arXiv subjects

Eric Brown

Publications and source records attributed to Eric Brown.

At least 37 records · Page 2Linked to original sources

arXiv2015

Simulating the Dynamic Behavior of Shear Thickening Fluids

While significant research has been dedicated to the simulation of fluids, not much attention has been given to exploring new interesting behavior that can be generated with the different types of non-Newtonian fluids with non-constant viscosity. Going in this direction, this paper introduces a computational model for simulating the interesting phenomena observed in non-Newtonian shear thickening fluids, which are fluids where the viscosity increases with increased stress. These fluids have unique and unconventional behavior, and they often appear in real world scenarios such as when sinking in quicksand or when experimenting with popular cornstarch and water mixtures. While interesting behavior of shear thickening fluids can be easily observed in the real world, the most interesting phenomena of these fluids have not been simulated before in computer graphics. The fluid exhibits unique phase changes between solid and liquid states, great impact resistance in its solid state and strong hysteresis effects. Our proposed approach builds on existing non-Newtonian fluid models in computer graphics and introduces an efficient history-based stiffness term that is essential to produce the most interesting shear thickening phenomena. The history-based stiffness is formulated through the use of fractional derivatives, leveraging the fractional calculus ability to depict both the viscoelastic behavior and the history effects of history-dependent systems. Simulations produced by our method are compared against real experiments and the results demonstrate that the proposed model successfully captures key phenomena observed in shear thickening fluids.

cs.GR↗

arXiv2014

Shear thickening of highly viscous granular suspensions

We experimentally investigate shear thickening in dense granular suspensions under oscillatory shear. Directly imaging the suspension-air interface, we observe dilation beyond a critical strain $γ_c$ and the end of shear thickening as the maximum confining stress is reached and the contact line moves. Analyzing the shear profile, we extract the viscosity contributions due to hydrodynamics $η_μ$, dilation $η_c$ and sedimentation $η_g$. While $η_g$ governs the shear thinning regime, $η_μ$ and $η_c$ together determine the shear thickening behavior. As the suspending liquid's viscosity varies from 10 to 1000 cst, $η_μ$ is found to compete with $η_c$ and soften the discontinuous nature of shear thickening.

cond-mat.soft↗

arXiv2013

Particle Shape Effects on the Stress Response of Granular Packings

We present measurements of the stress response of packings formed from a wide range of particle shapes. Besides spheres these include convex shapes such as the Platonic solids, truncated tetrahedra, and triangular bipyramids, as well as more complex, non-convex geometries such as hexapods with various arm lengths, dolos, and tetrahedral frames. All particles were 3D-printed in hard resin. Well-defined initial packing states were established through preconditioning by cyclic loading under given confinement pressure. Starting from such initial states, stress-strain relationships for axial compression were obtained at four different confining pressures for each particle type. While confining pressure has the largest overall effect on the mechanical response, we find that particle shape controls the details of the stress-strain curves and can be used to tune packing stiffness and yielding. By correlating the experimentally measured values for the effective Young's modulus under compression, yield stress and energy loss during cyclic loading, we identify trends among the various shapes that allow for designing a packing's aggregate behavior.

cond-mat.soft↗

arXiv2013

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.

cond-mat.soft↗

arXiv2013

Impact Dynamics of Oxidized Liquid Metal Drops

With exposure to air, many liquid metals spontaneously generate an oxide layer on their surface. In oscillatory rheological tests, this skin is found to introduce a yield stress that typically dominates the elastic response but can be tuned by exposing the metal to hydrochloric acid solutions of different concentration. We systematically studied the normal impact of eutectic gallium-indium (eGaIn) drops under different oxidation conditions and show how this leads to two different dynamical regimes. At low impact velocity (or low Weber number), eGaIn droplets display strong recoil and rebound from the impacted surface when the oxide layer is removed. In addition, the degree of drop deformation or spreading during the impact is controlled by the oxide skin. We show that the scaling law known from ordinary liquids for the maximum spreading radius as a function of impact velocity can still be applied to the case of oxidized eGaIn if an effective Weber number $We^{\star}$ is employed that uses an effective surface tension factoring in the yield stress. In contrast, no influence on spreading from different oxidations conditions is observed for high impact velocity. This suggests that the initial kinetic energy is mostly damped by bulk viscous dissipation. Results from both regimes can be collapsed in an impact phase diagram controlled by two variables, the maximum spreading factor $P_m = R_0/R_m$, given by the ratio of initial to maximum drop radius, and the impact number $K = We^{\star}/Re^{4/5}$, which scales with the effective Weber number $We^{\star}$ as well as the Reynolds number $Re$. The data exhibit a transition from capillary to viscous behavior at a critical impact number $K_c \sim 0.1$.

