Testing the Wyart-Cates model for non-Brownian shear thickening using bidisperse suspensions

Sub-Newtonian coalescence dynamics in shear-thickening non-Brownian colloidal droplets

Recent investigations into coalescence dynamics of complex fluid droplets revealed the existence of sub-Newtonian behaviour in polymeric fluids (elastic and shear thinning). We hypothesize that such delayed coalescence or sub-Newtonian coalescence dynamics may be extended to the general class of shear thickening fluids. To investigate this, droplets of aqueous corn-starch suspensions were chosen and their coalescence in the sessile-pendant configuration was probed by real-time high-speed imaging. Temporal evolution of the neck (growth) during coalescence was quantified as a function of suspended particle weight fraction, ϕw. The necking behavior was found to evolve as the power-law relation, R = atb, where R is the neck radius, with exponent b ≤ 0.5, implying that it is a subset of the generic sub-Newtonian coalescence. Furthermore, the coalescence dynamics could be demarcated into two distinct regimes, b ∼ 0.5 and b < 0.5, where the emergence of visco-elastic pinch-off response was observed in the latter regime. The particle fraction demarcating these regimes, designated as the critical particle weight fraction, ϕw ∼ ϕc > 0.35, also coincides with the existence of 'jamming' and 'flowing' regions within the neck during viscoelastic pinch-off of cornstarch suspensions (Roché et al., Phys. Rev. Lett., 2011, 107, 134503). We also propose a simplistic theoretical model that captures the observed delay in coalescence dynamics implicitly through altered suspension viscosity stemming from increased particle content.

Scalability of a graph neural network in accurate prediction of frictional contact networks in suspensions

Dense suspensions often exhibit shear thickening, characterized by a dramatic increase in viscosity under large external forcing. This behavior has recently been linked to the formation of a system-spanning frictional contact network (FCN), which contributes to increased resistance during deformation. However, identifying these frictional contacts poses experimental challenges and is computationally expensive. This study introduces a graph neural network (GNN) model designed to accurately predict FCNs by two dimensional simulations of dense shear thickening suspensions. The results demonstrate the robustness and scalability of the GNN model across various stress levels (σ), packing fractions (ϕ), system sizes, particle size ratios (Δ), and amounts of smaller particles. The model is further able to predict both the occurrence and structure of a FCN. The presented model is accurate and interpolates and extrapolates to conditions far from its control parameters. This machine learning approach provides an accurate, lower cost, and faster predictions of suspension properties compared to conventional methods, while it is trained using only small systems. Ultimately, the findings in this study pave the way for predicting frictional contact networks in real-life large-scale polydisperse suspensions, for which theoretical models are largely limited owing to computational challenges.

Pairing-specific microstructure in depletion gels of bidisperse colloids

We report the ensemble-averaged and pairing-specific network microstructure formed by short-range depletion attractions in hard sphere-like colloidal systems. Gelation is induced by adding polystyrene molecules at a fixed concentration to colloids with different colloid bidispersity ratios (α = 1, 0.72, and 0.60) across a range of volume fractions (0.10 ≤ ϕ ≤ 0.40). 3D confocal microscopy imaging combined with a scale-invariant feature transform algorithm show that monodisperse colloids pack more efficiently, whereas increasing the size disparity leads to looser, more disordered, and sub-isostatic packings. Categorizing the structures formed by small and large particles reveal that certain cluster configurations may be favored due to the complex interplay between the differences in particle surface areas and attractive potentials. These pairwise bonds assemble to affect the density of tetrahedral and poly-tetrahedral clusters in bidisperse systems. With the exception of non-percolating samples at ϕ = 0.10, increasing the gel volume fraction leads to an increase in the number of nearest neighbors. However, the internal density within each cluster decreases, possibly due to kinetic arrest from the deeper potential wells of tetrahedral clusters at low volume fractions in which vertices are primarily made out of larger particles.

Rheology of bidisperse non-Brownian suspensions

We study the rheology of bidisperse non-Brownian suspensions using particle-based simulation, mapping the viscosity as a function of the size ratio of the species, their relative abundance, and the overall solid content. The variation of the viscosity with applied stress exhibits shear-thickening phenomenology irrespective of composition, though the stress-dependent limiting solids fraction governing the viscosity and its divergence point are nonmonotonic in the mixing ratio. Contact force data demonstrate an asymmetric exchange in the dominant stress contribution from large-large to small-small particle contacts as the mixing ratio of the species evolves. Combining a prior model for shear thickening with one for composition-dependent jamming, we obtain a full description of the rheology of bidisperse non-Brownian suspensions capable of predicting effects such as the viscosity reduction observed upon adding small particles to a suspension of large particles.

