The onset of thermal convection in a horizontal layer of a colloidal suspension is investigated in terms of a continuum model for binary-fluid mixtures where the viscosity depends on the local concentration of colloidal particles. With an increasing difference between the viscosity at the warmer and the colder boundary the threshold of convection is reduced in the range of positive values of the separation ratio psi with the onset of stationary convection as well as in the range of negative values of psi with an oscillatory Hopf bifurcation. Additionally the convection rolls are shifted downwards with respect to the center of the horizontal layer for stationary convection (psi>0) and upwards for the Hopf bifurcation (psi<0).
In this review article, we focus on collective motion in externally driven colloidal suspensions, as well as how these collective effects can be harnessed for use in microfluidic applications. We highlight the leading role of hydrodynamic interactions in the self-assembly, emergent behavior, transport, and mixing properties of colloidal suspensions. A special emphasis is given to recent numerical methods to simulate driven colloidal suspensions at large scales. In combination with experiments, they help us to understand emergent dynamics and to identify control parameters for both individual a…
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…
Coalescence event in pendant and sessile drop is distinguished by the formation and evolution of the liquid bridge created upon singular contact. The bridge radius, $R$, is known to evolve as $R\sim t^b$, with power-law exponent, $b$, signifying the dominant governing forces. In this work, we experimentally explore the phenomenon in sub-classes of complex fluids namely, colloidal and non-colloidal suspensions that have particle hydrodynamic interactions as origin of viscoelasticity. Our observations suggest that such fluids have flow dependent thinning response with finite elasticity in shear …
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).
We develop a fully continuous model for colloidal suspensions with hydrodynamic interactions. The Navier Stokes Phase Field Crystal (NS-PFC) model combines ideas of dynamic density functional theory with particulate flow approaches and is derived in detail and related to other dynamic density functional theory approaches with hydrodynamic interactions. The derived system is numerically solved using adaptive finite elements and used to analyse colloidal crystallization in flowing environments demonstrating a strong coupling in both directions between the crystal shape and the flow field. We fur…
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.
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.
Shear thickening is a widespread phenomenon in suspension flow that, despite sustained study, is still the subject of much debate. The longstanding view that shear thickening is due to hydrodynamic clusters has been challenged by recent theory and simulations suggesting that contact forces dominate, not only in discontinuous, but also in continuous shear thickening. Here, we settle this dispute using shear reversal experiments on micron-sized silica and latex colloidal particles to measure directly the hydrodynamic and contact force contributions to shear thickening. We find that contact force…
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…
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…
This fluid dynamics video depicts the evolution of a suspension of paramagnetic colloids under the influence of a uniform, pulsed magnetic field. At low pulse frequencies, the suspension condenses into columns which decompose via a Rayleigh-Plateau instability. At high pulse frequencies, the suspension forms a kinetically arrested, system spanning network. We demonstrate the degeneration of the Rayleigh-Plateau instability with increasing pulse frequency.
We investigate the sedimentation equilibrium of a charge stabilized colloidal suspension in the regime of low ionic strength. We analyze the asymptotic behaviour of the density profiles on the basis of a simple Poisson--Boltzmann theory and show that the effective mass we can deduce from the barometric law corresponds to the actual mass of the colloidal particles, contrary to previous studies.
Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e. Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian Dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature.
We explore the effects of counterion condensation on fluid-fluid phase separation in charged colloidal suspensions. It is found that formation of double layers around the colloidal particles stabilizes suspensions against phase separation. Addition of salt, however, produces an instability which, in principle, can lead to a fluid-fluid separation. The instability, however, is so weak that it should be impossible to observe a fully equilibrated coexistence experimentally.
An approach is proposed which allows to self-consistently calculate the structural and thermodynamic properties of highly charged aqueous colloidal suspensions. The method is based on the renormalized Jellium model with the background charge distribution related to the colloid-colloid correlation function. The theory is used to calculate the correlation functions and the effective colloidal charges for suspension containing additional monovalent electrolyte. The predictions of the theory are in excellent agreement with the Monte Carlo simulations.
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 study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential, by means of dynamical density functional theory. We consider a non-linear diffusion equation for the density and show that spatial patterns emerge from a sinusoidal external potential with a time-dependent wavelength. These patterns are characterized by a sinusoidal density with the average wavelength and a Bessel-function envelope with an induced wavelength that depends only on the amplitude of the temporal oscillations. As a generalization of this result, we propose a design strategy to o…
The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can p…
We present molecular dynamics simulations of aggregation kinetics in a colloidal suspension modeled as a highly asymmetric binary mixture. Starting from a configuration with largely uncorrelated colloidal particles the system relaxes by coagulation-fragmentation dynamics to a structured state of low-dimensionality clusters with an exponential size distribution. The results show that short-range repulsive interactions alone can give rise to so-called cluster phases. For the present model and probably other, more common colloids, the observed clusters appear to be equilibrium phase fluctuations …
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…
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 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.
