Nonmonotonic settling of a sphere in a cornstarch suspension

Effective viscosity and elasticity in dense suspensions under impact: Toward a modeling of walking on suspensions

The elastic response of dense suspensions under an impact is studied using coupled lattice Boltzmann method and discrete element method (LBM-DEM) and its reduced model. We succeed to extract the elastic force acting on the impactor in dense suspensions, which can exist even in the absence of percolating clusters of suspended particles. We then propose a reduced model to describe the motion of the impactor and demonstrate its relevancy through the comparison of the solution of the reduced model and that of LBM-DEM. Furthermore, we illustrate that the perturbation analysis of the reduced model captures the short-time behavior of the impactor motion quantitatively. We apply this reduced model to the impact of a foot-spring-body system on a dense suspension, which is the minimal model to realize walking on the suspension. Due to the spring force of the system and the stiffness of the suspension, the foot undergoes multiple bounces. We also study the parameter dependencies of the hopping motion and find that multiple bounces are suppressed as the spring stiffness increases.

Impact-Protective Bicontinuous Hydrogel/Ultrahigh-Molecular Weight Polyethylene Fabric Composite with Multiscale Energy Dissipation Structures for Soft Body Armor

Soft body armor greatly improves the comfort and security of the wearers. Although laminates based on high-performance fabrics have been adopted, it remains an enormous challenge to develop fabric laminates having flexibility, low bulge deformation, and ballistic protection capability simultaneously. Herein, we report a bullet-proof bicontinuous hydrogel (BH)/ultrahigh-molecular weight polyethylene fabric (UPF) composite. The presence of the BH significantly improves the impact resistance performance of the UPF, without compromising its flexibility. In specific, the multiscale energy dissipation structures composed of hydrogen bond associations in the chain scale, bicontinuous phase structures in the nanoscale, and fibers in the microscale are broken to dissipate energy. As a result, the impact energy of the bullet is greatly absorbed and the bulge height of the composites is significantly reduced in contrast to the neat UPF laminates. This study indicates that the flexible BH-UPF composites with multiscale energy dissipation structures have a promising application in soft body armor.

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.

Competing Timescales Lead to Oscillations in Shear-Thickening Suspensions

Competing timescales generate novelty. Here, we show that a coupling between the timescales imposed by instrument inertia and the formation of interparticle frictional contacts in shear-thickening suspensions leads to highly asymmetric shear-rate oscillations. Experiments tuning the presence of oscillations by varying the two timescales support our model. The observed oscillations give access to a shear-jamming portion of the flow curve that is forbidden in conventional rheometry. Moreover, the oscillation frequency allows us to quantify an intrinsic relaxation time for particle contacts. The coupling of fast contact network dynamics to a slower system variable should be generic to many other areas of dense suspension flow, with instrument inertia providing a paradigmatic example.

Viscoelastic and shear-thinning effects of aqueous exopolymer solution on disk and sphere settling

In this study, xanthan gum is used as a model exopolymer to demonstrate potential effects of non-Newtonian properties of natural aquatic systems on settling dynamics of particles. Rheological measurements combined with settling experiments using visualization methods revealed that instantaneous velocity fluctuations and a flow pattern formed around a particle are the effects of solution viscoelasticity and shear-thinning properties and that the average settling velocity depends on the exopolymer concentration and particle size. Our study showed that in the considered conditions a disk-shaped particle settles preferably in vertical position with a negative wake behind. The understanding of these processes is essential in technology and engineering and is necessary to improve prediction accuracy of large-scale sedimentation processes and biogeochemical cycles in the ocean involving settling of minerals, marine snow, microplastics, and locomotion of microorganisms.

