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Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. We found that the graph Laplacian accurately predicts the effective resistance of the structure, but is highly sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity., Comment: 9 pages, 8 figures

The bulk behaviour of granular materials is tied to its mesoscale and particle-scale features: strength properties arise from the buildup of various anisotropic structures at the particle-scale induced by grain connectivity (fabric), force transmission, and frictional mobilization. More fundamentally, these anisotropic structures work collectively to define features like the bulk friction coefficient and the stress tensor at the macroscale and can be explained by the Stress-Force-Fabric (SFF) relationship stemming from the microscale. Although the SFF relation has been extensively verified by discrete numerical simulations, a laboratory realization has remained elusive due to the challenge of measuring both normal and frictional contact forces. In this study, we analyze experiments performed on a photoelastic granular system under four different loading conditions: uniaxial compression, isotropic compression, pure shear, and annular shear. During these experiments, we record particle locations, contacts, and normal and frictional forces vectors to measure the particle-scale response to progressing strain. We track microscale measures like the packing fraction, average coordination number and average normal force along with anisotropic distributions of contacts and forces. We match the particle-scale anisotropy to the bulk using the SFF relation, which is founded on two key principles, a Stress Rule to describe the stress tensor and a Sum Rule to describe the bulk friction coefficient; we find that the Sum and Stress Rules accurately describe bulk measurements. Additionally, we test the assumption that fabric and forces transmit load equally through our granular packings and show that this assumption is sufficient at large strain values, and can be applied to areas like rock mechanics, soft colloids, or cellular tissue where force information is inaccessible., Comment: 10 pages, 5 figures, 5 pages supplemental with 6 figures

The bulk dynamics of dense granular materials arise through a combination of particle-scale and mesoscale effects. Theoretical and numerical studies have shown that collective effects are created by particle-scale anisotropic structures such as grain connectivity (fabric), force transmission, and frictional mobilization, all of which influence bulk properties like bulk friction and the stress tensor through the Stress-Force-Fabric (SFF) relationship. To date, establishing the relevance of these effects to laboratory systems has remained elusive due to the challenge of measuring both normal and frictional contact forces at the particle scale. In this study, we perform experiments on a sheared photoelastic granular system in an quasi-2D annular (Couette) cell. During these experiments, we measure particle locations, contacts, and normal and frictional forces vectors during loading. We reconstruct the angular distributions of the contact and force vectors, and extract the corresponding emergent anisotropies for each of these metrics. Finally, we show that the SFF relation quantitatively predicts the relationship between particle scale anisotropies, the stress tensor components, and the bulk friction coefficient, capturing even transient behaviors. As such, this method shows promise for application to other dense particulate systems where fabric anisotropy can provide a useful measure of bulk friction., Comment: 6 pages, 4 figures

When in a pristine state, gallium and its alloys have the largest interfacial tensions of any liquid at room temperature. Nonetheless, applying as little as 0.8 V of electric potential across eutectic gallium indium (EGaIn) placed within aqueous NaOH (or other electrolyte) solution will cause the metal to behave as if its interfacial tension is near zero. The mechanism behind this phenomenon has remained poorly understood because NaOH dissolves the oxide species, making it difficult to directly measure the concentration, thickness, or chemical composition of the film that forms at the interface. In addition, the oxide layers formed are atomically-thin. Here, we present a suite of techniques which allow us to simultaneously measure both electrical and interfacial properties as a function of applied electric potential, allowing for new insights into the mechanisms which cause the dramatic decrease in interfacial tension. A key discovery from this work is that the interfacial tension displays hysteresis while lowering the applied potential. We combine these observations with electrochemical impedance spectroscopy to evaluate how these changes in interfacial tension arise from chemical, electrical, and mechanical changes on the interface, and close with ideas for how to build a free energy model to predict these changes from first principles.

Faraday waves are gravity-capillary waves that emerge on the surface of a vertically vibrated fluid when the energy injected via vibration exceeds the energy lost due to viscous dissipation. Because this dissipation primarily occurs in the free surface boundary layer, their emergence is particularly sensitive to free surface properties including the surface tension, elasticity, and viscosity of surfactants present at the free surface. We study this sensitivity by considering a Newtonian fluid bath covered by an insoluble surfactant subject to vertical vibrations which produce sub-harmonic Faraday waves. By assuming a finite-depth, infinite-breadth, low-viscosity bulk fluid and accounting for surface tension, Marangoni, and Boussinesq effects, we derive an expression for the onset acceleration up to second order in the expansion parameter $\Upsilon = \sqrt{\tfrac{1}{\mathcal{R}e}}$. We recover the results of previous numerical investigations, but only by modifying the Marangoni and Boussinesq numbers to account for the low-viscosity limit. The analytic expression allows us to consider a range of parameters not previously studied, including a wide variety of fluid depths and driving frequencies. In addition, we uncover regions of parameter space for which our model predicts that the addition of surfactant would lower, rather than elevate, the onset acceleration. We discuss the possible use of this model in developing a surface viscometer for surfactant monolayers., Comment: 31 pages , 12 figures , 3 tables , 3 appendices

