We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the Péclet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.
We study the percolation properties for a system of functionalized colloids on patterned substrates via Monte Carlo simulations. The colloidal particles are modeled as hard disks with three equally-distributed attractive patches on their perimeter. We describe the patterns on the substrate as circular potential wells of radius $R_p$ arranged in a regular square or hexagonal lattice. We find a nonmonotonic behavior of the percolation threshold (packing fraction) as a function of $R_p$. For attractive wells, the percolation threshold is higher than the one for clean (non-patterned) substrates if…
Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints, and demonstrate a percolation transition near glass transition, accompanied by the emergenc…
Using computer simulations, we study the dynamic arrest in a schematic model of colloid-polymer mixtures combining short-ranged attractions with long-ranged repulsions. The arrested gel is a dilute rigid network of colloidal particles bonded due to the strong attractions. Without repulsions, the gel forms at the spinodal through arrested phase separation. In the ergodic suspension at sufficiently high densities, colloidal clusters form temporary networks that percolate space. Recently [Nat. Commun. 7, 11817 (2016)], it has been proposed that the transition of these networks to directed percola…
When strained beyond the linear regime, soft colloidal glasses yield to steady-state plastic flow in a way that is similar to the deformation of conventional amorphous solids. Due to the much larger size of the colloidal particles with respect to the atoms comprising an amorphous solid, colloidal glasses allow to obtain microscopic insight into the nature of the yielding transition, as we illustrate here combining experiments, atomistic simulations, and mesoscopic modeling. Our results unanimously show growing clusters of non-affine deformation percolating at yielding. In agreement with percol…
Using a novel approximation scheme within the convective diffusion (two body Smoluchowski) equation framework, we unveil the shear-driven aggregation mechanism at the origin of structure-formation in sheared colloidal systems. The theory, verified against numerics and experiments, explains the induction time followed by explosive (irreversible) rise of viscosity observed in charge-stabilized colloidal and protein systems under steady shear. The Arrhenius-type equation with shear derived here, extending Kramers theory in the presence of shear, is the first analytical result clearly showing the …
Colloidal suspensions have a rich rheology and can exhibit shear-thinning as well as shear-thickening. Numerical simulations recently suggested that shear-thickening may be attributed to the inertia of the colloids, besides the hydrodynamic interactions between them. Here, we consider the ideal limit of a dense bath of soft colloids following an underdamped Langevin dynamics. We use a mean-field equation for the colloidal density to get an analytical expression of the drag force felt by a probe pulled at constant velocity through the suspension. Our results show that inertia can indeed induce …
We study the self-assembly of branching-chain networks and crystals in a binary colloidal system with tunable interactions. The particle positions are extracted from microscope images and order parameters are extracted by image processing and statistical analysis. With these, we construct phase diagrams with respect to particle density, ratio and interaction. In order to draw a more complete picture, we complement the experiments with computer simulations. We establish a region in the phase diagram, where bead ratios and interactions are symmetric, promoting percolated structures.
