Session X45: Suspensions: Rheology

Average stress in a dilute suspension of rigid spheroids in a second-order fluid in a linear flow field

The stress response of a suspension of rigid particles in a non-Newtonian fluid is a key variable of interest in studying the rheology of various biological suspensions. While such investigations have been theoretically studied for suspensions of rigid spheres in weakly viscoelastic fluids, the effect of the non-sphericity of particles on the stress remains relatively unexplored. The interplay between the response of the polymeric fluid and the particle orientation yields rich physics. We determine the average extra stress in a dilute suspension of rigid, non-Brownian spheroids in a second-order fluid subject to shear and extensional flows by performing a perturbation expansion of the extra stress up to order Wi (Weissenberg number). We obtain the particle contribution to the first and second normal stress differences, the effective shear viscosity, and the effective extensional viscosity. This analysis also elucidates the time dependence of the average stress for short-term and long-term orientations of the particle.   

Motility-induced shear thickening in dense colloidal suspensions

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 behaviour in the presence of steady shear flow. In this study, 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 passive suspension shows a solid-like behaviour, turning on particle motility fluidises the system and, at low self-propulsion, the suspension behaves as a shear-thinning fluid. Increasing the self-propulsion of the colloids induces a crossover from a shear-thinning to a shear-thickening behaviour, which we attribute to clustering in the suspensions induced by motility, a general phenomenon that occurs close to motility-induced phase separation (MIPS) [I. Buttinoni, et al., Physical Review Letters. 110, 238301 (1-5) (2013)]. This novel behaviour of motility-induced shear thickening (MIST) can be used to tailor the rheological response of colloidal suspensions.   

Tunable rheology of dense suspensions of conductive particles via an applied electric field

Electric-field-driven microhydrodynamics promises a novel approach to tune or control the suspension rheology of conductive particles. Upon the application of an electric field, these suspensions are known to undergo dipolophoresis (DIP), the combination of two nonlinear electrokinetic phenomena, namely induced-charge electrophoresis (ICEP) and dielectrophoresis (DEP). In this study, we perform large-scale numerical simulations of dense suspensions of ideally conductive particles undergoing DIP in the presence of shear flow using our Stokesian dynamics-based model. The control parameters are the magnitude, direction, and frequency of the electric field. When an electric field is applied along the shear-gradient direction, increasing the field magnitude results in a significant decrease in viscosity at low-frequency fields due to the dominant ICEP effect. Conversely, a high-frequency field leads to an increase in viscosity with the field magnitude due to the DEP dominance. It is also observed that changing the field direction leads to different rheological responses. We further analyze the effects of these control parameters on microstructure, normal stress differences, and suspension dynamics. Lastly, the transient behaviors resulting from sudden changes in the control parameters will be discussed.   

The “roll” of constraints in yielding of soft particulate gels

Soft particulate gels, encompassing a wide range of materials applicable to consumables, injectables, and 3D printing, exhibit intriguing rheological properties due to their unique structure. These gels are composed of a small volume fraction of particles dispersed within a fluid medium, forming an aggregated network through attractive interactions such as Van der Waals or depletion forces. The resulting complexity in their rheological behavior, including yield stress and shear thinning, makes them promising candidates for various in-situ solidifying applications from cosmetics to tissues. While it is widely acknowledged that system-spanning particulate structures contribute to the observed yield stress, a comprehensive understanding of the underlying microscopic mechanisms remains elusive. In this study, we present coarse-grained simulations focusing on model depletion gels to shed light on this intriguing phenomenon. Contrary to conventional belief, our simulations reveal that the mere presence of attractive interactions and aggregate formation does not sufficiently explain the observed yield stress. Instead, we identify a crucial physics element in the form of microscopic constraints on the relative rotational motion between bonded particles. Through a detailed analysis of microstructure and particle dynamics, we elucidate how these constraints lead to the emergence of yield stress in soft particulate gels. This research provides essential insights into the micromechanical origins of yield stress in soft particulate gels, paving the way for improved understanding and engineering of these versatile materials for a wide range of real-world applications.   