Inspired by presentations by the authors during a workshop organized at the Princeton Center for Theoretical Science (PCTS) in January 2022, we present a perspective on some of the outstanding questions related to the "physics of the ground beneath our feet." These identified challenges are intrinsically shared with the field of Soft Matter but also have unique aspects when the natural environment is studied., Comment: Perspective Paper, 30 pages, 15 figures

The stability of a granular material is a collective phenomenon controlled by individual particles through their interactions. Forecasting when granular materials will undergo an abrupt failure is an ongoing challenge due to the intricate interactions between particles. Here, we report experiments on photoelastic disks undergoing intermittent stick-slip dynamics in a quasi-2D annular shear apparatus, with the evolving network of contact forces made visible via polarized light. We characterize the system by interpreting the interparticle forces as a multilayer network, and apply GenLouvin community detection to identify strongly correlated groups of particles. We observe that the community structure becomes increasingly volatile as the material approaches failure, and that this volatility provides a forecast that precedes what is detectable by considering the forces alone. We additionally observe that both weak and strong forces contribute to the strength of this forecast. These findings provide a new approach to detect patterns of causality and forecast impending failures.

Granular media are soft matter systems that exhibit some of the extreme behavior of complex fluids. Understanding of the natural formation of planetary bodies, landing on and exploring them, future engineering of structures beyond Earth and planetary defense all hinge on the ability to predict the complex mechanical behavior of granular matter. As we understand them, these behaviors are linked to the granular fluid to solid transition. In this white paper, we describe issues that emerge for granular systems under reduced gravity and their implications for basic science and space exploration. (Topical White Paper submitted to the NASA Biological and Physical Sciences in Space Decadal Survey 2023-2032), Comment: arXiv admin note: text overlap with arXiv:1002.2478

As a result of extreme weather conditions, such as heavy precipitation, natural hillslopes can fail dramatically; these slope failures can occur on a dry day due to time lags between rainfall and pore-water pressure change at depth, or even after days to years of slow-motion. While the pre-failure deformation is sometimes apparent in retrospect, it remains challenging to predict the sudden transition from gradual deformation (creep) to runaway failure. We use a network science method -- multilayer modularity optimization -- to investigate the spatiotemporal patterns of deformation in a region near the 2017 Mud Creek, California landslide. We transform satellite radar data from the study site into a spatially-embedded network in which the nodes are patches of ground and the edges connect the nearest neighbors, with a series of layers representing consecutive transits of the satellite. Each edge is weighted by the product of the local slope (susceptibility to failure) measured from a digital elevation model and ground surface deformation (current rheological state) from interferometric synthetic aperture radar (InSAR). We use multilayer modularity optimization to identify strongly-connected clusters of nodes (communities) and are able to identify both the location of Mud Creek and nearby creeping landslides which have not yet failed. We develop a metric, community persistence, to quantify patterns of ground deformation leading up to failure, and find that this metric increases from a baseline value in the weeks leading up to Mud Creek's failure. These methods promise as a technique for highlighting regions at risk of catastrophic failure., Comment: 10 pages, 7 figures

Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary condition, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the later is selected from among 6 walls with various roughness, local concavity, and compliance. We find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observe how the internal stresses fluctuate more for rougher boundaries, corresponding to lower wall slip, and connect this observation to the propagation of nonlocal effects originating at the wall.

While stress visualization within 3-dimensional particles would greatly advance our understanding of the behaviors of complex particles, traditional photoelastic methods suffer from a lack of available technology for producing suitable complex particles. Recently, 3D-printing has created new possibilities for enhancing the scope of stress analysis within physically representative granules. Here, we investigate and evaluate opportunities offered by 3D-printing a single particle with a complex external shape with photoelastic properties. We report the results of X-ray computed tomography and 3D-printing, combined with traditional photoelastic analysis, to visualize strain for particles ranging from simple 2D discs to complex 3D printed coffee beans, including with internal voids. We find that the relative orientation of the print layers and the loading force affects the optical response of the discs, but without a significant difference in their mechanical properties. Furthermore, we present semi-quantitative measurements of stresses within 3D-printed complex particles. The paper outlines the potential limitations and areas of future interest for stress visualization of 3-dimensional particles.