We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. Interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in 2 dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly …
We explore structural and dynamical behavior of concentrated colloidal suspensions made up by C-shape particles using Brownian dynamics computer simulations and theory. In particular, we focus on the entanglement process between nearby particles for almost closed C-shapes with a small opening angle. Depending on the opening angle and the particle concentration, there is a percolation transition for the cluster of entangled particles which shows the classical scaling characteristics. In a broad density range below the percolation threshold, we find a stretched exponential function for the dynam…
The authors previously introduced an activation model for the onset of shear thickening in electrically stabilized colloidal suspensions. It predicts that shear thickening occurs, when particles arranged along the compression axis in a sheared suspension do overcome the electrostatic repulsion at a critical shear stress, and are captured in the primary minimum of the DLVO interaction potential. A comparison with an experimental investigation on non-aqueous silica suspensions, carried out by Maranzano and Wagner, is performed. For particle systems that fall into the applicability range of the t…
Particles that are immersed in a fluid exchange momentum via the fluid, hence their Brownian motion is correlated. By means of multiparticle-collision dynamics simulations we study the interactions between two colloidal beads in a sheared fluid suspension. Recently, this topic has been addressed in experiments on colloidal particles trapped by optical tweezers in a microfluidic device [PRL, 103, 230602 (2009)] and theoretically by means of a Langevin model [Eur. Phys. J E, 33, 313 (2010)]. Although we neglect the rotational degrees of freedom of the colloids, and employ a very simple coupling …
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…
We investigate percolation in binary and ternary mixtures of patchy colloidal particles theoretically and using Monte Carlo simulations. Each particle has three identical patches, with distinct species having different types of patch. Theoretically we assume tree-like clusters and calculate the bonding probabilities using Wertheim's first-order perturbation theory for association. For ternary mixtures we find up to eight fundamentally different percolated states. The states differ in terms of the species and pairs of species that have percolated. The strongest gel is a trigel or tricontinuous …
We report experiments on hard sphere colloidal glasses that reveal a type of shear banding hitherto unobserved in soft glasses. We present a scenario that relates this to an instability arising from shear-concentration coupling, a mechanism previously thought unimportant in this class of materials. Below a characteristic shear rate $\dotγ_c$ we observe increasingly non-linear velocity profiles and strongly localized flows. We attribute this trend to very slight concentration gradients (likely to evade direct detection) arising in the unstable flow regime. A simple model accounts for both the o…
Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two parallel and structureless walls (slit-pore). We focus on temperatures above the critical temperature of the (metastable) condensation transition of the 3D system. Investigating a broad range of systems sizes, we first determine the percolation thresholds, i. e., the critical packing fraction for percolation $η_{c}$. For the slit-pore systems, $η_{c}$ is found to …
The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with…
Recent computational and theoretical studies have shown that the deformation of colloidal suspensions under a steady shear is highly heterogeneous at the particle level and demonstrate a critical influence on the macroscopic deformation behavior. Despite its relevance to a wide variety of industrial applications of colloidal suspensions, scattering studies focusing on addressing the heterogeneity of the non-equilibrium colloidal structure are scarce thus far. Here, we report the first experimental result using small-angle neutron scattering. From the evolution of strain heterogeneity, we concl…
We report experimental and computational observations of dynamic contact networks for colloidal suspensions undergoing shear thickening. The dense suspensions are comprised of sterically stabilized poly(methyl methacrylate) hard sphere colloids that are spherically symmetric and have varied surface roughness. Confocal rheometry and dissipative particle dynamics simulations show that the shear thickening strength scales exponentially with the scaled deficit contact number and the scaled jamming distance. Rough colloids, which experience additional tangential and rolling constraints, require an …
We study numerically the crystallization process in a supersaturated suspension of repulsive colloidal particles driven by simple shear flow. The effect of the shear flow on crystallization is two-fold: while it suppresses the initial nucleation, once a large enough critical nucleus has formed its growth is enhanced by the shear flow. Combining both effects implies an optimal strain rate at which the overall crystallization rate has a maximum. To gain insight into the underlying mechanisms, we employ a discrete state model describing the transitions between the local structural configurations …
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…
We examine microstructural and mechanical changes which occur during oscillatory shear flow and reformation after flow cessation of an intermediate volume fraction colloidal gel using rheometry and Brownian Dynamics (BD) simulations. A model depletion colloid-polymer mixture is used, comprising of a hard sphere colloidal suspension with the addition of non-adsorbing linear polymer chains. Results reveal three distinct regimes depending on the strain amplitude of oscillatory shear. Large shear strain amplitudes fully break the structure which results into a more homogenous and stronger gel afte…
Ultrasoft colloids typically do not spontaneously crystallize, but rather vitrify, at high concentrations. Combining in-situ rheo-SANS experiments and numerical simulations we show that shear facilitates crystallization of colloidal star polymers in the vicinity of their glass transition. With increasing shear rate well beyond rheological yielding, a transition is found from an initial bcc-dominated structure to an fcc-dominated one. This crystal-to-crystal transition is not accompanied by intermediate melting but occurs via a sudden reorganization of the crystal structure. Our results provide…
Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. …
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…
A confined colloidal glass, under the imposition of a uniform shear stress, is investigated using numerical simulations. Both at macro- and microscales, the consequent dynamics during the onset of flow is studied. When the imposed stress is gradually decreased, the time scale for the onset of steady flow diverges, associated with long-lived spatial heterogeneities. Near this yield-stress regime, persistent creep in the form of shear-banded structures is observed.
