surface are considered. The velocity field generated by a single active particle, changing its orientation randomly, and the different time scales involved are characterized in detail. The steady state speed distribution in the fluid, resulting from the activity, is shown to deviate considerably from the equilibrium distribution.
We discuss the peculiarities of the Seebeck effect in stabilized electrolytes containing the colloidal particles. Its unusual feature is the two-stage character, with the linear increase of differential thermopower as the function of colloidal particles concentration $n_{\odot}$ during the first stage and dramatic drop of it at small $n_{\odot}$ during the second one (steady state). We show that the properties of the initial state are governed by the thermo-diffusion flows of the mobile ions of the stabilizing electrolyte medium itself and how the colloidal particles participate in formation o…
A model is presented for the solution of electrokinetic phenomena of colloidal suspensions in fluid mixtures. We solve the discrete Boltzmann equation with a BGK collision operator using the lattice Boltzmann method to simulate binary fluid flows. Solvent-solvent and solvent-solute interactions are implemented using a pseudopotential model. The Nernst-Planck equation, describing the kinetics of dissolved ion species, is solved using a finite difference discretization based on the link-flux method. The colloids are resolved on the lattice and coupled to the hydrodynamics and electrokinetics thr…
We study self-diffusion and sedimentation in colloidal suspensions of nearly-hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne--Prager--Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the…
Dense, stabilized, frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, $ϕ$, increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. The rheology and networks of frictional forces from two and three-dimensional simulations of shear-thickening suspensions are studied. These are a…
We image the flow of a nearly random close packed, hard-sphere colloidal suspension (a `paste') in a square capillary using confocal microscopy. The flow consists of a `plug' in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this behavior both for smooth…
An extension of the renormalized Jellium model which allows to study colloidal suspensions containing trivalent counterions is proposed. The theory is based on a modified Poisson-Boltzmann equation which incorporates the effects of counterion correlations near the colloidal surfaces using a new boundary condition. The renormalized charges, the counterion density profiles, and osmotic pressures can be easily calculated using the modified renormalized Jellium model. The results are compared with the ones obtained using the traditional Wigner-Seitz (WS) cell approximation also with a new boundary…
A long controversy of ice lensing exists in the research of frost heave. By elucidating the mechanical and thermodynamics equilibria at the interface, we present the thermodynamics of the water/ice interface from macroscale to microscale for the freezing of colloidal suspensions. The application of the Clapeyron equation is confirmed both at macroscale to microscale via curvature effect. The thermodynamics at the interface indicates the initial of ice lensing/banding from the growth of pore ice, determined by the critical curvature undercooling instead of the critical fracture of frozen fringe…
We investigate the origin of yield stress aging in semi-dense, saline, and turbid suspensions in which structural evolution is rapidly arrested by the formation of thermally irreversible roll-resisting interparticle contacts. By performing optical tweezer (OT) three-point bending tests on particle rods, we show that these contacts yield by overcoming a rolling threshold, the critical bending moment of which grows logarithmically with time. We demonstrate that this time-dependent contact-scale rolling threshold controls the suspension yield stress and its aging kinetics. We identify a simple co…
A theory is presented which allow us to accurately calculate the critical coagulation concentration (CCC) of hydrophobic colloidal suspensions. For positively charged particles the CCC's follow the Hofmeister (lyotropic) series. For negatively charged particles the series is reversed. We find that strongly polarizable chaotropic anions are driven towards the colloidal surface by electrostatic and hydrophobic forces. Within approximately one ionic radius from the surface, the chaotropic anions loose part of their hydration sheath and become strongly adsorbed. The kosmotropic anions, on the othe…
We provide a general microscopic theory of the scattering cross-section and of the refractive index for a system of interacting colloidal particles, exact at second order in the molecular polarizabilities. In particular: a) we show that the structural features of the suspension are encoded into the forward scattered field by multiple scattering effects, whose contribution is essential for the so-called "optical theorem" to hold in the presence of interactions; b) we investigate the role of radiation reaction on light extinction; c) we discuss our results in the framework of effective medium th…
We study experimentally and numerically a (quasi) two dimensional colloidal suspension of self-propelled spherical particles. The particles are carbon-coated Janus particles, which are propelled due to diffusiophoresis in a near-critical water-lutidine mixture. At low densities, we find that the driving stabilizes small clusters. At higher densities, the suspension undergoes a phase separation into large clusters and a dilute gas phase. The same qualitative behavior is observed in simulations of a minimal model for repulsive self-propelled particles lacking any alignment interactions. The obse…
The lack of detailed balance in active colloidal suspensions allows dissipation to determine stationary states. Here we show that slow viscous flow produced by polar or apolar active colloids near plane walls mediates attractive hydrodynamic forces that drive crystallization. Hydrodynamically mediated torques tend to destabilize the crystal but stability can be regained through critical amounts of bottom-heaviness or chiral activity. Numerical simulations show that crystallization is not nucleational, as in equilibrium, but is preceded by a spinodal-like instability. Harmonic excitations of th…
Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation and experiment. The mixture exhibits a partial clustering in equilibrium: in the voids of the matrix of unclustered big particles, the small particles form subclusters with a sponge-like topology which is accompanied by a characteristic small-wave vector peak in the small-small structure factor. This partial clustering is a general phenomenon occurring for strongly coupled negatively non-additive mixtures.
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.
Thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) particles of a nearly constant swelling ratio and with polydispersity indices (PDIs) varying over a wide range (7.4% - 48.9%) are synthesized to study the effects of polydispersity on the dynamics of suspensions of soft PNIPAM colloidal particles. The PNIPAM particles are characterized using dynamic light scattering (DLS) and scanning electron microscopy (SEM). The zero shear viscosity ($η_{0}$) data of these colloidal suspensions, estimated from rheometric experiments as a function of the effective volume fraction $ϕ_{eff}$ of the suspensi…
We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accomodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple sc…
The settling dynamics of falling spheres inside a Laponite suspension is studied. Laponite is a colloidal synthetic clay that shows physical aging in aqueous suspension due to the spontaneous evolution of inter-particle electrostatic interactions. In our experiments, millimeter-sized steel balls are dropped in aqueous Laponite suspensions of different ages (i.e., time elapsed since sample preparation). The motion of the falling balls are captured using a high-speed camera and the velocities of their centroids are estimated from the images. Interestingly, we observe that balls of larger diamete…
There is now convincing evidence that inter-particle frictional contacts are essential for observing shear-thickening in concentrated suspensions of compact particles. While this has inspired many strategies to tailor the rheology in these systems, in the more general case, viz-a-viz suspensions of anisotropic particles, the mechanism of shear-thickening remains unclear. Here through simultaneous measurements of the bulk viscosity and the first Normal stress difference, we show that strong shear thickening in suspensions of colloidal rods is accompanied by large positive normal stresses, indic…