We report experimental evidence of a Gardner-like transition from variable to persistent force contacts in a two-dimensional, bidisperse granular crystal by analyzing the variability of both particle positions and force networks formed under uniaxial compression. Starting from densities just above the freezing transition, and for variable amounts of additional compression, we compare configurations to both their own initial state, and to an ensemble of equivalent, reinitialized states. This protocol shows that force contacts are largely undetermined when the density is below a Gardner-like transition, after which they gradually transition to being persistent, being fully so only above the jamming point. We associate the disorder that underlies this effect to the size of the microscopic asperities of the photoelastic disks used, by analogy to other mechanisms that have been previously predicted theoretically.

Nonlocal rheologies allow for the modeling of granular flows from the creeping to intermediate flow regimes, using a small number of parameters. In this paper, we report on experiments testing how particle properties affect model parameters, using particles of three different shapes (circles, ellipses, and pentagons) and three different materials, including one which allows for measurements of stresses via photoelasticity. Our experiments are performed on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall. Each type of particle is found to exhibit flows which are well-fit by nonlocal rheology, with each particle having a distinct triad of the local, nonlocal, and frictional parameters. While the local parameter b is always approximately unity, the nonlocal parameter A depends sensitively on both the particle shape and material. The critical stress ratio mu_s, above which Coulomb failure occurs, varies for particles with the same material but different shapes, indicating that geometric friction can dominate over material friction.

The mechanical strength and flow of granular materials can depend strongly on the shapes of individual grains. We report quantitative results obtained from photoelasticimetry experiments on locally loaded, quasi-two-dimensional granular packings of either disks or pentagons exhibiting stick-slip dynamics. Packings of pentagons resist the intruder at significantly lower packing fractions than packings of disks, transmitting stresses from the intruder to the boundaries over a smaller spatial extent. Moreover, packings of pentagons feature significantly fewer back-bending force chains than packings of disks. Data obtained on the forward spatial extent of stresses and back-bending force chains collapse when the packing fraction is rescaled according to the packing fraction of steady state open channel formation, though data on intruder forces and dynamics do not collapse. We comment on the influence of system size on these findings and highlight connections with the dynamics of the disks and pentagons during slip events., Comment: Updated after referee comments - new subsection 3.3 added along with a new figure; introduction reorganized; a few more details specified in the Methods section

While memory effects emerge from systems of wildly varying length- and time-scales, the reduction of a complex system with many interacting elements into one simple enough to be understood without also losing the complex behavior continues to be a challenge. Here, we investigate how bistable cylindrical origamis provide such a reduction via tunably-interactive memory behaviors. We base our investigation on folded sheets of Kresling patterns that function as two-state memory units. By linking several units, each with a selected activation energy, we construct a one-dimensional material that exhibits return-point memory. After a comprehensive experimental analysis of the relation between the geometry of the pattern and the mechanical response for a single bit, we study the memory of a bellows composed of 4 bits arranged in series. Since these bits are decoupled, the system reduces to the Preisach model and we can drive the bellows to any of its 16 allowable states by following a prescribed sequence of compression and extension. We show how to reasonably discriminate between states by measuring the system's total height and stiffness near equilibrium. Furthermore, we establish the existence of geometrically-disallowed defective stable configurations which expand the configuration space to 64 states with a more complex transition pattern. Using empirical considerations of the mechanics, we analyze the hierarchical structure of the corresponding diagram, which includes Garden of Eden states and subgraphs. We highlight two irreversible transformations, shifting and erasure of the defect, leading to memory behaviors reminiscent of those observed with more complex glassy systems., Comment: Submitted to PRResearch

This progress report summarizes recent studies of electrochemical oxidation to modulate the interfacial tension of gallium-based alloys. These alloys, which are liquid at ambient conditions, have the largest interfacial tension of any liquid at room temperature. The ability to modulate the tension offers the possibility to create forces that change the shape and position of the metal. It has been known since the late 1800s that electrocapillarity-the use of potential to modulate the electric double layer on the surface of metals in electrolyte-lowers the interfacial tension of liquid metal. Yet, this phenomenon can only achieve modest changes in interfacial tension since it is limited to potential windows that avoid reactions. A recent discovery suggests that reactions driven by the electrochemical oxidation of gallium alloys cause the interfacial tension to decrease from ~500 mN/m at 0 V to ~0 mN/m at ~0.8 V, a change in tension that goes well beyond what is possible via conventional electrocapillarity or surfactants. The changes in tension are reversible; reductive potentials return the metal back to a state of high interfacial tension. This report aims to summarize key work and introduce beginners to this field by including electrochemistry basics while addressing misconceptions. We discuss applications that utilize modulations in interfacial tension of liquid metal and conclude with remaining opportunities and challenges that need further investigation.