Order-disorder transition during shear thickening in bidisperse dense suspensions

Shear thickening of multimodal suspensions has proven difficult to understand because the rheology depends largely on the microscopic details of stress-induced frictional contacts at different particle size distributions (PSDs). Our discrete particle simulations below a critical volume fraction ϕc over a broad range of shear rates and PSDs elucidate the basic mechanism of order-disorder transition. Around the theoretical optimal PSD (relative content of small particles ζ1= 0.26), particles order into a layered structure in the Newtonian regime. At the onset of shear thickening, this layered structure transforms to a disordered one, accompanied by an abrupt viscosity jump. Minor increase in large-large particle contacts after the order-disorder transition causes apparent increase in radial force along the compressional axis. Bidisperse suspensions with less regular but stable layered structure at ζ1= 0.50 show good fluidity in the shear thickening regime. This work shows that in inertial flows where particle collisions dominate, order-disorder transition could play an essential role in shear thickening for bidisperse suspensions.

Scaling relationships between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated state to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity η and diffusivity D/ of the particles increase under characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relationship between viscosity and diffusivity using the length scale ξ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that η and D/ are controlled by ξ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relationship is described as a crossover from D/ ∼ η (frictionless) to η1/3 (frictional). We also confirm that the proposed power laws are insensitive to the interparticle friction and system size.

Rheology of particulate suspensions with non-Newtonian fluids in capillaries

Particulate suspensions occur in situations from blood flow to slurries in drilling applications. Existing investigations of these suspensions generally concentrate on the impact of particle volume fraction for suspensions in Newtonian fluids under free-flow conditions. Recently, particulate-polymer composites have been used in additive manufacturing (AM). Here, the polymer becomes a shear-thinning non-Newtonian fluid during extrusion, creating a particulate suspension. Motivated by the challenges in AM of particulate composites, this study investigates the rheology of suspensions of micrometre-sized particles in shear-thinning silicone while extruded through AM-scaled nozzles (millimetre-scale diameters). The suspensions were observed to follow a power-law behaviour and their rheology was investigated through the measured flow consistency (K) and behaviour (n) indices. The impact of the particle volume fraction (ϕ) and the ratio (ω) of the capillary inside diameter to the particle diameter on both indices were measured. n was found to be only impacted by the suspension fluid type and ϕ. K was found to be constant at large ω, but decreased and then increased to infinity with ω decreasing. Based on its behaviour, K was categorized into two conditions and analysed separately with semi-empirical models. The impact of particle size distribution was also investigated.

Jamming Distance Dictates Colloidal Shear Thickening

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) colloids that are spherically symmetric and have varied surface roughness. Confocal rheometry and dissipative particle dynamics simulations show that the shear thickening strength β scales exponentially with the scaled deficit contact number and the scaled jamming distance. Rough colloids, which experience additional rotational constraints, require an average of 1.5-2 fewer particle contacts as compared to smooth colloids, in order to generate the same β. This is because the surface roughness enhances geometric friction in such a way that the rough colloids do not experience a large change in the free volume near the jamming point. The available free volume for colloids of different roughness is related to the deficiency from the maximum number of nearest neighbors at jamming under shear. Our results further suggest that the force per contact is different for particles with different morphologies.

Magnetic propulsion of colloidal microrollers controlled by electrically modulated friction

Precise control over the motion of magnetically responsive particles in fluidic chambers is important for probing and manipulating tasks in prospective microrobotic and bio-analytical platforms. We have previously exploited such colloids as shuttles for the microscale manipulation of objects. Here, we study the rolling motion of magnetically driven Janus colloids on solid substrates under the influence of an orthogonal external electric field. Electrically induced attractive interactions were used to tune the load on the Janus colloid and thereby the friction with the underlying substrate, leading to control over the forward velocity of the particle. Our experimental data suggest that the frictional coupling required to achieve translation, transitions from a hydrodynamic regime to one of mixed contact coupling with increasing load force. Based on this insight, we show that our colloidal microrobots can probe the local friction coefficient of various solid surfaces, which makes them potentially useful as tribological microsensors. Lastly, we precisely manipulate porous cargos using our colloidal rollers, a feat that holds promise for bio-analytical applications.

Autonomously Probing Viscoelasticity in Disordered Suspensions

Recent experiments show a strong rotational diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions.