Packing grains by thermal cycling

Thermal shakedown in granular materials with irregular particle shapes

Granular materials with irregular particle shapes undergo a myriad of temperature variations in natural and engineered systems. However, the impacts of cyclic temperature variations on the mechanics of granular materials remain poorly understood. Specifically, little is known about the response of granular materials to cyclic temperature variations as a function of the following central variables: particle shape, applied stress level, relative density, and temperature amplitude. This paper presents advanced laboratory experiments to explore the impacts of cyclic temperature variations on the mechanics of granular materials, with a focus on sands. The results show that cyclic temperature variations applied to sands induce thermal shakedown: the accumulation of irreversible bulk deformations due to microstructural rearrangements caused by thermal expansions and contractions of the constituting particles. The deformation of sands caused by thermal shakedown strongly depends on particle shape, stress level, relative density, and temperature amplitude. This deformation is limited for individual thermal cycles but accumulates and becomes significant for multiple thermal cycles, leading to substantial compaction in sands and other granular materials, which can affect various natural and engineered systems.

Peering into lunar permanently shadowed regions with deep learning

The lunar permanently shadowed regions (PSRs) are expected to host large quantities of water-ice, which are key for sustainable exploration of the Moon and beyond. In the near future, NASA and other entities plan to send rovers and humans to characterize water-ice within PSRs. However, there exists only limited information about the small-scale geomorphology and distribution of ice within PSRs because the orbital imagery captured to date lacks sufficient resolution and/or signal. In this paper, we develop and validate a new method of post-processing LRO NAC images of PSRs. We show that our method is able to reveal previously unseen geomorphological features such as boulders and craters down to 3 meters in size, whilst not finding evidence for surface frost or near-surface ice. Our post-processed images significantly facilitate the exploration of PSRs by reducing the uncertainty of target selection and traverse/mission planning.

Analytical and DEM studies of thermal stress in granular materials

The ability to predict thermal-induced stresses in granular materials is of practical importance across a range of disciplines ranging from process engineering to geotechnical engineering. This study presents an analytical formula to predict thermal-induced stress increments in mono-disperse granular materials subject to an initial isotropic stress state. A complementary series of DEM simulations were carried out to explore the applicability of the proposed analytical formula. The comparative analysis showed that the proposed expression can accurately predict stress changes in packings where there are negligible particle displacements as a consequence of the thermal loading (e.g. regular packings and medium/dense random packings); however large errors were observed in loose samples with a random packing.

Homogeneous Crystallization in Cyclically Sheared Frictionless Grains

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear via Newtonian dynamics with linear viscous drag at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction ϕ=0.646±0.001. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media. Understanding how crystal formation is initiated within a homogeneous disordered state gives key insights into the old open problem of glass formation in fluids.

Memory in Nonmonotonic Stress Relaxation of a Granular System

We demonstrate experimentally that a granular packing of glass spheres is capable of storing memory of multiple strain states in the dynamic process of stress relaxation. Modeling the system as a noninteracting population of relaxing elements, we find that the functional form of the predicted relaxation requires a quantitative correction which grows in severity with each additional memory and is suggestive of interactions between elements. Our findings have implications for the broad class of soft matter systems that display memory and anomalous relaxation.

Improved packing of preparative biochromatography columns by mechanical vibration

The bioprocessing industry relies on packed-bed column chromatography as its primary separation process to attain the required high product purities and fulfill the strict requirements from regulatory bodies. Conventional column packing methods rely on flow packing and/or mechanical compression. In this work, the application of ultrasound and mechanical vibration during packing was studied with respect to packing density and homogeneity. We investigated two widely used biochromatography media, incompressible ceramic hydroxyapatite, and compressible polymethacrylate-based particles, packed in a laboratory-scale column with an inner diameter of 50 mm. It was shown that ultrasonic irradiation led to reduced particle segregation during sedimentation of a homogenized slurry of polymethacrylate particles. However, the application of ultrasound did not lead to an improved microstructure of already packed columns due to the low volumetric energy input (~152 W/L) caused by high acoustic reflection losses. In contrast, the application of pneumatic mechanical vibration led to considerable improvements. Flow-decoupled axial linear vibration was most suitable at a volumetric force output of ~1,190 N/L. In the case of the ceramic hydroxyapatite particles, a 13% further decrease of the packing height was achieved and the reduced height equivalent to a theoretical plate (rHETP) was decreased by 44%. For the polymethacrylate particles, a 18% further packing consolidation was achieved and the rHETP was reduced by 25%. Hence, it was shown that applying mechanical vibration resulted in more efficiently packed columns. The application of vibration furthermore is potentially suitable for in situ elimination of flow channels near the column wall.