Dense granular systems subjected to an imposed shear stress undergo stick-slip dynamics with systematic patterns of dilation-compaction. During each stick phase, as the frictional strength builds up, the granular system dilates to accommodate shear strain, developing stronger force networks. During each slip event, when the stored energy is released, particles experience large rearrangements and the granular network can significantly change. Here, we use numerical simulations of 3D, sheared frictional packings to show that the mean betweenness centrality -- a property of network of interparticle connections -- follows consistent patterns during the stick-slip dynamics, showing sharp spikes at each slip event. We identify the source of this behavior as arising from the connectivity and contact arrangements of granular network during dilation-compaction cycles, and find that a lower potential for connection between particles leads to an increase of mean betweenness centrality in the system. Furthermore, we show that at high confinements, few particles lose contact during slip events, leading to a smaller change in granular connectivity and betweenness centrality.

The surfaces of many planetary bodies, including asteroids and small moons, are covered with dust to pebble-sized regolith held weakly to the surface by gravity and contact forces. Understanding the reaction of regolith to an external perturbation will allow for instruments, including sensors and anchoring mechanisms for use on such surfaces, to implement optimized design principles. We analyze the behavior of a flexible probe inserted into loose regolith simulant as a function of probe speed and ambient gravitational acceleration to explore the relevant dynamics. The EMPANADA experiment (Ejecta-Minimizing Protocols for Applications Needing Anchoring or Digging on Asteroids) flew on several parabolic flights. It employs a classic granular physics technique, photoelasticity, to quantify the dynamics of a flexible probe during its insertion into a system of bi-disperse, cm-sized model grains. We identify the force-chain structure throughout the system during probe insertion at a variety of speeds and for four different levels of gravity: terrestrial, martian, lunar, and microgravity. We identify discrete, stick-slip failure events that increase in frequency as a function of the gravitational acceleration. In microgravity environments, stick-slip behaviors are negligible, and we find that faster probe insertion can suppress stick-slip behaviors where they are present. We conclude that the mechanical response of regolith on rubble pile asteroids is likely quite distinct from that found on larger planetary objects, and scaling terrestrial experiments to microgravity conditions may not capture the full physical dynamics.

Eutectic gallium-indium (EGaIn), a room-temperature liquid metal alloy, has the largest tension of any liquid at room temperature, and yet can nonetheless undergo fingering instabilities. This effect arises because, under an applied voltage, oxides deposit on the surface of the metal, which leads to a lowering of the interfacial tension, allowing spreading under gravity. Understanding the spreading dynamics of room temperature liquid metals is important for developing soft electronics and understanding fluid dynamics of liquids with extreme surface tensions. When the applied voltage or the oxidation rate becomes too high, the EGaIn undergoes fingering instabilities, including tip-splitting, which occur due to a Marangoni stress on the interface. Our experiments are performed with EGaIn droplets placed in an electrolyte (sodium hydroxide); by placing the EGaIn on copper electrodes, which EGaIn readily wets, we are able to control the initial width of EGaIn fingers, setting the initial conditions of the spreading. Two transitions are observed: (1) a minimum current density at which all fingers become unstable to narrower fingers; (2) a current density at which the wider fingers undergo a single splitting event into two narrower fingers. We present a phase diagram as a function of current density and initial finger width, and identify the minimum width below which the single tip-splitting does not occur.

We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity percolation, agree with each other and identify similar rigid structures. As the system becomes jammed, at a contact number of $z=2.4\pm 0.1$, a rigid backbone interspersed with floppy, particle-filled holes of a broad range of sizes emerges, creating a sponge-like morphology. We also find that the pressure within rigid structures always exceeds the pressure outside the rigid structures, i.e. that the backbone is load-bearing. These findings shows that it is necessary to go beyond mean-field theory to capture the physics of frictional jamming and also suggests that mechanical stability arises through arch structures and hinges at the mesoscale., Comment: 19 pages, 19 figures

Flow-stabilized solids are a class of fragile matter that forms when a dense suspension of colloids accumulates against a semi-permeable barrier, for flow rates above a critical value. In order to probe the effect of particle size on the formation of these solids, we perform experiments on micron-sized monodisperse spherical polystyrene spheres in a Hele-Shaw geometry. We examine the spatial extent, internal fluctuations, and fluid permeability of the solids deposited against the barrier, and find that these do not scale with the P\'eclet number. Instead, we find distinct behaviors at higher Peclet numbers, suggesting a transition from thermal- to athermal-solids which we connect to particle-scale fluctuations in the liquid-like layer at the upstream surface of the solid. We further observe that while the Carman-Kozeny model does not accurately predict the permeability of flow-stabilized solids, we do find a new scaling which predicts the permeability.

Soft materials are known to deform due to a variety of mechanisms, including capillarity, buoyancy, and swelling. In this paper, we present experiments on polyvinylsiloxane gel threads partially-immersed in three liquids with different solubility, wettability, and swellability. Our results demonstrate that deformations due to capillarity, buoyancy, and swelling can be of similar magnitude as such threads come to static equilibrium. To account for all three effects being present in a single system, we derive a model capable of explaining the observed data and use it to determine the force law at the three-phase contact line. The results show that the measured forces are consistent with the expected Young-Dupr\'e equation, and do not require the inclusion of a tangential contact line force.

