Hysteretic Behavior of Capillary Bridges between Flat Plates.

We studied the evolution of capillary bridges between nominally flat plates undergoing multiple cycles of compression and stretching in experiments and simulations. We varied the distance between the plates in small increments to study the full evolution of the bridge shape. Experiments show that contact angle hysteresis determines the shape of the bridge. In sliding drops, hysteresis can be modeled using a contact angle-dependent resistive force F̃R applied at the contact line. We developed a model that accurately captures the evolution of the bridge shape by combining F̃R and constrained energy minimization. Unlike previous work, this allows for both complete and partial contact line pinning. We also explored the effect of using nonparallel plates. The asymmetry in the bridge shape causes the movement of the center of mass of the bridge and can be explained by contact angle hysteresis. We find that even a slight misalignment between the flat plates can have a measurable effect.

Taylor-Couette flow of hard-sphere suspensions: overview of current understanding.

Although inertial particle-laden flows occur in a wide range of industrial and natural processes, there is both a lack of fundamental understanding of these flows and continuum-level governing equations needed to predict transport and particle distribution. Towards this effort, the Taylor-Couette flow (TCF) system has been used recently to study the flow behaviour of particle-laden fluids under inertia. This article provides an overview of experimental, theoretical and computational work related to the TCF of neutrally buoyant non-Brownian suspensions, with an emphasis on the effect of finite-sized particles on the series of flow transitions and flow structures. Particles, depending on their size and concentration, cause several significant deviations from Newtonian fluid behaviour, including shifting the Reynolds number corresponding to transitions in flow structure and changing the possible structures present in the flow. Furthermore, particles may also migrate depending on the flow structure, leading to hysteretic effects that further complicate the flow behaviour. The current state of theoretical and computational modelling efforts to describe the experimental observations is discussed, and suggestions for potential future directions to improve the fundamental understanding of inertial particle-laden flows are provided. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Shear-induced glass-to-crystal transition in anisotropic clay-like suspensions.

A new numerical framework based on Stokesian dynamics is used to study a shear-induced glass-to-crystal transition in suspensions of clay-like anisotropically charged platelets. The structures obtained in quiescent conditions are in agreement with previous Monte Carlo results: a liquid phase at very short interaction range (high salt concentration), phase separation and a gel without large scale density fluctuations at intermediate interaction ranges, and glassy states at very large interaction ranges. When initially glassy suspensions are sheared, hydrodynamic torques first rotate platelets so they can reach a transient quasi-nematic disordered state. These orientational correlations permit to unlock translational degrees of freedom and the platelets then form strings aligned with the velocity direction and hexagonally packed in the gradient-vorticity plane. Under steady shear, platelet orientations are correlated but the system is not nematic. After flow cessation and relaxation in quiescent conditions, positional and orientational order are further improved as the platelet suspension experiences a transition to a nematic hexagonal crystal. Energy calculations and the existence of residual stress anisotropy after relaxation show that this final structure is not an equilibrium state but rather a new ordered, arrested state. The transient, nematic, disordered state induced by shear immediately after startup and unlocking translational degrees of freedom is thought to be an initial step that may be generic for other suspensions of strongly anisotropic colloids with important translation-orientation coupling induced by long-range interactions.

Shear stress dependence of force networks in 3D dense suspensions.

The geometric organization and force networks of 3D dense suspensions that exhibit both shear thinning and thickening have been examined as a function of varying strength of interparticle attractive interactions using lubrication flow discrete element simulations. Significant rearrangement of the geometric topology does not occur at either the local or global scale as these systems transition across the shear thinning and shear thickening regimes. In contrast, massive rearrangements in the balance of attractive, lubrication, and contact forces are observed with interesting behavior of network growth and competition. In agreement with prior work, in shear thinning regions the attractive force is dominant, however as the shear thickening region is approached there is growth of lubrication forces. Lubrication forces oppose the attraction forces, but as viscosity continues to increase under increasing shear stress, the lubrication forces are dominated by contact forces that also resist attraction. Contact forces are the dominant interactions during shear thickening and are an order of magnitude higher than their values in the shear-thinning regime. At high attractive interaction strength, contact networks can form even under shear thinning conditions, however high shear stress is still required before contact networks become the driving mechanism of shear thickening. Analysis of the contact force network during shear thickening generally indicates a uniformly spreading network that rapidly forms across empty domains; however the growth patterns exhibit structure that is significantly dependent upon the strength of interparticle interactions, indicating subtle variations in the mechanism of shear thickening.

Microstructure of the near-wall layer of filtration-induced colloidal assembly.