The role of microstructure in the rheology of sheared dense frictionless non-Brownian suspensions

We use Discrete Element Simulations (DEM) to characterize the shear rheology of frictionless non-Brownian suspensions close to jamming. The particles experience a short-range soft repulsive force sufficient to prevent frictional contacts at all the volume fractions and shear rates studied. Sheared frictionless dense suspensions exhibit a transition with increasing shear rate, from a regime of constant viscosity to one where the viscosity increases linearly with the strain-rate owing to the increased role of particle inertia. The drastic variation of transition shear-rates reported in literature necessitates a better understanding of the suspension microstructure. Our simulations show that the rheology of a suspension converges above a critical system size that is dependent on the shear rate. The viscosity in smaller systems has a dependence on the system size that increases with increasing shear rate. We find stresses due to contact forces to be higher than stresses due to hydrodynamic lubrication forces. Hence, we attribute the critical system size to the length scale associated with the formation of contacting particle clusters. This work explores the role of these particle clusters within the microstructure in influencing the suspension rheology.   

Effect of polydispersity and bubble interactions on the linear viscoelastic behaviour of semidilute bubble suspensions in Newtonian media

We examined the effect of polydispersity on the linear viscoelastic moduli (G΄,G΄΄) of semidilute bubble suspensions. Theoretical analysis showed that polydispersity affects G΄,G΄΄ only if the bubble size distribution is bimodal with equal volume fractions of small and large bubbles. Otherwise, the polydisperse suspension can be treated as monodisperse with a volume-weighted mean bubble radius. To confirm the theory, we conducted small amplitude oscillatory shear tests. The measured G΄ values exceeded the theoretical ones for average dynamic capillary numbers (〈Cd〉) lower than 1. Visualizing the bubbles under oscillatory shear showed minimal changes in the suspension microstructure, suggesting that the enhanced elasticity at low 〈Cd〉 arises from bubble fluid dynamic interactions, whose effect is revealed at longer characteristic flow times. At low bubble volume fraction, stronger and prolonged pre-shear can reduce the interactions among the bubbles, by increasing the mean inter-bubble distance. But in denser suspensions, pre-shear has little impact on the bubble spatial distribution. Fitting a multi-mode Jeffreys model to the experimental data revealed that bubble interactions induce multiple relaxation modes.   

Nonlinear Rheology of Dense Non-Brownian Suspensions: What is the role of particle shape?

Suspensions of non-Brownian particles in viscous fluids are relevant in engineered processes and in natural phenomena. These suspensions typically consist of solid particles of

nonspherical shape and often exhibit nonlinear behavior such as shear thinning and/or shear thickening even when the suspending fluid is Newtonian. This talk focuses on such nonlinear rheological behaviors and it is motivated by one central question: ``What is the role of particle shape?". We will present our recent results concerning the rheology of two suspensions, which differ solely through the particle shapes. One suspension was made of spheres, and the other of globular facetted particles produced by crushing identical spheres. The suspension of crushed particles exhibited a higher viscosity than the suspension of spheres for the same volume fraction and applied stress and displayed a steeper shear thinning behavior. The results show that the stronger nonlinear rheology of crushed particles stems from a combination of stress-weakening sliding friction and extra resistance to rolling motion due to the angular shape of the crushed particles.  We will use these recent findings to put forward a scaling analysis to systematically explore the nonlinear rheology of dense non-Brownian suspensions made of nonspherical particles of arbitrary shape with the interplay of shape with hydrodynamic, colloidal, and contact forces.   

Structure, memory, and rheology in sheared dense suspensions

Recent work [Galloway et al. Nat. Phy. 2022] has uncovered a connection between the structure, memory formation, and rheology of sheared dense suspensions. The relationships found there are demonstrated in bulk and system averaged quantities. Though, as is well known in disordered systems, the microstructure and local dynamics of these systems are strongly heterogeneous. Structural descriptors, like machine-learned softness and local excess entropy, have helped recently in connecting this local, heterogeneous dynamics to the disordered structure. In this work, we explore the connection between the local structural indicators and memory formed in steady state. Between the athermal and supercooled regimes we observe nontrivial behaviour of the steady-state particle dynamics that depends upon the preparation protocol. We connect this to the local structure as represented by excess entropy and softness. These results inform us at a microstructural level how preparation affects the structure, and subsequent memory/dynamics, which leads to distinct rheology.   

