Granular flows are ubiquitous in nature and industrial applications, yet a complete continuum theory remains a long-standing challenge. The leading empirical approach, μ(I) rheology, lacks microscopic foundations and becomes multivalued in dense, slowly sheared flows where nonlocal corrections are required. Exploiting state-of-the-art high-speed X-ray tomography to investigate microscopic dynamics of dense granular flows in a Couette geometry, we establish a new, universal constitutive law spanning quasi-static to inertial regimes based on structural relaxation, resolving the fundamental difficulty in the original μ(I) framework. By further establishing a non-equilibrium statistical framework for granular flows, we demonstrate an intrinsic analogy between driven granular matter and hard-sphere liquids owing to their identical Carnahan-Starling equation of state, naturally explaining our rheological approach and the emergence of glassy behaviors. Our framework unifies granular rheology with the broader physics of disordered systems and provides a complete, microscopically-based theoretical framework for dense granular flow.

The partial coordination number and contact proportion associated with different contact types are key microscale parameters for understanding the macroscopic behavior of granular mixtures. However, experimental data for binary mixtures with large size ratios remain scarce, and direct comparisons among the Dodds, Clusel, and Biazzo models are lacking, hindering a comprehensive evaluation of their predictive accuracy. Moreover, the hypothesis proposed by Biazzo et al. (2009) that significant prediction discrepancies at large size ratios arise from the presence of numerous rattlers has not yet been experimentally supported. To address these gaps, we conducted a series of high-resolution optical experiments on two-dimensional (2D) dense binary mixtures with size ratios alpha=3, 5, 7, and 9. Our findings confirm the validity of Dodds and Biazzo models for lower size ratios (1 6.46), the positive correlation between fine rattler fraction and prediction errors not only probably supports Biazzo et al.'s hypothesis but also suggests that excluding fine rattlers from the theoretical input may improve model accuracy. Quantitatively, the Dodds and Biazzo models outperform the Clusel model, with Biazzo's model showing slightly better predictive accuracy due to its incorporation of spatial correlations. However, the Dodds model offers practical simplicity owing to its lower parameter requirements. This study provides a practical basis for accurately characterizing local packing structures and their relation to macroscopic properties in 2D granular systems, but also lays a foundation for modeling more complex 3D systems.

Using X-ray tomography, we compare granular packings prepared under buoyancy-reduced effective gravity with normal gravity packings of particles with systematically varied friction. We show that reducing gravity lowers the random loose packing limit in a manner analogous to increasing friction. Granular packings under reduced gravity and with enhanced friction exhibit identical volume distributions, compactivity, and entropy, indicating that both routes sample statistically equivalent Edwards volume ensembles of mechanically stable states. This equivalence originates from a common relaxation of the mechanical stability constraint: under both conditions, fewer particles are required to participate in the underlying load-bearing bridge structures, leading to a lower contact-number requirement and a higher density of mechanically stable states. Nevertheless, reduced gravity retains a distinct contact-scale signature through more isotropic contact orientations. These findings identify gravity as a physical control governing the statistical accessibility of mechanically stable states within the Edwards framework and provide a unified statistical description of granular packings formed through different physical routes.

Highly anisotropic granular particles can form very loose and stable piles with a large repose angle due to the geometric cohesion effect. The random geometric features of such structures and the origin of their stability against external mechanical perturbations remain to be explored. Here, using magnetic resonance imaging techniques, we perform an accurate structural reconstruction of columns built with long granular rods. We study the structural evolution during the gradual disentangling and collapse of a randomly poured free-standing pile of long rods under consecutive vertical shaking. The average height of the column decreases exponentially upon shaking, accompanied by a nonmonotonic evolution of the average packing fraction and an increasing negative nematic order of the rod orientations. Yet, the distributions of the relative position and orientation of contacting rod pairs remain roughly unchanged during the disentangling process. Distribution and spatial correlation between contact points as well as the evolution of contact network have also been analysed, providing insights into the micromechanics of nest-like structures.

Disordered granular packings share many similarities with supercooled liquids, particu-larly in the rapid increase of structural relaxation time within a narrow range of temperature or packing fraction. However, it is unclear whether the dynamics of granular materials align with those of their corresponding thermal hard sphere liquids, and the particular influence of friction of a granular system remains largely unexplored. Here, we experimentally study the slow relaxation and the steady state of monodisperse granular sphere packings with X-ray tomography. We first quantify the thermodynamic parameters under the Edwards' ensemble, (i.e., effective temperature and configurational entropy), of granular spheres with varying friction, and measure their characteristic relaxation time during compaction processes. We then demonstrate a unified picture of the relaxation process in granular systems in which the Adam-Gibbs (AG) relationship is generally followed. These results clarify the close relation-ship between granular materials and the ideal frictionless hard sphere model.

The presence of gravity and friction results in the formation of cooperative bridge structures in granular systems, where neighboring particles support each other for mutual stability. These bridge structures serve as unique mechanical backbones in both static granular packings and dynamic granular flows, significantly influencing their mechanical responses and rheological behaviors. Using high-resolution x-ray tomography, we experimentally investigate the bridge structures in tapped granular packings composed of particles with varying friction coefficients. We find that gravity can induce subtle structural changes on the load-bearing contacts, allowing us to identify the correct load-bearing contacts based on structural information alone. Using these identified load-bearing contacts, we investigate the cooperative bridge structures which are mechanical backbones of the system. We characterize the geometric properties of these bridges and find that their cooperativity increases as the packing fraction decreases. The knowledge of bridges can enhance our understanding of the mechanical stability and rheological properties of granular materials, since bridges represent localized, mutually stabilizing configurations that bear load collectively.

Using X-ray tomography, we experimentally investigate the structural evolution of packings composed of 3D-printed hexapod particles, each formed by three mutually orthogonal spherocylinders, during tap-induced compaction. We identify two distinct structural compaction mechanisms: an initial stage dominated by enhanced particle interlocking, which yields local mechanically stable structures through strong geometric entanglement, and a later stage characterized by the formation of dense polytetrahedral aggregates and a sharp increase in the number of five-ring motifs. The emergence of these five-fold symmetric structures indicates that, despite their highly concave geometry, hexapod packings can be effectively treated as hard-sphere-like systems and exhibit similar glass-like disordered configurations. The frustration between local mechanically stable structures and global glassy order suggests a universal organizational principle underlying the structure of uniform and isotropic disordered granular materials.

The packing geometry of granular solids and other amorphous materials is important to understand their macroscopic behaviors. However, their particle-scale assembly mechanism and the underlying statistical mechanical laws remain unclear. In this work, we develop a model to generate the local packing structures of granular spheres by parking them sequentially and stochastically, and connect the fluctuating structures to the thermodynamic equations of state. The influences of entropy, friction, and mechanical action on local configurations are decomposed with the aid of an effective interparticle interaction, a parking sequence of neighboring particles, and an external potential. Quasiuniversal laws of granular sphere packings observed in previous experiments are replicated by our model and their empirical dependences on particle friction and packing protocol are rationalized. This model provides a general statistical mechanical approach to understanding the nonequilibrium assembly mechanism of amorphous particle packing systems.

With magnetic resonance imaging experiments, we study packings of granular spherocylinders with merely 2% asphericity. Evident structural anisotropies across all length scales are identified. Most interestingly, the global nematic order decreases with increasing packing fraction, while the local contact anisotropy shows an opposing trend. We attribute this counterintuitive phenomenon to a competition between gravity-driven ordering aided by frictional contacts and a geometric frustration effect at the marginally jammed state. It is also surprising to notice that such slight particle asphericity can trigger non-negligible correlations between contact-level and mesoscale structures, manifested in drastically different nonaffine structural rearrangements upon compaction from that of granular spheres. These observations can help improve statistical mechanical models for the orientational order transformation of nonspherical granular particle packings, which involves complex interplays between particle shape, frictional contacts, and external force field.

Dense granular flow is common in nature and industrial applications. A hallmark behaviour of granular flow is the emergence of a critical state when sufficient strain is applied, which has traditionally been understood with empirical constitutive theories. However, these theories are macroscopic ones without microscopic basis and, therefore, the physical origin of the critical state remains unknown. Here we demonstrate that the critical state corresponds to the random loose packing state where all the microstates are sampled with equal probability. X-ray tomography and shear force measurements allow us to monitor the microscopic processes of sheared granular materials and show that interparticle frictional contacts alter the density of states. This, consequently, leads to different critical state volume fractions. Despite this qualitative difference, we find universal equations of rescaled state variables (effective temperature, entropy and contact number as functions of volume fraction) for systems with different friction coefficients ( μ = 0.52, 0.66 and 0.86), which suggests that frictional granular packings can be mapped directly to the frictionless hard-sphere system. In addition, we show that shear force barely affects the Edwards ensemble statistics, while its behaviour can be empirically explained by simply adding the contributions from particle structural rearrangements and frictional dissipation on contacts.

We utilize magnetic resonance imaging (MRI) techniques to study granular sphere packings prepared with vertical vibration, and reveal the extremely slight global anisotropies of the void phase with systematic analyses on Delaunay pores and chords. Unexpectedly, the global orientational orders of the eigenvectors of tensors quantifying (i) pore throats, (ii) chords going through individual pores, (iii) shape of Voronoi cells and (iv) contact fabrics have consistent evolution laws when packing fraction changes, but the orientational order of the eigenvectors of a pore volume tensor exhibits a peculiarly different trend. With an orientation-dependent spatial correlation function, we attribute their different behaviors to the fact that different anisotropy variables probe the void phase at different length scales, so that their dependences on packing fraction are different. The segmentation of the void region into pores sensitively captures a unique and intricate structural anisotropy at an intermediate length scale.