Fluid droplets can be induced to move over rigid or flexible surfaces under external or body forces. We describe the effect of variations in material properties of a flexible substrate as a mechanism for motion. In this paper, we consider a droplet placed on a substrate with either a stiffness or surface energy gradient, and consider its potential for motion via coupling to elastic deformations of the substrate. In order to clarify the role of contact angles and to obtain a tractable model, we consider a two-dimensional droplet. The gradients in substrate material properties give rise to asymmetric solid deformation and to unequal contact angles, thereby producing a force on the droplet. We then use a dynamic viscoelastic model to predict the resulting dynamics of droplets. Numerical results quantifying the effect of the gradients establish that it is more feasible to induce droplet motion with a gradient in surface energy. The results show that the magnitude of elastic modulus gradient needed to induce droplet motion exceeds experimentally feasible limits in the production of soft solids and is therefore unlikely as a passive mechanism for cell motion. In both cases, of surface energy or elastic modulus, the threshold to initiate motion is achieved at lower mean values of the material properties., Comment: 13 pages, 3 figures

We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a 2D granular material comprised of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: a frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows., Comment: 10 pages, 11 figures, 1 table. V2: What is now Fig. 5 was added to clarify the raw data measured. References [27] and [37] were updated since they were published only recently

The Earth's surface is composed of a staggering diversity of particulate-fluid mixtures: dry to wet, dilute to dense, colloidal to granular, and attractive to repulsive particles. This material variety is matched by the range of relevant stresses and strain rates, from laminar to turbulent flows, and steady to intermittent forcing, leading to anything from rapid and catastrophic landslides to the slow relaxation of soil and rocks over geologic timescales. Geophysical flows sculpt landscapes, but also threaten human lives and infrastructure. From a physics point of view, virtually all Earth and planetary landscapes are composed of soft matter, in the sense they are both deformable and sensitive to collective effects. Geophysical materials, however, often involve compositions and flow geometries that have not yet been examined in physics. In this review we explore how a soft-matter perspective has helped to illuminate, and even predict, the rich dynamics of Earth materials and their associated landscapes. We also highlight some novel phenomena of geophysical flows that challenge, and will hopefully inspire, more fundamental work in soft matter.

A photoelastic material will reveal its internal stresses when observed through polarizing filters. This eye-catching property has enlightened our understanding of granular materials for over half a century, whether in the service of art, education, or scientific research. In this review article in honor of Robert Behringer, we highlight both his pioneering use of the method in physics research, and its reach into the public sphere through museum exhibits and outreach programs. We aim to provide clear protocols for artists, exhibit-designers, educators, and scientists to use in their own endeavors. It is our hope that this will build awareness about the ubiquitous presence of granular matter in our lives, enlighten its puzzling behavior, and promote conversations about its importance in environmental and industrial contexts. To aid in this endeavor, this paper also serves as a front door to a detailed wiki containing open, community-curated guidance on putting these methods into practice., Comment: 13 pages

Forecasting fracture locations in a progressively failing disordered structure is of paramount importance when considering structural materials. We explore this issue for gradual deterioration via beam breakage of two-dimensional disordered lattices, which we represent as networks, for various values of mean degree. We study experimental samples with geometric structures that we construct based on observed contact networks in 2D granular media. We calculate geodesic edge betweenness centrality, which helps quantify which edges are on many shortest paths in a network, to forecast the failure locations. We demonstrate for the tested samples that, for a variety of failure behaviors, failures occur predominantly at locations that have larger geodesic edge betweenness values than the mean one in the structure. Because only a small fraction of edges have values above the mean, this is a relevant diagnostic to assess failure locations. Our results demonstrate that one can consider only specific parts of a system as likely failure locations and that, with reasonable success, one can assess possible failure locations of a structure without needing to study its detailed energetic states., Comment: Extended discussion, added supplementary information

In ordinary solids, material disorder is known to increase the size of the process zone in which stress concentrates at the crack tip, causing a transition from localized to diffuse failure. Here, we report experiments on disordered 2D lattices, derived from frictional particle packings, in which the mean coordination number $\langle z \rangle$ of the underlying network provides a similar control. Our experiments show that tuning the connectivity of the network provides access to a range of behaviors from brittle to ductile failure. We elucidate the cooperative origins of this transition using a frictional pebble game algorithm on the original, intact lattices. We find that the transition corresponds to the isostatic value $\langle z \rangle = 3$ in the large-friction limit, with brittle failure occurring for structures vertically spanned by a rigid cluster, and ductile failure for floppy networks containing nonspanning rigid clusters. Furthermore, we find that individual failure events typically occur within the floppy regions separated by the rigid clusters.