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…
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 show that geometric confinement dramatically affects the shear-induced configurations of dense mono-disperse colloidal suspensions; a new structure emerges, where layers of particles buckle to stack in a more efficient packing. The volume fraction in the shear zone is controlled by a balance between the viscous stresses and the osmotic pressure of a contacting reservoir of unsheared particles. We present a model that accounts for our observations and helps elucidate the complex interplay between particle packing and shear stress for confined suspensions.
Interfacial undercooling is of significant importance on microscopic pattern formation in the solidification of colloidal suspensions. Two kinds of interfacial undercooling are supposed to be involved in freezing colloidal suspensions, i.e. solute constitutional supercooling (SCS) caused by additives in the solvent and particulate constitutional supercooling (PCS) caused by particles. However, quantitatively identification of the interfacial undercooling of freezing colloidal suspensions is still absent and it is still unknown which undercooling is dominant. The revealing of interfacial underc…
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…
Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. In this article, the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved simulations. First, the interplay between activity and shear in the solid to the liquid transition of the suspension is analysed. While both self-propulsion and shear destroy order and melt the system b…
Theoretical calculations for colloidal charge-stabilized and hard sphere suspensions show that hydrodynamic interactions yield a qualitatively different particle concentration dependence of the short-time self-diffusion coefficient. The effect, however, is numerically small and hardly accessible by conventional light scattering experiments. Applying multiple-scattering decorrelation equipment and a careful data analysis we show that the theoretical prediction for charged particles is in agreement with our experimental results from aqueous polystyrene latex suspensions.
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…
Thermodynamic properties of charge-stabilised colloidal suspensions depend sensitively on the effective charge of the macroions, which can be substantially lower than the bare charge in the case of strong counterion-macroion association. A theory of charge renormalization is proposed, combining an effective one-component model of charged colloids with a thermal criterion for distinguishing between free and associated counterions. The theory predicts, with minimal computational effort, osmotic pressures of deionized suspensions of highly charged colloids in close agreement with large-scale simu…
Freezing colloidal suspensions widely exists in nature and industry. Interface instability has attracted much attention for the understandings of the pattern formation in freezing colloidal suspensions. However, the interface instability modes, the origin of the ice banding or ice lamellae, are still unclear. In-situ experimental observation of the onset of interface instability is still absent up to now. Here, by directly imaging the initial transient stage of planar interface instability in directional freezing colloidal suspensions, we proposed three interface instability modes, Mullins-Sek…
By combining confocal microscopy and Stress Assessment from Local Structural Anisotropy (SALSA), we directly measure stresses in 3D quiescent colloidal liquids. Our non-invasive and non-perturbative method allows us to measure forces $\lesssim$ 50 fN with a small and tunable probing volume, enabling us to resolve the stress fluctuations arising from particle thermal motions. We use the Green-Kubo relation to relate these measured stress fluctuations to the bulk Brownian viscosity at different volume fractions and comparing against simulations and conventional rheometry measurements. We demonst…
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…
The resolution of Brownian motion in simulations of micro-particle suspensions can be crucial to reproducing the correct dynamics of individual particles, as well as providing an accurate characterisation of suspension properties. Including these effects in simulations, however, can be computationally intensive due to the configuration dependent random displacements that would need to be determined at every time step. In this paper, we introduce the fluctuating force-coupling method (FCM) to overcome this difficulty, providing a fast approach to simulate colloidal suspensions at large-scale. W…
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…
The freezing of colloidal suspensions is encountered in many natural and engineering processes such as the freezing of soils, food engineering, and cryobiology. It can also be used as a bio-inspired, versatile, and environmentally-friendly processing route for porous materials and composites. Yet, it is still a puzzling phenomenon with many unexplained features, due to the complexity of the system and the space and time scales at which the process should be investigated. We demonstrate here the interest of fast X-ray computed tomography to provide time-lapse, three-dimensional, in situ imaging…
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…
This paper adopts a previously developed activation model of shear thickening, published by the authors, to sterically stabilized colloidal suspensions. When particles arranged along the compression axis of a sheared suspension, they may overcome the repulsive interaction and form hydroclusters associated with shear thickening. Taking advantage of the total interaction potential of polymeric brush coating and van der Waals attraction, the applicability of the activation model is shown within the validity range of a continuum theory. For the comparison with an extensive experimental investigati…
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…