physics.flu-dyn↗

arXiv2012

Effect of oxidation on the Mechanical Properties of Liquid Gallium and Eutectic Gallium-Indium

Liquid metals exhibit remarkable mechanical properties, in particular large surface tension and low viscosity. However, these properties are greatly affected by oxidation when exposed to air. We measure the viscosity, surface tension, and contact angle of gallium (Ga) and a eutectic gallium-indium alloy (eGaIn) while controlling such oxidation by surrounding the metal with an acid bath of variable concentration. Rheometry measurements reveal a yield stress directly attributable to an oxide skin that obscures the intrinsic behavior of the liquid metals. We demonstrate how the intrinsic viscosity can be obtained with precision through a scaling technique that collapses low- and high-Reynolds number data. Measuring surface tension with a pendant drop method, we show that the oxide skin generates a surface stress that mimics surface tension and develop a simple model to relate this to the yield stress obtained from rheometry. We find that yield stress, surface tension, and contact angle all transition from solid-like to liquid behavior at the same critical acid concentration, thereby quantitatively confirming that the wettability of these liquid metals is due to the oxide skin.

physics.flu-dyn↗

arXiv2012

Shear thickening and jamming in densely packed suspensions of different particle shapes

We investigated the effects of particle shape on shear thickening in densely packed suspensions. Rods of different aspect ratios and non-convex hooked rods were fabricated. Viscosity curves and normal stresses were measured using a rheometer for a wide range of packing fractions for each shape. Suspensions of each shape exhibit qualitatively similar Discontinuous Shear Thickening. The logarithmic slope of the stress/shear-rate relation increases dramatically with packing fraction and diverges at a critical packing fraction phi_c which depends on particle shape. The packing fraction dependence of the viscosity curves for different convex shapes can be collapsed when the packing fraction is normalized by phi_c. Intriguingly, viscosity curves for non-convex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. The value of phi_c is found to coincide with the onset of a yield stress at the jamming transition, suggesting the jamming transition also controls shear thickening. The yield stress is found to correspond with trapped air in the suspensions, and the scale of the stress can be attributed to interfacial tension forces which dramatically increase above phi_c due to the geometric constraints of jamming. The relationship between shear and normal stresses is found to be linear in both the shear thickening and jammed regimes, indicating that the shear stresses come from friction. In the limit of zero shear rate, normal stresses pull the rheometer plates together due to the surface tension of the liquid below phi_c, but push the rheometer plates apart due to jamming above phi_c.

cond-mat.soft↗

arXiv2012

The role of dilation and confining stresses in shear thickening of dense suspensions

Many densely packed suspensions and colloids exhibit a behavior known as Discontinuous Shear Thickening in which the shear stress jumps dramatically and reversibly as the shear rate is increased. We performed rheometry and video microscopy measurements on a variety of suspensions to determine the mechanism for this behavior. Shear profiles and normal stress measurements indicate that, in the shear thickening regime, stresses are transmitted through frictional rather than viscous interactions, and come to the surprising conclusion that the local constitutive relation between stress and shear rate is not necessarily shear thickening. If the suspended particles are heavy enough to settle we find the onset stress of shear thickening tau_min corresponds to a hydrostatic pressure from the weight of the particle packing where neighboring particles begin to shear relative to each other. Above tau_min, dilation is seen to cause particles to penetrate the liquid-air interface of the sheared sample. The upper stress boundary tau_max of the shear thickening regime is shown to roughly match the ratio of surface tension divided by a radius of curvature on the order of the particle size. These results suggest a new model in which the increased dissipation in the shear thickening regime comes from frictional stresses that emerge as dilation is frustrated by a confining stress from surface tension at the liquid-air interface. When instead the suspensions are confined by solid walls and have no liquid-air interface, we find tau_max is set by the stiffness of the most compliant boundary which frustrates dilation. This rheology can be described by a non-local constitutive relation in which the local relation between stress and shear rate is shear thinning, but where the stress increase comes from a normal stress term which depends on the global dilation.