Modeling Segregation in Granular Flows

Accurate continuum models of flow and segregation of dense granular flows are now possible. This is the result of extensive comparisons, over the last several years, of computer simulations of increasing accuracy and scale, experiments, and continuum models, in a variety of flows and for a variety of mixtures. Computer simulations-discrete element methods (DEM)-yield remarkably detailed views of granular flow and segregation. Conti-nuum models, however, offer the best possibility for parametric studies of outcomes in what could be a prohibitively large space resulting from the competition between three distinct driving mechanisms: advection, diffusion, and segregation. We present a continuum transport equation-based framework, informed by phenomenological constitutive equations, that accurately predicts segregation in many settings, both industrial and natural. Three-way comparisons among experiments, DEM, and theory are offered wherever possible to validate the approach. In addition to the flows and mixtures described here, many straightforward extensions of the framework appear possible.

Decompaction of wet granular materials under freeze-thaw cycling

The packing fraction dynamics of a wet granular material submitted to freeze-thaw cycling is investigated experimentally. The dynamics is strongly influenced by the liquid volume fraction ω in the considered range of 0.03<ω<0.32. This range of liquid contents covers different regimes of wetness from the creation of the capillary network until the formation of large clusters and finally close to the saturated case. For the liquid contents ω≳0.15, the pile experiences a decompaction until a particular value of the packing fraction 0.56 corresponding to a random loose packing configuration for monosized spheres. Moreover, the decompaction starts after a cycling number that decreases exponentially with the liquid content. Finally, we show that the packing dynamics can be well modeled on the basis of a Landau potential with an asymmetric double-well structure. The onset of decompaction represents the tendency of the system to stay in a metastable state. After several cycles, the forces induced by the thermal cycling and local stochastic rearrangements of the grains can drive the system to overcome the energy barrier of the cohesive forces.

Nucleation in Sheared Granular Matter

We present an experiment on crystallization of packings of macroscopic granular spheres. This system is often considered to be a model for thermally driven atomic or colloidal systems. Cyclically shearing a packing of frictional spheres, we observe a first order phase transition from a disordered to an ordered state. The ordered state consists of crystallites of mixed fcc and hcp symmetry that coexist with the amorphous bulk. The transition, initiated by homogeneous nucleation, overcomes a barrier at 64.5% volume fraction. Nucleation consists predominantly of the dissolving of small nuclei and the growth of nuclei that have reached a critical size of about ten spheres.

Effective Thermal Expansion Property of Consolidated Granular Materials

Thermally-assisted compaction of granular materials is of keen interest in many engineering applications. A proper estimation of the material behavior of compacted granular materials is contingent upon the knowledge of microstructure formation, which is highly dependent on the bulk material properties and processing conditions, during the deformation stage. Originating from the pair interactions between particles, the macroscopic properties are obtained using various homogenization techniques and postulating continuum constitutive laws. While pioneers in this field have laid fundamental groundwork regarding effective medium descriptions, there exists a discrepancy between discrete and continuum level solutions. In our previous work, we elaborated a Particle Mechanics Approach (PMA) that integrates thermal contact and Hertzian deformation models to understand the thermo-mechanically-coupled consolidation problem. We also considered the analogous problem from the perspective of the conventional Continuum Mechanics Approach (CMA). In this study, following the multi-scale modeling framework, we propose an effective thermal expansion coefficient for the thermally-assisted compaction of granular materials.

Shear-Rate-Independent Diffusion in Granular Flows

We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a function of γd2, where d is the local mean particle diameter and γ is the local shear rate. When γ is large, D is proportional to γd2, as in previous studies. However, for γd2 below a critical value, D is independent of γd2. The acceleration due to gravity g and particle stiffness (or, equivalently, the binary collision time t(c)) together determine the transition in D between regimes. This suggests that while shear rate and particle size determine diffusion at relatively high shear rates in surface-driven flows, diffusion at low shear rates is an elastic phenomenon with time and length scales dependent on gravity (sqrt d/g) and particle stiffness (t(c)sqrt(dg), respectively.

Bernal random loose packing through freeze-thaw cycling

We study the effect of freeze-thaw cycling on the packing fraction of equal spheres immersed in water. The water located between the grains experiences a dilatation during freezing and a contraction during melting. After several cycles, the packing fraction converges to a particular value η(∞)=0.595 independently of its initial value η(0). This behavior is well reproduced by numerical simulations. Moreover, the numerical results allow one to analyze the packing structural configuration. With a Voronoï partition analysis, we show that the piles are fully random during the whole process and are characterized by two parameters: the average Voronoï volume μ(v) (related to the packing fraction η) and the standard deviation σ(v) of Voronoï volumes. The freeze-thaw driving modify the volume standard deviation σ(v) to converge to a particular disordered state with a packing fraction corresponding to the random loose packing fraction η(BRLP) obtained by Bernal during his pioneering experimental work. Therefore, freeze-thaw cycling is found to be a soft and spatially homogeneous driving method for disordered granular materials.