A load applied to a jammed frictional granular system will be localized into a network of force chains making inter-particle connections throughout the system. Because such systems are typically under-constrained, the observed force network is not unique to a given particle configuration, but instead varies upon repeated formation. In this paper, we examine the ensemble of force chain configurations created under repeated assembly in order to develop tools to statistically forecast the observed force network. In experiments on a gently suspended 2D layer of photoelastic particles, we subject the assembly to hundreds of repeated cyclic compressions. As expected, we observe the non-unique nature of the force network, which differs for each compression cycle, by measuring all vector inter-particle contact forces using our open source PeGS software. We find that total pressure on each particle in the system correlates to its betweenness centrality value extracted from the geometric contact network. Thus, the mesoscale network structure is a key control on individual particle pressures.

Stress-based ensembles incorporating temperature-like variables have been proposed as a route to an equation of state for granular materials. To test the efficacy of this approach, we perform experiments on a two-dimensional photoelastic granular system under three loading conditions: uniaxial compression, biaxial compression, and simple shear. From the interparticle forces, we find that the distributions of the normal component of the coarse-grained force-moment tensor are exponential-tailed, while the deviatoric component is Gaussian-distributed. This implies that the correct stress-based statistical mechanics conserves both the force-moment tensor and the Maxwell-Cremona force-tiling area. As such, two variables of state arise: the tensorial angoricity ($\hat{\alpha}$) and a new temperature-like quantity associated with the force-tile area which we name {\it keramicity} ($\kappa$). Each quantity is observed to be inversely proportional to the global confining pressure; however only $\kappa$ exhibits the protocol-independence expected of a state variable, while $\hat{\alpha}$ behaves as a variable of process.

The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate physical, mathematical, statistical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures across different scales in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials. In this paper, we review work on network-based approaches to studying granular matter and explore the potential of such frameworks to provide a useful description of these systems and to enhance understanding of their underlying physics. We also outline a few open questions and highlight particularly promising future directions in the analysis and design of granular matter and other kinds of material networks.

In granular physics experiments, it is a persistent challenge to obtain the boundary stress measurements necessary to provide full a rheological characterization of the dynamics. Here, we describe a new technique by which the outer boundary of a 2D Couette cell both confines the granular material and provides spatially- and temporally- resolved stress measurements. This key advance is enabled by desktop laser-cutting technology, which allows us to design and cut linearly-deformable walls with a specified spring constant. By tracking the position of each segment of the wall, we measure both the normal and tangential stress throughout the experiment. This permits us to calculate the amount of shear stress provided by basal friction, and thereby determine accurate values of $\mu(I)$., Comment: 4 pages, 5 figures, powder and grains 2017 conference

We present an experiment in which a horizontal quasi-2D granular system with a fixed neighbor network is cyclically compressed and decompressed over 1000 cycles. We remove basal friction by floating the particles on a thin air cushion, so that particles only interact in-plane. As expected for a granular system, the applied load is not distributed uniformly, but is instead concentrated in force chains which form a network throughout the system. To visualize the structure of these networks, we use particles made from photoelastic material. The experimental setup and a new data-processing pipeline allow us to map out the evolution subject to the cyclic compressions. We characterize several statistical properties of the packing, including the probability density function of the contact force, and compare them with theoretical and numerical predictions from the force network ensemble theory., Comment: accepted for publication in the conference proceedings of Powders and Grains 2017

We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lowers the effective interfacial tension of a gallium-based liquid metal alloy to values approaching zero, thereby inducing drastic shape changes, including the formation of fractals. The measured fractal dimension ($D = 1.3 \pm 0.05$) places the instability in a different universality class than other fingering instabilities. By characterizing changes in morphology and dynamics as a function of droplet volume and applied electric potential, we identify the three main forces involved in this process: interfacial tension, gravity, and oxidative stress. Importantly, we find that electrochemical oxidation can generate compressive interfacial forces that oppose the tensile forces at a liquid interface. Thus, the surface oxide layer not only induces instabilities, but ultimately provides a physical barrier that halts the instabilities at larger positive potentials. Controlling the competition between surface tension and oxidative (compressive) stresses at the interface is important for the development of reconfigurable electronic, electromagnetic, and optical devices that take advantage of the metallic properties of liquid metals.