This paper describes an experimental study of filtration of a colloidal suspension using microfluidic devices. A suspension of micrometer-scale colloids flows through parallel slit-shaped pores at fixed pressure drop. Clogs and cakes are systematically observed at pore entrance, for variable applied pressure drop and ionic strength. Based on image analysis of the layer of colloids close to the device wall, global and local studies are performed to analyse in detail the near-wall layer microstructure. Whereas global porosity of this layer does not seem to be affected by ionic strength and applied pressure drop, a local study shows some heterogeneity: clogs are more porous at the vicinity of the pore than far away. An analysis of medium-range order using radial distribution function shows a slightly more organized state at high ionic strength. This is confirmed by a local analysis using two-dimension continuous wavelet decomposition: the typical size of crystals of colloids is larger for low ionic strength, and it increases with distance from the pores. We bring these results together in a phase diagram involving colloid-colloid repulsive interactions and fluid velocity.

From Yielding to Shear Jamming in a Cohesive Frictional Suspension.

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 levels, with an intermediate region of stress in which the material is flowable.

Microscopic Origin of Frictional Rheology in Dense Suspensions: Correlations in Force Space.

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress (σ_{xy}) and packing fraction (ϕ). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, µ=σ_{xy}/P. We find that µ decreases (i) as ϕ is increased and (ii) as σ_{xy} is increased. Using a new constitutive relation between µ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a discontinuous shear thickening flow diagram that is in good agreement with numerical simulations, and the qualitative features of µ that lead to the generic flow diagram of a discontinuous shear thickening fluid observed in experiments.

Shear thickening in concentrated suspensions of smooth spheres in Newtonian suspending fluids.

Shear thickening is a phenomenon in which the viscosity of a suspension increases with increasing stress or shear rate, sometimes in a discontinuous fashion. While the phenomenon, when observed in suspensions of corn starch in water, or Oobleck, is popular as a science experiment for children, shear thickening is actually of considerable importance for technological applications and exhibited by far simpler systems. Concentrated suspensions of smooth hard spheres will exhibit shear thickening, and understanding this behavior has required a fundamental change in the paradigm of describing low-Reynolds-number solid-fluid flows, in which contact forces have traditionally been absent. Here, we provide an overview of our understanding of shear thickening and the methods that have been developed to describe it, as well as outstanding questions.

Discontinuous shear thickening in Brownian suspensions by dynamic simulation.

Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in noncolloidal suspensions, i.e., a stress-induced transition from a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The thickening obtained in a colloidal suspension of purely hard frictional spheres is qualitatively similar to experimental observations. However, the agreement cannot be made quantitative with only hydrodynamics, frictional contacts, and Brownian forces. Therefore, the role of a short-range repulsive potential mimicking the stabilization of actual suspensions on the thickening is studied. The effects of Brownian and repulsive forces on the onset stress can be combined in an additive manner. The simulations including Brownian and stabilizing forces show excellent agreement with experimental data for the viscosity η and the second normal stress difference N2.

Simulation of shear thickening in attractive colloidal suspensions.

The influence of attractive forces between particles under conditions of large particle volume fraction, ϕ, is addressed using numerical simulations which account for hydrodynamic, Brownian, conservative and frictional contact forces. The focus is on conditions for which a significant increase in the apparent viscosity at small shear rates, and possibly the development of a yield stress, is observed. The high shear rate behavior for Brownian suspensions has been shown in recent work [R. Mari, R. Seto, J. F. Morris and M. M. Denn PNAS, 2015, 112, 15326-15330] to be captured by the inclusion of pairwise forces of two forms, one a contact frictional interaction and the second a repulsive force often found in stabilized colloidal dispersions. Under such conditions, shear thickening is observed when shear stress is comparable to the sum of the Brownian stress, kT/a3, and a characteristic stress based on the combination of interparticle force, i.e. σ ∼ F0/a2 with kT the thermal energy, F0 the repulsive force scale and a the particle radius. At sufficiently large ϕ, this shear thickening can be very abrupt. Here it is shown that when attractive interactions are present with the noted forces, the shear thickening is obscured, as the viscosity shear thins with increasing shear rate, eventually descending from an infinite value (yield stress conditions) to a plateau at large stress; this plateau is at the same level as the large-shear rate viscosity found in the shear thickened state without attractive forces. It is shown that this behavior is consistent with prior observations in shear thickening suspensions modified to be attractive through depletion flocculation [V. Gopalakrishnan and C. F. Zukoski J. Rheol., 2004, 48, 1321-1344]. The contributions of the contact, attractive, and hydrodynamics forces to the bulk stress are presented, as are the contact networks found at different attractive strengths.

