Focused force transmission through an aqueous suspension of granules

Rheological Properties of Dense Particle Suspensions of Starches: Shear Thickening, Shear Jamming, and Shock Absorption Properties

Concentrated suspensions of Brownian and non-Brownian particles display distinctive rheological behavior highly dependent on shear rate and shear stress. Cornstarch suspensions, composed of starch particles from corn plants, served as a model for concentrated non-Brownian suspensions, demonstrating discontinuous shear thickening (DST) and dynamic shear jamming (SJ). However, starch particles from other plant sources have not yet been investigated, despite their different sizes and shapes. This study is focused on the evaluation of the effects of the structural parameters of starch particles by preparing concentrated suspensions of starch particles from 13 different plants at particle fractions of 25-50% and their rheological behavior through steady shear, pull-out, and ball-drop tests. Starch particles can be roughly classified as polygonal and ellipsoidal. The DST and SJ behavior typically reported for concentrated cornstarch suspensions were confirmed for other starch particles in both particle groups. The ball-drop test demonstrated excellent shock absorption properties for 11 concentrated suspensions of starch particles, except for sago palms. In the case of concentrated suspensions of starch particles, the particle fraction and shear applied were the dominant factors that significantly affected the rheological behavior, whereas the particle shape was not a primary contributor. The findings of this study drive further investigation on the effect of liquid and particle surface properties in concentrated particle suspensions on DST and SJ behaviors.

Stress Controlled Rheology of Dense Suspensions Using Transient Flows

Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we can track how a dense suspension approaches its shear-jammed state dynamically and quantitatively map out the onset stress for solidification in a state diagram.

Controlling shear jamming in dense suspensions via the particle aspect ratio

Dense suspensions of particles in a liquid exhibit rich, non-Newtonian behaviors such as shear thickening (ST) and shear jamming (SJ). ST has been widely studied and is known to be enhanced by increasing the particles' frictional interactions and also by making their shape more anisotropic. SJ however has only recently been understood to be a distinct phenomenon and, while the role of interparticle friction has been investigated, the role of particle anisotropy in controlling the SJ regime has remained unknown. To address this we here synthesize silica particles for use in water/glycerol suspensions. This pairing of hydrogen-bonding particle surfaces and suspension solvent has been shown to elicit SJ with spherical particles. We then vary particle aspect ratio from Γ = 1 (spheres) to Γ = 11 (slender rods), and perform rheological measurements to determine the effect of particle anisotropy on the onset of shear jamming. We also show that the effect on the precursor to SJ, discontinuous shear thickening (DST), is consistent with prior work. We find that increasing aspect ratio significantly reduces φm, the minimum particle packing fraction at which SJ can be observed, to values as low φm = 33% for Γ = 11. The ability to fix the properties of the solvated particle surfaces, and thus the particle interactions at contact, while varying shape anisotropy, yields fundamental insights about the SJ capabilities of suspensions and provides a framework to rationally design and tune these behaviors.

Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress-on the order of MPa-with a delay after the impactor hits the suspension surface. We show that neither the delay nor the magnitude of the stress can yet be explained by either standard rheological models of shear thickening in terms of steady-state viscosities, or impact models based on added mass or other inertial effects. The stress increase occurs when a dynamically jammed region of the suspension in front of the impactor propagates to the opposite boundary of the container, which can support large stresses when it spans between solid boundaries. We present a constitutive relation for impact rheology to relate the force on the impactor to its displacement. This can be described in terms of an effective modulus but only after the delay required for the dynamically jammed region to span between solid boundaries. Both the modulus and the delay are reported as a function of impact velocity, fluid height, and weight fraction. We report in a companion paper the structure of the dynamically jammed region when it spans between the impactor and the opposite boundary [Allen et al., Phys. Rev. E 97, 052603 (2018)10.1103/PhysRevE.97.052603]. In a direct follow-up paper, we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water [Mukhopadhyay et al., Phys. Rev. E 97, 052604 (2018)10.1103/PhysRevE.97.052604].

System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions

We experimentally characterize the structure of concentrated suspensions of cornstarch and water in response to impact. Using surface imaging and particle tracking at the boundary opposite the impactor, we observed that a visible structure and particle flow at the boundary occur with a delay after impact. We show the delay time is about the same time as the strong stress response, confirming that the strong stress response results from deformation of the dynamically jammed structure once it spans between the impactor and a solid boundary. A characterization of this strong stress response is reported in a companion paper [Maharjan, Mukhopadhyay, Allen, Storz, and Brown, Phys. Rev. E 97, 052602 (2018)10.1103/PhysRevE.97.052602]. We observed particle flow in the outer part of the dynamically jammed region at the bottom boundary, with a net transverse displacement of up to about 5% of the impactor displacement, indicating shear at the boundary. Direct imaging of the surface of the outer part of the dynamically jammed region reveals a change in surface structure that appears the same as the result of dilation in other cornstarch suspensions. Imaging also reveals cracks, like a brittle solid. These observations suggest the dynamically jammed structure can temporarily support stress according to an effective modulus, like a soil or dense granular material, along a network of frictional contacts between the impactor and solid boundary.