Granular materials are complex multi-particle ensembles in which macroscopic properties are largely determined by inter-particle interactions between their numerous constituents. In order to understand and to predict their macroscopic physical behavior, it is necessary to analyze the composition and interactions at the level of individual contacts and grains. To do so requires the ability to image individual particles and their local configurations to high precision. A variety of competing and complementary imaging techniques have been developed for that task. In this introductory paper accompanying the Focus Issue, we provide an overview of these imaging methods and discuss their advantages and drawbacks, as well as their limits of application., Comment: Submitted to Review of Scientific Instruments as introduction for: Focus on Imaging Methods in Granular Physics

Photoelastic techniques are used to make both qualitative and quantitative measurements of the forces within idealized granular materials. The method is based on placing a birefringent granular material between a pair of polarizing filters, so that each region of the material rotates the polarization of light according to the amount of local of stress. In this review paper, we summarize past work using the technique, describe the optics underlying the technique, and illustrate how it can be used to quantitatively determine the vector contact forces between particles in a 2D granular system. We provide a description of software resources available to perform this task, as well as key techniques and resources for building an experimental apparatus.

Granular materials can fail through spontaneous events like earthquakes or brittle fracture. However, measurements and analytic models which forecast failure in this class of materials, while of both fundamental and practical interest, remain elusive. Materials including numerical packings of spheres, colloidal glasses, and granular materials have been known to develop an excess of low-frequency vibrational modes as the confining pressure is reduced. Here, we report experiments on sheared granular materials in which we monitor the evolving density of excited modes via passive monitoring of acoustic emissions. We observe a broadening of the distribution of excited modes coincident with both bulk and local plasticity, and clear evolution in the shape of the distribution before and after bulk failure. These results provide a new interpretation of the changing state of the material on its approach to stick-slip failure., Comment: 5 pages, 5 figures

A droplet of surfactant spreading on an ultrasoft ($E \lesssim 100$ Pa) gel substrate will produce capillary fractures at the gel surface; these fractures originate at the contact-line and propagate outwards in a starburst pattern. There is an inherent variability in both the number of fractures formed and the time delay before fractures form. In the regime where single fractures form, we observe a Weibull-like distribution of delay times, consistent with a thermally-activated process. The shape parameter is close to 1 for softer gels (a Poisson process), and larger for stiffer gels (indicative of aging). For single fractures, the characteristic delay time is primarily set by the elastocapillary length of the system, calculated from the differential in surface tension between the droplet and the substrate, rather than the elastic modulus as for stiffer systems. For multiple fractures, all fractures appear simultaneously and long delay times are suppressed. The delay time distribution provides a new technique for probing the energy landscape and fracture toughness of ultrasoft materials.

On a sufficiently-soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates which deform under loading. It remains an open question whether the contact line transmits a non-zero radial force to the substrate surface in addition to the conventional vertical force. We present an analytic Fourier transform solution technique that includes general interfacial energy conditions which govern the contact angle of a 2D droplet. This includes evaluating the effect of gravity on the droplet shape in order to determine the correct fluid pressure at the substrate surface for larger droplets. Importantly, we find that in order to avoid a strain singularity at the contact line under a nonzero radial contact line force, it is necessary to include a previously-neglected radial traction boundary condition. To quantify the effects of the contact line and identify key quantities that will be experimentally-accessible for testing the model, we evaluate solutions for the substrate surface displacement field as a function of Poisson's ratio and zero/non-zero radial contact line forces., Comment: 16 pages, 5 figures, Partial Differential Equations

Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts to a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force chain structure, with the goal of identifying shape differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here, we discuss a trio of related but fundamentally distinct measurements of mesoscale structure of force chains in arbitrary 2D packings, including a novel statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain., Comment: 13 pages, 5 figures

Understanding the particle-scale transition from elastic deformation to plastic flow is central to making predictions about the bulk material properties and response of disordered materials. To address this issue, we perform experiments on flow-stabilized solids composed of micron-scale spheres within a microfluidic channel, in a regime where particle inertia is negligible. Each solid heap exists within a stress gradient imposed by the flow, and we track the positions of particles in response to single impulses of fluid-driven compression or decompression. We find that the resulting deformation field is well-decomposed into an affine field, with a constant strain profile throughout the solid, and a non-affine field. The magnitude of this non-affine response decays with the distance from the free surface in the long-time limit, suggesting that the distance from jamming plays a significant role in controlling the length scale of plastic flow. Finally, we observe that compressive pulses create more rearrangements than decompressive pulses, an effect that we quantify using the $D^2_\mathrm{min}$ statistic for non-affine motion. Unexpectedly, the time scale for the compression response is shorter than for decompression at the same strain (but unequal pressure), providing insight into the coupling between deformation and cage-breaking.

As a granular material is compressed, the particles and forces within the system arrange to form complex heterogeneous structures. Force chains are a prime example and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, characterizing the dynamic nature of mesoscale architectures in granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend current approaches by utilizing multilayer networks as a framework for directly quantifying the evolution of mesoscale architecture in a compressed granular system. We examine a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial compression through a series of small, quasistatic steps. Treating particles as network nodes and inter-particle forces as network edges, we construct a multilayer network by linking together the series of static force networks that exist at each strain step. We then extract the inherent mesoscale structure from the system by using a generalization of community detection methods, and we define quantitative measures to characterize the reconfiguration and evolution of this structure throughout compression. By separately considering the network of normal and tangential forces, we find that they display different structural evolution. To test the sensitivity of the network model to particle properties, we examine whether the method can distinguish a subsystem of low-friction particles within a bath of higher-friction particles. We find that this can be done by considering the network of tangential forces. The results discussed throughout this study suggest that these novel network science techniques may provide a direct way to compare and classify data from systems under different external conditions or with different physical makeup.