Airflows generated by an impacting drop.

A drop impacting a solid surface with sufficient velocity will splash and emit many small droplets. However, lowering the ambient air pressure suppresses splashing completely. This effect, robustly found for different liquid and substrate properties, raises the fundamental question of how air affects a spreading drop. In a combined experimental and numerical study we characterize the flow of air induced by the drop after it hits the substrate, using a modified Schlieren optics technique combined with high-speed video imaging and Lattice-Boltzmann simulations. Our experiments reveal the emergence of air structures on different length scales. On large scales, the airflow induced in the drop's wake leads to vortex structures due to interaction with the substrate. On smaller scales, we visualize a ring structure above the outer edge of the spreading liquid generated by the spreading of the drop. Our simulations reveal the interaction between the wake vorticity and the flows originating from the rapidly escaping air from below the impacting drop. We show that the vorticity is governed by a balance between inertial and viscous forces in the air, and is unrelated to the splashing threshold.

Thermocapillary migration of a drop with a thermally conducting stagnant cap.

Hypothesis The thermocapillary migration of a spherical drop with a stagnant cap in the presence of a constant applied temperature gradient can be strongly affected by the finite thermal conductivity of the stagnant cap. Numerics The heat conduction of the stagnant cap is analytically modeled. The effects of the additional interfacial stresses generated by the disturbances to the local temperature field due to the presence of the cap at the fluid-fluid interface and the corresponding velocity of migration of the drop are evaluated by solving for the temperature and hydrodynamic field equations in and around the drop. An asymptotic model is derived to predict the terminal velocity in the presence of an infinitely conducting stagnant cap. Findings The effects of the surface conductivity and size of the stagnation region alongside the bulk thermal conductivities and viscosities of the drop and surrounding media are evaluated. The terminal velocity of the drop is shown to have a monotonic dependence on the conductivity of the stagnant cap. The bounds to the terminal velocity increment due to the stagnant cap are derived. These bounds can be of significance to multiphysics problems involving particle laden drops, Pickering emulsions and other multi-phase technologies where the conductivity of the surface adsorbents is non-negligible.

Hydrodynamically driven colloidal assembly in dip coating.

We study the hydrodynamics of dip coating from a suspension and report a mechanism for colloidal assembly and pattern formation on smooth substrates. Below a critical withdrawal speed where the coating film is thinner than the particle diameter, capillary forces induced by deformation of the free surface prevent the convective transport of single particles through the meniscus beneath the film. Capillary-induced forces are balanced by hydrodynamic drag only after a minimum number of particles assemble within the meniscus. The particle assembly can thus enter the thin film where it moves at nearly the withdrawal speed and rapidly separates from the next assembly. The interplay between hydrodynamic and capillary forces produces periodic and regular structures below a critical ratio Ca(2/3)/sqrt[Bo] < 0.7, where Ca and Bo are the capillary and Bond numbers, respectively. An analytical model and numerical simulations are presented for the case of two-dimensional flow with circular particles in suspension. The hydrodynamically driven assembly documented here is consistent with stripe pattern formations observed experimentally in dip coating.

Colloidal adsorption at fluid interfaces: regime crossover from fast relaxation to physical aging.

The adsorption of a colloidal particle at a fluid interface is studied theoretically and numerically, documenting distinctly different relaxation regimes. The adsorption of a perfectly smooth particle is characterized by a fast exponential relaxation to thermodynamic equilibrium where the interfacial free energy reaches the global minimum. The short relaxation time is given by the ratio of viscous damping to capillary forces. Physical and/or chemical heterogeneities, however, can result in multiple minima of the free energy giving rise to metastability. In the presence of metastable states we observe a crossover to a slow logarithmic relaxation reminiscent of physical aging in glassy systems; sufficiently close to equilibrium the slow relaxation becomes exponential. The long relaxation time is determined by the Kramers escape rate from metastable states. Derived analytical expressions yield quantitative agreement with molecular dynamics simulations and recent experimental observations. This work provides new insights on the adsorption of colloidal particles with surface microstructure.

Discontinuous shear thickening of frictional hard-sphere suspensions.

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.

Threshold concentration and random collision determine the growth of the huntingtin inclusion from a stable core.