cond-mat.soft↗

arXiv2011

Strain-stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds a the scale of the confining pressure, similar to packings of spherical particles. In contrast, packings of chains which are long enough to form loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.

cond-mat.soft↗

arXiv2010

Instability of the Noncommutative Geometry Inspired Black Hole

Non-commutative geometries have been proposed as an approach to quantum gravity and have led to the construction of non-commutative black holes, whose interior singularities are purportedly eliminated due to quantum effects. Here we find evidence that these black holes are in fact unstable, with infalling matter near the Cauchy (inner) horizon being subject to an infinite blueshift of the type that has been repeatedly demonstrated for the Reissner-Nordstr$\ddot{\text{o}}$m black hole. This instability is present even when an ultraviolet cutoff (induced by anticipated non-commutative geometric effects) to a field propagating in that spacetime is included. We demonstrate this by following an analogous argument made for Reissner-Nordstr$\ddot{\text{o}}$m black holes, and conclude that stability is dependent on the surface gravities $κ_-$ and $κ_+$ of the inner and outer horizons respectively. In general if $κ_- > κ_+$, as we show to be the case here, then the stability of the Cauchy horizon becomes highly questionable, contrary to recent claims.

hep-th↗

arXiv2010

Universal Robotic Gripper based on the Jamming of Granular Material

Gripping and holding of objects are key tasks for robotic manipulators. The development of universal grippers able to pick up unfamiliar objects of widely varying shape and surface properties remains, however, challenging. Most current designs are based on the multi-fingered hand, but this approach introduces hardware and software complexities. These include large numbers of controllable joints, the need for force sensing if objects are to be handled securely without crushing them, and the computational overhead to decide how much stress each finger should apply and where. Here we demonstrate a completely different approach to a universal gripper. Individual fingers are replaced by a single mass of granular material that, when pressed onto a target object, flows around it and conforms to its shape. Upon application of a vacuum the granular material contracts and hardens quickly to pinch and hold the object without requiring sensory feedback. We find that volume changes of less than 0.5% suffice to grip objects reliably and hold them with forces exceeding many times their weight. We show that the operating principle is the ability of granular materials to transition between an unjammed, deformable state and a jammed state with solid-like rigidity. We delineate three separate mechanisms, friction, suction and interlocking, that contribute to the gripping force. Using a simple model we relate each of them to the mechanical strength of the jammed state. This opens up new possibilities for the design of simple, yet highly adaptive systems that excel at fast gripping of complex objects.

cond-mat.soft↗

arXiv2010

Stability of self-dual black holes

We study the stability properties of the Cauchy horizon for two different self-dual black hole solutions obtained in a model inspired by Loop Quantum Gravity. The self-dual spacetimes depend on a free dimensionless parameter called a polymeric parameter P. For the first metric the Cauchy horizon is stable for supermassive black holes only if this parameter is sufficiently small. For small black holes, however the stability is easily implemented. The second metric analyzed is not only self-dual but also "form-invariant" under the transformation r -> r*^2/r and r* = 2 m P. We find that this symmetry protects the Cauchy horizon for any value of the polymeric parameter.

gr-qc↗

arXiv2010

Shear thickening in densely packed suspensions of spheres and rods confined to few layers

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.

cond-mat.soft↗

arXiv2010

Generality of shear thickening in suspensions

Suspensions are of wide interest and form the basis for many smart fluids. For most suspensions, the viscosity decreases with increasing shear rate, i.e. they shear thin. Few are reported to do the opposite, i.e. shear thicken, despite the longstanding expectation that shear thickening is a generic type of suspension behavior. Here we resolve this apparent contradiction. We demonstrate that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased below a threshold. We show the generality of this argument and quantify the threshold in rheology experiments where we control yield stresses arising from a variety of sources, such as attractions from particle surface interactions, induced dipoles from applied electric and magnetic fields, as well as confinement of hard particles at high packing fractions. These findings open up possibilities for the design of smart suspensions that combine shear thickening with electro- or magnetorheological response.