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…
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…
Cellulose nanocrystals (CNC) can be considered as model colloidal rods and have practical applications in the formation of soft materials with tailored anisotropy. Here, we employ two contrasting microfluidic devices to quantitatively elucidate the role of shearing and extensional flows on the alignment of a dilute CNC dispersion. Characterization of the flow field by micro-particle image velocimetry is coupled to flow-induced birefringence analysis to quantify the deformation rate--alignment relationship. The deformation rate required for CNC alignment is 4$\times$ smaller in extension than i…
Shear history plays an important role in determining the linear and nonlinear rheological response of colloidal gels and can be used for tuning their structure and flow properties. Increasing colloidal particle aspect ratio lowers the critical volume fraction for gelation due to an increase of the particle excluded volume. Using a combination of rheology and confocal microscopy we investigate the effect of steady and oscillatory pre-shear history on the structure and rheology of colloidal gels formed by silica spheres and rods of length L and diameter D (L/D = 10) dispersed in 11 M CsCl soluti…
Using high-speed confocal microscopy, we measure the particle positions in a colloidal suspension under large amplitude oscillatory shear. Using the particle positions we quantify the in situ anisotropy of the pair-correlation function -- a measure of the Brownian stress. From these data, we find two distinct types of responses as the system crosses over from equilibrium to far-from-equilibrium states. The first is a nonlinear amplitude saturation that arises from shear-induced advection, while the second is a linear frequency saturation due to competition between suspension relaxation and she…
Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange in well-defined layers with solidlike in-plane structure, the confined films display complex, nonlinear behavior such as collective depinning and local transport via density excitations. These phenomena are reminiscent of colloidal monolayers driven over a periodic substrate potential. In order to deepen this connection, we present an effective model which ma…
Colloidal suspensions in industrial processes often exhibit shear thickening that is difficult to control actively. Here, we use piezoelectric transducers to apply acoustic perturbations to dynamically tune the suspension viscosity in the shear-thickening regime. We attribute the mechanism of dethickening to the disruption of shear-induced force chains via perturbations that are large relative to the particle roughness scale. The ease with which this technique can be adapted to various flow geometries makes it a powerful tool for actively controlling suspension flow properties and investigatin…
We present a new model of patchy particles in which the interaction sites can be activated or deactivated by varying the temperature of the system. We study the thermodynamics of the system by means of Wertheim's first order perturbation theory, and use Flory-Stockmayer theory of polymerization to analyse the percolation threshold. We find a very rich phase behaviour including lower critical points and reentrant percolation.
Using a dynamical density functional theory we analyze the density profile of a colloidal liquid near a wall under shear flow. Due to the symmetries of the system considered, the naive application of dynamical density functional theory does not lead to a shear induced modification of the equilibrium density profile, which would be expected on physical grounds. By introducing a physically motivated dynamic mean field correction we incorporate the missing shear induced interparticle forces into the theory. We find that the shear flow tends to enhance the oscillations in the density profile of ha…
We demonstrate that application of an increasing shear field on a glass leads to an intriguing dynamic first order transition in analogy to equilibrium transitions. By following the particle dynamics as a function of the driving field in a colloidal glass, we identify a critical shear rate upon which the diffusion time scale of the glass exhibits a sudden discontinuity. Using a new dynamic order parameter, we show that this discontinuity is analogous to a first order transition, in which the applied stress acts as the conjugate field on the system's dynamic evolution. These results offer new p…
The response of glasses to mechanical loading often leads to the formation of inhomogeneous flow patterns that strongly affect materials properties. Among them, shear bands are ubiquitous in a wide variety of materials, ranging from soft matter systems to metallic alloys. Shear banding is associated with strain localization, i.e. the deformation of the sheared glassy solid is localized in space in form of band-like structures. These structures are often precursors to catastrophic failure, implying that a proper understanding of the underlying mechanisms could lead to the design of smarter mate…