(Ir)reversibility in dense granular systems driven by oscillating forces

We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of a simple local Stokes' drag is compared with non-linear and history-dependent frictional forces that act either between particle pairs or between particles and an external container wall. The Stokes' drag leads to particle motion that is periodic with the driving force, even at high densities around close packing where particles undergo frequent collisions. With the introduction of inter-particle frictional forces this "interacting absorbing state" is destroyed and particles start to diffuse around. By reducing the density of the material we go through another transition to a "non-interacting" absorbing state, where particles independently follow the force-induced oscillations without collisions. In the system with particle-wall frictional interactions this transition has signs of a discontinuous phase transition. It is accompanied by a diverging relaxation time, but not by a vanishing order parameter, which rather jumps to zero at the transition.

Intrinsic creep of a granular column subjected to temperature changes

Minute external perturbations, such as temperature variations, can lead to a creep of the fragile structures that are the granular piles. We report a study, resolved in space and time, of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. Avoiding the thermal dilations of the container, we observe that the material still creeps, even in the absence of external mechanical perturbations. The latter intrinsic creep of the material exhibits several surprising features: the compaction of the material is not homogeneous along the column height, and sudden collapses involve the entire system even if one could expect arches to screen the mechanical interaction between regions far apart from one another. In addition, the analysis of the dependence of the flow rate on the frequency of the temperature cycles suggests that the creep is mainly induced by the propagation of the temperature profile, slow temperature changes being less efficient than rapid ones in making the material flow.

Melting a granular glass by cooling

Driven granular systems readily form glassy phases at high particle volume fractions and low driving amplitudes. We use computer simulations of a driven granular glass to evidence a reentrance melting transition into a fluid state, which, contrary to intuition, occurs by reducing the amplitude of the driving. This transition is accompanied by anomalous particle dynamics and superdiffusive behavior on intermediate time scales. We highlight the special role played by frictional interactions, which help particles to escape their glassy cages. Such an effect is in striking contrast to what friction is expected to do: reduce particle mobility by making them stick.

Creep motion of a model frictional system

We report on the dynamics of a model frictional system submitted to minute external perturbations. The system consists of a chain of sliders connected through elastic springs that rest on an incline. By introducing cyclic expansions and contractions of the springs we observe a reptation of the chain. We account for the average reptation velocity theoretically. The velocity of small systems exhibits a series of plateaus as a function of the incline angle. Due to elastic effects, there exists a critical amplitude below which the reptation is expected to cease. However, rather than a full stop of the creep, we observe in numerical simulations a transition between a continuous-creep and an irregular-creep regime when the critical amplitude is approached. The latter transition is reminiscent of the transition between the continuous and the irregular compaction of granular matter submitted to periodic temperature changes.

Jamming phase diagram for frictional particles

We investigate the jamming transition of frictional particulate systems via discrete element simulations, reporting the existence of new regimes, which are conveniently described in a jamming phase diagram with axes density, shear stress, and friction coefficient. The resulting jammed states are characterized by different mechanical and structural properties and appear not to be "fragile" as speculated. In particular, we find a regime, characterized by extremely long processes, with a diverging time scale, whereby a suspension first flows but then suddenly jams. We link this sudden jamming transition to the presence of impeded dilatancy.

Creep and fluidity of a real granular packing near jamming

We study the internal dynamical processes taking place in a granular packing below yield stress. At all packing fractions and down to vanishingly low applied shear, a logarithmic creep is observed. The experiments are analyzed using a viscoelastic model which introduces an internal, time-dependent, fluidity variable. For all experiments, the creep dynamics can be rescaled onto a unique curve which displays jamming at the random-close-packing limit. At each packing fraction, we measure a stress corresponding to the onset of internal granular reorganization and a slowing down of the creep dynamics before the final yield.

Aging of the frictional properties induced by temperature variations

The dry frictional contact between two solid surfaces is well known to obey Coulomb friction laws. In particular, the static friction force resisting the relative lateral (tangential) motion of solid surfaces, initially at rest, is known to be proportional to the normal force and independent of the area of the macroscopic surfaces in contact. Experimentally, the static friction force has been observed to slightly depend on time. Such an aging phenomenon has been accounted for either by the creep of the material or by the condensation of water bridges at the microscopic contact points. By studying a toy model, we show that the small uncontrolled temperature changes of the system can also lead to a significant increase of the static friction force.