cond-mat.soft↗

arXiv2009

A dynamic jamming point for shear thickening suspensions

We report on rheometry measurements to characterize critical behavior in two model shear thickening suspensions: cornstarch in water and glass spheres in oil. The slope of the shear thickening part of the viscosity curve is found to increase dramatically with packing fraction and diverge at a critical packing fraction phi_c. The magnitude of the viscosity and the yield stress are also found to have scalings that diverge at phi_c. We observe shear thickening as long as the yield stress is less than the stress at the viscosity maximum. Above this point the suspensions transition to purely shear thinning. Based on these data we present a dynamic jamming phase diagram for suspensions and show that a limiting case of shear thickening corresponds to a jammed state.

cond-mat.soft↗

arXiv2009

Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh-Benard convection

Previously we published a dynamical model (E. Brown and G. Ahlers, Phys. Fluids, 20, 075101 (2008)) for the large-scale-circulation (LSC) dynamics of Rayleigh-Benard convection in cylindrical containers. The model consists of a pair of stochastic ordinary differential equations, motivated by the Navier-Stokes equations, one each for the strength delta and the orientation theta_0 of the LSC. Here we extend it to cases where the rotational invariance of the system is broken by one of several physically relevant perturbations. As an example we present experimental measurements of the LSC dynamics for a container tilted relative to gravity. In that case the model predicts that the buoyancy of the thermal boundary layers encourages fluid to travel along the steepest slope, that it locks the LSC in this direction, and that it strengthens the flow, as seen in experiments. The increase in LSC strength is shown to be responsible for the observed suppression of cessations and azimuthal fluctuations. We predict and observe that for large enough tilt angles, the restoring force that aligns the flow with the slope is strong enough to cause oscillations of the LSC around this orientation. This planar oscillation mode is different from coherent torsional oscillations that have been observed previously. The model was applied also to containers with elliptical cross-sections and predicts that the pressure due to the side walls forces the flow into a preferred orientation in the direction of the longest diameter. When the ellipticity is large enough, then oscillations around this orientation are predicted.

physics.flu-dyn↗

arXiv2009

The cause of oscillations of the large-scale circulation of turbulent Rayleigh-B{é}nard convection

In agreement with a recent experimental discovery by Xia et. al. (2009), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling and Ahlers (2004). We show that both modes can be described by an extension of a model developed previously [Brown and Ahlers (2008)] which consists of permitting a lateral displacement of the LSC circulation plane away from the vertical center line of the sample as well as a variation in displacements with height (such displacements had been excluded in the original model). Pressure gradients produced by the side wall of the container on average center the plane of the LSC so that it prefers to reach its longest diameter. If the LSC is displaced away from this diameter, the walls provide a restoring force. Turbulent fluctuations drive the LSC away from the central alignment, and combined with the restoring force they lead to oscillations. These oscillations are advected along with the LSC. This model predicts the correct wavenumber and phase of the oscillations, as well as estimates of the frequency, amplitude, and probability distributions of the displacements.

physics.flu-dyn↗

arXiv2008

A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection

Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a potential well for the LSC. The model consists of a pair of stochastic ordinary differential equations motivated by the Navier-Stokes equations. The two coupled equations are for the azimuthal orientation theta_0, and for the azimuthal temperature amplitude delta at the horizontal midplane. The dynamics is due to the driving by Gaussian distributed white noise that is introduced to represent the action of the small-scale turbulent fluctuations on the large-scale flow. Measurements of the diffusivities that determine the noise intensities are reported. Two time scales predicted by the model are found to be within a factor of two or so of corresponding experimental measurements. A scaling relationship predicted by the model between delta and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(delta) and p(\dotθ_0) are accurately described by the model; however the non-Gaussian tails of p(delta) are not. The frequency, angular change, and amplitude bahavior during cessations are accurately described by the model when the tails of the probability distribution of $δ$ are used as experimental input.

physics.flu-dyn↗