For more than two decades, a single model for the spreading of a surfactant-driven thin liquid film has dominated the applied mathematics literature on the subject. Recently, through the use of fluorescently-tagged lipids, it has become possible to make direct, quantitative comparisons between experiments and models. These comparisons have revealed two important discrepancies between simulations and experiments: the spatial distribution of the surfactant layer, and the timescale over which spreading occurs. In this paper, we present numerical simulations that demonstrate the impact of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension. Previous choices of the model EoS have been an ad-hoc decreasing function. Here, we instead propose an empirically-motivated equation of state; this provides a route to resolving some discrepancies and raises new issues to be pursued in future experiments. In addition, we test the influence of the choice of initial conditions and values for the non-dimensional groups. We demonstrate that the choice of EoS improves the agreement in surfactant distribution morphology between simulations and experiments, and impacts the dynamics of the simulations. The relevant feature of the EoS, the gradient, has distinct regions for empirically motivated choices, which suggests that future work will need to consider more than one timescale. We observe that the non-dimensional number controlling the relative importance of gravitational vs. capillary forces has a larger impact on the dynamics than the other non-dimensional groups. Finally, we observe that the experimental approach of using a ring to contain the surfactant could affect the surfactant and fluid dynamics if it disrupts the intended initial surfactant distribution. However, the meniscus itself does not significantly affect the dynamics., Comment: 21 pages, 12 figures

Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement., Comment: 5 pages, 1 figure

Optically-transparent immersion liquids with refractive index (n ~ 1.77) to match sapphire-based aplanatic numerical aperture increasing lens (aNAIL) are necessary for achieving deep 3D imaging with high spatial resolution. We report that antimony tribromide (SbBr$_{3}$) salt dissolved in liquid diiodomethane (CH$_{2}$I$_{2}$) provides a new high refractive index immersion liquid for optics applications. The refractive index is tunable from n = 1.74 (pure) to n = 1.873 (saturated), by adjusting either salt concentration or temperature; this allows it to match (or even exceed) the refractive index of sapphire. Importantly, the solution gives excellent light transmittance in the ultraviolet to near-infrared range, an improvement over commercially-available immersion liquids. This refractive index matched immersion liquid formulation has enabled us to develop a sapphire-based aNAIL objective that has both high numerical aperture (NA = 1.17) and long working distance (WD = 12 mm). This opens up new possibilities for deep 3D imaging with high spatial resolution.

Granular materials transmit stress via a network of force chains. Despite the importance of these chains to characterizing the stress state and dynamics of the system, there is no common framework for quantifying their their properties. Recently, attention has turned to the tools of network science as a promising route to such a description. In this paper, we apply community detection techniques to numerically-generated packings of spheres over a range of interparticle friction coefficients and confining pressures. In order to extract chain-like features, we use a modularity maximization with a recently-developed geographical null model \cite{Bassett2015}, and optimize the technique to detect branched structures by minimizing the normalized convex hull of the detected communities. We characterize the force chain communities by their size (number of particles), network strength (internal forces), and normalized convex hull ratio (sparseness). We find the that the first two exhibit an approximately linear correlation and are therefore largely redundant. For both pressure $P$ and interparticle friction $\mu$, we observe crossovers in behavior. For $\mu \lesssim 0.1$, the packings exhibit more sensitivity to pressure. In addition, we identify a crossover pressure where the frictional dependence switches from having more large/strong communities at low $\mu$ vs. high $\mu$. We explain these phenomena by comparison to the spatial distribution of communities along the vertical axis of the system. These results provide new tools for considering the mesoscale structure of a granular system and pave the way for reduced descriptions based on the force chain structure.

Entropy is a difficult concept to teach using real-world examples. Unlike temperature, pressure, volume, or work, it's not a quantity which most students encounter in their day-to-day lives. Even the way entropy is often qualitatively described, as a measure of disorder, is incomplete and can be misleading. In an effort to address these obstacles, we have developed a simple laboratory activity, the stretching of an elastic rubber sheet, intended to give students hands-on experience with the concepts of entropy, temperature and work in both adiabatic and quasistatic processes. We present two versions of the apparatus: a double-lever system, which may be reproduced with relatively little cost, and a commercial materials testing system, which provides students experience with scientific instrumentation that is used in research., Comment: Submitted to the American Journal of Physics