Impact-induced solidlike behavior and elasticity in concentrated colloidal suspensions

Modified drop weight impact tests were performed on SiO_{2}-ethylene glycol concentrated suspensions. Counterintuitive impact-induced solidlike behavior and elasticity, causing significant deceleration and rebound of the impactor, were observed. We provide evidence that the observed large deceleration force on the impactor mainly originates from the hydrodynamic force, and that the elasticity arises from the short-range repulsive force of a solvation layer on the particle surface. This study presents key experimental results to help understand the mechanisms underlying various stress-induced solidification phenomena.

Force and Mass Dynamics in Non-Newtonian Suspensions

Above a certain solid fraction, dense granular suspensions in water exhibit non-Newtonian behavior, including impact-activated solidification. Although it has been suggested that solidification depends on boundary interactions, quantitative experiments on the boundary forces have not been reported. Using high-speed video, tracer particles, and photoelastic boundaries, we determine the impactor kinematics and the magnitude and timings of impactor-driven events in the body and at the boundaries of cornstarch suspensions. We observe mass shocks in the suspension during impact. The shock front dynamics are strongly correlated to those of the intruder. However, the total momentum associated with this shock never approaches the initial impactor momentum. We also observe a faster second front associated with the propagation of pressure to the boundaries of the suspension. The two fronts depend differently on the initial impactor speed v_{0} and the suspension packing fraction. The speed of the pressure wave is at least an order of magnitude smaller than (linear) ultrasound speeds obtained for much higher frequencies, pointing to complex amplitude and frequency response of cornstarch suspensions to compressive strains.

Measuring the porosity and compressibility of liquid-suspended porous particles using ultrasound

A key parameter describing the behavior of suspensions is the volume fraction ϕ of the solid particles that are dispersed in the liquid. Obtaining accurate values for ϕ becomes difficult for porous particles, because they can absorb some of the liquid. A prime example are the widely used cornstarch suspensions, for which ϕ usually is only estimated from the mass fraction of particles. Here we present a method to measure the effective porosity and compressibility of porous particles with ultrasound. We obtain the speed of sound in dilute cornstarch suspensions at multiple particle concentrations and with different solvent compressibilities. With the measured particle porosity of 0.31 we are able to calculate the volume fraction of the saturated particles reliably.

Drag law for an intruder in granular sediments

We investigate the drag experienced by a spherical intruder moving through a medium consisting of granular hydrogels immersed in water as a function of its depth, size, and speed. The medium is observed to display a yield stress with a finite force required to move the intruder in the quasistatic regime at low speeds before rapidly increasing at high speeds. In order to understand the relevant time scales that determine drag, we estimate the inertial number I given by the ratio of the time scales required to rearrange grains due to the overburden pressure and imposed shear and the viscous number J given by the ratio of the time scales required to sediment grains in the interstitial fluid and imposed shear. We find that the effective friction μ_{e} encountered by the intruder can be parametrized by I=sqrt[ρ_{g}/P_{p}]v_{i}, where ρ_{g} is the density of the granular hydrogels, v_{i} is the intruder speed, and P_{p} is the overburden pressure due to the weight of the medium, over a wide range of I where the Stokes number St=I^{2}/J≫1. We then show that μ_{e} can be described by the function μ_{e}(I)=μ_{0}+αI^{β}, where μ_{0}, α, and β are constants that depend on the medium. This formula can be used to predict the drag experienced by an intruder of a different size at a different depth in the same medium as a function of its speed.

High-speed ultrasound imaging in dense suspensions reveals impact-activated solidification due to dynamic shear jamming

A remarkable property of dense suspensions is that they can transform from liquid-like at rest to solid-like under sudden impact. Previous work showed that this impact-induced solidification involves rapidly moving jamming fronts; however, details of this process have remained unresolved. Here we use high-speed ultrasound imaging to probe non-invasively how the interior of a dense suspension responds to impact. Measuring the speed of sound we demonstrate that the solidification proceeds without a detectable increase in packing fraction, and imaging the evolving flow field we find that the shear intensity is maximized right at the jamming front. Taken together, this provides direct experimental evidence for jamming by shear, rather than densification, as driving the transformation to solid-like behaviour. On the basis of these findings we propose a new model to explain the anisotropy in the propagation speed of the fronts and delineate the onset conditions for dynamic shear jamming in suspensions.