Effective packing fraction for better resolution near the critical point of shear thickening suspensions

We present a technique for obtaining an effective packing fraction for discontinuous shear thickening suspensions near a critical point. It uses a measurable quantity that diverges at the critical point-in this case the inverse of the shear rate γ[over ̇]_{c}^{-1} at the onset of discontinuous shear thickening-as a proxy for packing fraction ϕ. We obtain an effective packing fraction for cornstarch and water by fitting γ[over ̇]_{c}^{-1}(ϕ) and then invert the function to obtain ϕ_{eff}(γ[over ̇]_{c}). We further include the dependence of γ[over ̇]_{c}^{-1} on the rheometer gap d to obtain the function ϕ_{eff}(γ[over ̇]_{c},d). This effective packing fraction ϕ_{eff} has better resolution near the critical point than the raw measured packing fraction ϕ by as much as an order of magnitude. Furthermore, ϕ_{eff} normalized by the critical packing fraction ϕ_{c} can be used to compare rheology data for cornstarch and water suspensions from different laboratory environments with different temperature and humidity. This technique can be straightforwardly generalized to improve resolution in any system with a diverging quantity near a critical point.

Discontinuous rate-stiffening in a granular composite modeled after cornstarch and water

Cornstarch in water exhibits impact-activated solidification (IAS) and strong discontinuous shear thickening, with "shear jamming". However, these phenomena are absent in cornstarch in ethanol. Here we show that cornstarch granules swell under ambient conditions. We postulate that this granule swelling is linked to an interparticle force scale that introduces a discontinuous rate-dependence to the generation of stable contacts between granules. We studied this force scale by coating sand with ~ 2 μm-thick polydimethysiloxane, creating a material that exhibits a similar IAS and discontinuous deformation rate-stiffening despite being a granular composite, not a suspension. This result suggests rate-dependence can be tuned by coating granular materials, introducing an interparticle force scale from rate-dependent properties present in the coating material. Our work provides insights into the unique behavior of cornstarch in water, bridges our understanding of suspensions and dry granular materials, and introduces a method to make discontinuous rate-dependent materials without suspending particles.

Testing constitutive relations by running and walking on cornstarch and water suspensions

The ability of a person to run on the surface of a suspension of cornstarch and water has fascinated scientists and the public alike. However, the constitutive relation obtained from traditional steady-state rheology of cornstarch and water suspensions has failed to explain this behavior. In another paper we presented an averaged constitutive relation for impact rheology consisting of an effective compressive modulus of a system-spanning dynamically jammed structure [R. Maharjan et al., this issue, Phys. Rev. E 97, 052602 (2018)10.1103/PhysRevE.97.052602]. Here 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. The ability of the constitutive relation to predict the material behavior in a case with different forcing conditions and flow geometry than it was obtained from suggests that the constitutive relation could be applied more generally. We also present a detailed calculation of the added mass effect to show that while it may be able to explain some cases of people running or walking on the surface of cornstarch and water for pool depths H>1.2 m and foot impact velocities V_{I}>1.7 m/s, it cannot explain observations of people walking or running on the surface of cornstarch and water for smaller H or V_{I}.

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].

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.

Dramatic effect of fluid chemistry on cornstarch suspensions: Linking particle interactions to macroscopic rheology

Suspensions of cornstarch in water exhibit strong dynamic shear thickening. We show that partly replacing water with ethanol strongly alters the suspension rheology. We perform steady and nonsteady rheology measurements combined with atomic force microscopy to investigate the role of fluid chemistry on the macroscopic rheology of the suspensions and its link with the interactions between cornstarch grains. Upon increasing the ethanol content, the suspension goes through a yield-stress fluid state and ultimately becomes a shear-thinning fluid. On the cornstarch grain scale, atomic force microscopy measurements reveal the presence of polymers on the cornstarch surface, which exhibit a cosolvency effect. At intermediate ethanol content, a maximum of polymer solubility induces high microscopic adhesion which we relate to the macroscopic yield stress.

Dynamic shear jamming in dense granular suspensions under extension

Unlike dry granular materials, a dense granular suspension like cornstarch in water can strongly resist extensional flows. At low extension rates, such a suspension behaves like a viscous fluid, but rapid extension results in a response where stresses far exceed the predictions of lubrication hydrodynamics and capillarity. To understand this remarkable mechanical response, we experimentally measure the normal force imparted by a large bulk of the suspension on a plate moving vertically upward at a controlled velocity. We observe that, above a velocity threshold, the peak force increases by orders of magnitude. Using fast ultrasound imaging we map out the local velocity profiles inside the suspension, which reveal the formation of a growing jammed region under rapid extension. This region interacts with the rigid boundaries of the container through strong velocity gradients, suggesting a direct connection to the recently proposed shear-jamming mechanism.

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.