The processes underlying formation and growth of unfolded protein inclusions are relevant to neurodegenerative diseases but poorly characterized in living cells. In S. cerevisiae, inclusions formed by mutant huntingtin (mHtt) have some characteristics of biomolecular condensates but the physical nature and growth mechanisms of inclusion bodies remain unclear. We have probed the relationship between concentration and inclusion growth in vivo and find that growth of mHtt inclusions in living cells is triggered at a cytoplasmic threshold concentration, while reduction in cytoplasmic mHtt causes inclusions to shrink. The growth rate is consistent with incorporation of new material through collision and coalescence. A small remnant of the inclusion is relatively long-lasting, suggesting that it contains a core that is structurally distinct, and which may serve to nucleate it. These observations support a model in which aggregative particles are incorporated by random collision into a phase-separated condensate composed of a particle-rich mixture.

Rheology of hydrate forming emulsions.

Results are reported on an experimental study of the rheology of hydrate-forming water-in-oil emulsions. Density-matched concentrated emulsions were quenched by reducing the temperature and an irreversible transition was observed where the viscosity increased dramatically. The hydrate-forming emulsions have characteristic times for abrupt viscosity change dependent only on the temperature, reflecting the importance of the effect of subcooling. Mechanical transition of hydrate-free water-in-oil emulsions may require longer times and depends on the shear rate, occurring more rapidly at higher rates but with significant scatter which is characterized through a probabilistic analysis. This rate dependence together with dependence on subcooling reflects the importance of hydrodynamic forces to bring drops or particles together.

Correlation function approach for diffusion in confined geometries.

This paper describes a formalism for extracting spatially varying transport coefficients from simulations of a molecular fluid in a nanochannel. This approach is applied to self-diffusion of a Lennard-Jones fluid confined between two parallel surfaces. A numerical grid is laid over the domain confining the fluid, and fluid properties are projected onto the grid cells. The time correlation functions between properties in different grid cells are calculated and can be used as the basis for a fitting procedure for extracting spatially varying diffusion coefficients from the simulation. Results for the Lennard-Jones system show that transport behavior varies sharply near the liquid-solid boundary and that the changes depend on the details of the liquid-solid interaction. A quantitative difference between the reduced and detailed models is discussed. It is found that the difference could be associated with assumptions about the form of the transport equations at molecular scales in lieu of problems with the method itself. The study suggests that this approach to fitting molecular simulations to continuum equations may guide the development of appropriate coarse-grained equations to model transport phenomena at nanometer scales.

Soil granular dynamics on-a-chip: fluidization inception under scrutiny.

Predicting soil evolution remains a scientific challenge. This process involves poorly understood aspects of disordered granular matter and dense suspension dynamics. This study presents a novel two-dimensional experiment on a small-scale chip structure; this allows the observation of the deformation at the particle scale of a large-grained sediment bed, under conditions where friction dominates over cohesive and thermal forces, and with an imposed fluid flow. Experiments are performed under conditions which span the particle resuspension criterion, and particle motion is detected and analyzed. The void size population and statistics of particle trajectories bring insight into the sediment dynamics near fluidization conditions. Specifically, particle rearrangement and net bed compaction are observed at flow rates significantly below the criterion for instability growth. Above a threshold flowrate, a channel forms and grows in the vertical direction; and eventually it crosses the entire bed. In the range of flow rates where channelization can occur, the coexistence of compacting and dilating bed scenarios is observed. The results of the study enhance our capacity for modeling of both slow dynamics and eventual rapid destabilization of sediment beds. Microfluidic channel soil-on-a-chip studies open avenues to new investigations including dissolution-precipitation, fine particle transport, or micro-organism swimming and population growth, which may depend on the mechanics of the porous medium itself.

Global topology of contact force networks: Insight into shear thickening suspensions.

Highly concentrated particle suspensions (also called slurries) can undergo a sharp increase in viscosity, or shear thickening, under applied stress. Understanding the fundamental features leading to such rheological change is crucial to optimize flow conditions or to design flow modifiers for slurry processing. While local changes to the particle environment under applied shear can be related to changes in viscosity, there is a broader need to connect the shear thickening transition to the fundamental organization of particle-interaction forces which lead to long-range organization. In particular, at a high volume fraction of particles, recent evidence indicates frictional forces between contacting particles is of importance. Herein, the network of frictional contact forces is analyzed within simulated two-dimensional shear thickening suspensions. Two topological metrics are studied to characterize the response of the contact force network (CFN) under varying applied shear stress. The metrics, geodesic index and the void parameter, reflect complementary aspects of the CFN: One is the connectedness of the contact network and the second is the distribution of spatial areas devoid of particle-particle contacts. Considered in relation to the variation of the viscosity, the topological metrics show that the network grows homogeneously at large scales but with many local regions devoid of contacts, indicating clearly the role of CFN growth in causing the large change in the rheological response at the shear thickening transition.