Spatial stress correlation in strong colloidal gel systems

Colloidal gel systems exhibit increasingly slow relaxation and ultra-long-ranged spatial correlations of the dynamics similar to other jammed materials. These cooperative dynamics point to the presence of long-ranged stress correlation in these systems, which remain largely uninvestigated in the literature. In this work, we systematically investigate the nature of stress correlations in soft colloidal gel materials in the limit of moderate to high packing fractions and strong attraction. In this regime, centrosymmetric potential description for particle interaction fails as strong attraction can lead to frictional contacts, as shown explicitly in previous experiments. Accordingly, we model the system similarly to the cohesive granular media with Langevin dynamics to incorporate the effects of rolling and sliding resistant contacts and thermal fluctuations. We show that the spatial stress correlations are long ranged with very slow spatial decay close to the gel point. Similarly to previous studies on the frictional granular matter, the full stress autocorrelation matrix is dictated by the pressure and torque autocorrelations due to mechanical balance and material isotropy constraints. Surprisingly, it is observed that the gel materials do not behave as a normal elastic solid close to the gel point as assumed loosely in the literature because the real-space pressure fluctuations decay slower than normal. Furthermore, we link the abnormal pressure fluctuations to the non-hyperuniform behavior of the system (granular matter and gel) with respect to the local packing fraction fluctuations, thus relating the deviations from the normal elastic behavior across various jammed systems under a common framework.   

Shear-thickening in presence of adhesive contact forces: the singularity of cornstarch

A number of dense particle suspensions experience a dramatic increase in viscosity with the shear stress, up to a solid-like response. This shear-thickening process is understood as a transition under flow of the nature of the contacts – from lubricated to frictional – between initially repellent particles. Most systems are now assumed to fit in with this scenario, which is questionable.

To better understand the mechanism of shear thickening of cornstarch solutions, we study the structure of the suspensions under flow, with a focus on the high shear region.

 Using in-house sensors, we probe at the millimeter-scale, in a new way, the normal stresses that develop. The nature of this signal changes with the constraining conditions: at low weight fractions and large gap widths he signal is consistent with a stress wave moving 1 to 1.5 times faster than the geometry. At high weight fractions  and small gap, the signal arises from the passage of a solid aggregate rolling between the plates. This transition is explained by taking into account the presence of adhesive forces between the particles at high shera stress. The presence these forces, combined with the existence of a yield stress (showing that the particles are also in contact at low stress) clearly indicates that cornstarch particles are in contact all along the flow curve.

From the previous discussion, we see that cornstarch suspensions stand out of the classical shear-thickening frame. We suggest here that cornstarch particles are very weakly attractive in suspensions in CsCl brine (to account for the yield stress), and strongly adhesive once the normal stresses pushes them into contact. More precisely, the initial contact between particles induces a small yield stress. When subjected to stress, the fragile bonds break and the suspension turns to a liquid, exhibiting a strongly shear thinning behavior. Beyond a critical stress, the particle pressure pushes the particles in contact and involves an important indentation. The polysaccharide chains surrounding the starch granules become entangled. An adhesive force coming from hydrogen bonds is set up. In this regime, there is a competition between the time for the polysaccharide to disentangle and the contact time ($propto1/dotgamma$) between the particles. When the first is larger than the latter, the system thickens.   

The Rheology of Temperature-Responsive Volume-Phase Transition Hydrogels for the Improved Thermal Performance and Lifetime of Geothermal Systems.

With the massive rise in investment towards renewable energy to combat climate change, geothermal energy represents a major economically viable alternative in many parts of the world. Geothermal systems purposely contain many flow paths to maximize heat transfer area, but many paths do not meet desired temperatures or are drained of their thermal energy over time, providing "short circuit" routes that harm thermal performance. Previous models predict plugging these routes and redirecting flow can extensively improve both the thermal performance and lifetime of the system. Volume-phase transition (VPT) particles present an excellent candidate to plug these flows as they expand in low temperatures and contract in high temperatures above a lower critical solution temperature (LCST), drastically changing the volume fraction of the system and thus important parameters such as viscosity and yield stress. Rheological characterization is performed to better understand and compare these properties to obtain an ideal hydrogel recipe that is optimized for temperature-sensitive and plugging capabilities.