Direct observation of dynamic shear jamming in dense suspensions

Liquid-like at rest, dense suspensions of hard particles can undergo striking transformations in behaviour when agitated or sheared. These phenomena include solidification during rapid impact, as well as strong shear thickening characterized by discontinuous, orders-of-magnitude increases in suspension viscosity. Much of this highly non-Newtonian behaviour has recently been interpreted within the framework of a jamming transition. However, although jamming indeed induces solid-like rigidity, even a strongly shear-thickened state still flows and thus cannot be fully jammed. Furthermore, although suspensions are incompressible, the onset of rigidity in the standard jamming scenario requires an increase in particle density. Finally, whereas shear thickening occurs in the steady state, impact-induced solidification is transient. As a result, it has remained unclear how these dense suspension phenomena are related and how they are connected to jamming. Here we resolve this by systematically exploring both the steady-state and transient regimes with the same experimental system. We demonstrate that a fully jammed, solid-like state can be reached without compression and instead purely with shear, as recently proposed for dry granular systems. This state is created by transient shear-jamming fronts, which we track directly. We also show that shear stress, rather than shear rate, is the key control parameter. From these findings we map out a state diagram with particle density and shear stress as variables. We identify discontinuous shear thickening with a marginally jammed regime just below the onset of full, solid-like jamming. This state diagram provides a unifying framework, compatible with prior experimental and simulation results on dense suspensions, that connects steady-state and transient behaviour in terms of a dynamic shear-jamming process.

Quasi-2D dynamic jamming in cornstarch suspensions: visualization and force measurements

We report experiments investigating jamming fronts in a floating layer of cornstarch suspension. The suspension has a packing fraction close to jamming, which dynamically turns into a solid when impacted at a high speed. We show that the front propagates in both axial and transverse direction from the point of impact, with a constant ratio between the two directions of propagation of approximately 2. Inside the jammed solid, we observe an additional compression, which results from the increasing stress as the solid grows. During the initial growth of the jammed solid, we measure a force response that can be completely accounted for by added mass. Only once the jamming front reaches a boundary, the added mass cannot account for the measured force anymore. We do not, however, immediately see a strong force response as we would expect when compressing a jammed packing. Instead, we observe a delay in the force response on the pusher, which corresponds to the time it takes for the system to develop a close to uniform velocity gradient that spans the complete system.

Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming

Shear thickening is a type of non-Newtonian behavior in which the stress required to shear a fluid increases faster than linearly with shear rate. Many concentrated suspensions of particles exhibit an especially dramatic version, known as Discontinuous Shear Thickening (DST), in which the stress suddenly jumps with increasing shear rate and produces solid-like behavior. The best known example of such counter-intuitive response to applied stresses occurs in mixtures of cornstarch in water. Over the last several years, this shear-induced solid-like behavior together with a variety of other unusual fluid phenomena has generated considerable interest in the physics of densely packed suspensions. In this review, we discuss the common physical properties of systems exhibiting shear thickening, and different mechanisms and models proposed to describe it. We then suggest how these mechanisms may be related and generalized, and propose a general phase diagram for shear thickening systems. We also discuss how recent work has related the physics of shear thickening to that of granular materials and jammed systems. Since DST is described by models that require only simple generic interactions between particles, we outline the broader context of other concentrated many-particle systems such as foams and emulsions, and explain why DST is restricted to the parameter regime of hard-particle suspensions. Finally, we discuss some of the outstanding problems and emerging opportunities.

Velocity oscillations and stop-go cycles: the trajectory of an object settling in a cornstarch suspension

We present results for objects settling in a cornstarch suspension. Two surprising phenomena can be found in concentrated suspensions. First, the settling object does not attain a terminal velocity but exhibits oscillations around a terminal velocity when traveling through the bulk of the liquid. Second, close to the bottom, the object comes to a full stop but then reaccelerates before coming to another stop. This cycle can be repeated up to 6 or 7 times before the object reaches the bottom to come to a final stop. For the bulk, we show that shear-thickening models are insufficient to account for the observed oscillations and that the history of the suspension needs to be taken into account. A hysteretic model, that goes beyond the traditional viscoelastic ones, describes the experiments quite well but still misses some details. The behavior at the bottom can be modeled with a minimal jamming model.

Smart multifunctional fluids for lithium ion batteries: enhanced rate performance and intrinsic mechanical protection

Lithium ion batteries are attractive power sources for the consumer electronics market and are being aggressively developed for road transportation. Nevertheless, issues with safety and reliability need to be solved prior to the large-scale uptake of these batteries. There have recently been significant development and assessment of materials with resistance to mechanical abuse, with the aims of reinforcing the battery and preventing puncturing during a crash. Most of the work on battery mechanical safety has concentrated on the external packaging of batteries, with little attention being paid to the enclosed electrolyte. We report on smart multifunctional fluids that act as both highly conductive electrolytes and intrinsic mechanical protectors for lithium ion batteries. These fluids exhibit a shear thickening effect under pressure or impact and thus demonstrate excellent resistance to crushing. Also, the fluids show higher ionic conductivities and comparable redox stability windows to the commercial liquid electrolytes.

Nonmonotonic settling of a sphere in a cornstarch suspension

Cornstarch suspensions exhibit remarkable behavior. Here, we present two unexpected observations for a sphere settling in such a suspension: In the bulk of the liquid the velocity of the sphere oscillates around a terminal value, without damping. Near the bottom the sphere comes to a full stop, but then accelerates again toward a second stop. This stop-go cycle is repeated several times before the object reaches the bottom. We show that common shear thickening or linear viscoelastic models cannot account for the observed phenomena, and propose a minimal jamming model to describe the behavior at the bottom.