Diffusive waves in a dilating scattering medium

We consider the propagation of a diffusive wave in a scattering medium submitted to a homogeneous expansion. The light multiply scattered by a glass spheres sample is measured. We analyze the variations of the scattered light when the material and the optical wavelength are dilated. We experimentally show that an isotropic expansion of the material is equivalent to a contraction of the wavelength. Moreover, the effect of an expansion of the material on the scattered wave may be canceled by a proportional increase of the wavelength, keeping the phase of the scattered wave unchanged. Applications to the characterization of deformation of disordered materials are outlined.

Correlation between particle motion and Voronoi-cell-shape fluctuations during the compaction of granular matter

We track particle motions in a granular material subjected to compaction using a laser scattering-based imaging method where compaction is achieved through thermal cycling. Particle displacements in this jammed fluid correlate strongly with rearrangements of the Voronoi cells defining the local environment about the particles, similar to previous observations of Rahman on cooled liquids. Our observations provide further evidence of commonalities between particle dynamics in granular matter close to jamming and supercooled liquids.

Creep motion of a granular pile induced by thermal cycling

We report a time-resolved study of the dynamics associated with the slow compaction of a granular column submitted to thermal cycles. The column height displays a complex behavior: for a large amplitude of the temperature cycles, the granular column settles continuously, experiencing a small settling at each cycle. By contrast, for a small-enough amplitude, the column exhibits a discontinuous and intermittent activity: successive collapses are separated by quiescent periods whose duration is exponentially distributed. We then discuss potential mechanisms which would account for both the compaction and the transition at finite amplitude.

Avalanche statistics and time-resolved grain dynamics for a driven heap

We probe the dynamics of intermittent avalanches caused by steady addition of grains to a quasi-two-dimensional heap. To characterize the time-dependent average avalanche flow speed v(t) , we image the top free surface. To characterize the grain fluctuation speed deltav(t) , we use speckle-visibility spectroscopy. During an avalanche, we find that the fluctuation speed is approximately one-tenth the average flow speed, deltav approximately equal to 0.1v , and that these speeds are largest near the beginning of an event. We also find that the distribution of event durations is peaked, and that event sizes are correlated with the time interval since the end of the previous event. At high rates of grain addition, where successive avalanches merge into smooth continuous flow, the relationship between average and fluctuation speeds changes to deltav approximately v(1/2) .

Thermal expansion effects and heat conduction in granular materials

In this paper, we report results and analysis on a simulation study of the effects of thermal expansion in granular systems. We show that these effects impact the force distribution inside a two-dimensional system of disks that are subject to thermal heating under two different boundary conditions. A significant increase in the average force is observed for steel particles confined within a box with fixed walls at temperature rises of 50 degrees C and 100 degrees C, respectively. As previously noted in the literature, thermal expansion also induces compaction. The results show that a systematic and controllable increase in granular packing can be induced by simply raising and then lowering the temperature, without the input of mechanical energy in agreement with previous experimental observations. We find that the evolution of the packing fraction is well described by a fractional relaxation model, which follows the Mittag-Leffler law.

Some aspects of electrical conduction in granular systems of various dimensions

We report on measurements of the electrical conductivity in both a 2D triangular lattice of metallic beads and in a chain of beads. The voltage/current characteristics are qualitatively similar in both experiments. At low applied current, the voltage is found to increase logarithmically in good agreement with a model of widely distributed resistances in series. At high enough current, the voltage saturates due to the local welding of microcontacts between beads. The frequency dependence of the saturation voltage gives an estimate of the size of these welded microcontacts. The DC value of the saturation voltage ( approximately 0.4 V per contact) gives an indirect measure of the number of welded contact carrying the current within the 2D lattice. Also, a new measurement technique provides a map of the current paths within the 2D lattice of beads. For an isotropic compression of the 2D granular medium, the current paths are localized in few discrete linear paths. This quasi-one-dimensional nature of the electrical conductivity thus explains the similarity between the characteristics in the 1D and 2D systems.

Gelling of oil-in-water emulsions comprising crystallized droplets

We fabricate oil-in-water emulsions above the melting temperature of the oil phase (hexadecane and/or paraffin). Upon cooling, the oil droplets crystallize and the initially fluid emulsions turn into hard gels. The systems evolve by following two distinct regimes that depend on the average droplet size and on the oil nature. In some cases gelling involves partial coalescence of the droplets, i.e., film rupturing with no further shape relaxation because of the solid nature of the droplets. In some other cases, gelling occurs without film rupturing and is reminiscent of a jamming transition induced by surface roughness. We prepare blends of oils having different melting temperatures, and we show that it is possible to reinforce the gel stiffness by applying a temperature cycle that produces partial melting of the crystal mass, followed by recrystallization.