Centrifugation is one of the most commonly used methods for separation in biology and chemistry. However, effective fractionation is not always easy to obtain, as preparative centrifuge experiments are mostly conducted in an empirical way, even when it is guided by the quantitative results from analytical ultracentrifuge (AUC). Very few works have been performed to enhance the fractionation resolution of the differential centrifugation method in a swing-out rotor. This is primarily due to the absence of a characterization tool for sedimentation in the preparative centrifuge. In this study, we utilized image analysis to map the particle concentration distribution throughout the preparative centrifuge tube, revealing an unexpected and abnormal sedimentation process. By characterizing the sedimentation coefficient distributions of the fractionated product via AUC, we demonstrated that the overall sedimentation efficiency in a swing-out preparative centrifuge was significantly reduced. Furthermore, effective fractionation was confined to the intermediate phase of the entire sedimentation process. We propose that the mechanism here is a combination of the inverse Boycott effect and droplet sedimentation. The actual sedimentation process within a preparative centrifuge can be described by modifying the Lamm equation phenomenologically, which simply results in an effective sedimentation coefficient. Our work builds a foundation for determining the optimal preparative centrifugation conditions for various systems.

The microscopic stress field inhomogeneity in the interfacial region adjacent to the liquid surface is the fundamental origin of the liquid surface tension, but because of broadening due to capillary fluctuations, a detailed molecular level understanding of the stress field remains elusive. In this work, we deconvolute the capillary fluctuations to reveal the intrinsic stress field and show that the atomic-level contributions to the surface tension are similar in functional form across a variety of monatomic systems. These contributions are confined to an interfacial region approximately 1.5±0.1 times the particle diameter for all systems studied. In addition, the intrinsic density and stress profiles show a strong spatial correlation that should be useful in the development of a statistical mechanical theory for the prediction of surface stress and surface tension.

Using x-ray tomography, we experimentally investigate the nematic transition in granular spherocylinder packings induced by tapping. Upon the validation of the Edwards ensemble framework in spherocylinders, we introduce an empirical free energy that accounts for the influence of gravity and the mechanical stability requirements specific to granular systems. This free energy can predict not only the correct phase transition behavior of the system from a disordered state to a nematic phase, but also a phase coexistence range and nucleation energy barriers that agree with experimental observations.

Packing structures of granular disks are reconstructed using magnetic resonance imaging techniques. As packing fraction increases, the packing structure transforms from a nematic loose packing to a dense packing with randomly oriented stacks. According to our model based on Edwards' volume ensemble, stack structures are statistically favored when the effective temperature decreases, which has a lower structural anisotropy than single disks, and brings down the global orientational order consequently. This mechanism identified in athermal granular materials can help us understand the nonergodic characteristics of disklike particle assemblies such as discotic mesogens and clays.

浮沉子是与浮力相关的趣味装置,浮沉子的不可逆现象是研究其运动机制的关键问题.设计了参量可控的浮沉子实验装置,研究了浮沉子的运动过程,利用夹逼的方法获得了浮沉子不可逆现象的临界深度,并且研究了影响临界深度的参量,验证了基础的理论模型和修正后的理论模型的适用性.实验结果表明:浮沉子的初始气柱越长,临界深度越深,二者基本呈线性关系;浮沉子的长度越小,临界深度越深;浮沉子的截面积越大,临界深度越深.

Packing structures of granular cylinders with the aspect ratio close to one have been reconstructed with the help of magnetic resonance imaging techniques. By controlling the container boundary conditions and preparation protocols, a structural transformation from a disordered liquid-like state to an orientationally ordered state with cubatic symmetry at a high packing fraction is observed. This ordering process is accompanied by the formation of more faceted contacts, which lower the elastic energy between jammed granular particles to drive the transformation. With the help of Edwards' volume ensemble theory, this granular structural transformation is explained using a phenomenological thermodynamic model and a self-consistent mean-field statistical mechanical model. Both models predict a sharp but continuous change of order parameter when the effective granular temperature is lowered. The intrinsic difference and connection between this granular structural transformation and the entropy-driven phase transition of conventional thermal hard-particle systems are discussed.

Packings of granular particles may transform into ordered structures under external agitation, which is a special type of out-of-equilibrium self-assembly. Here, evolution of the internal packing structures of granular cubes under cyclic rotating shearing has been analyzed using magnetic resonance imaging techniques. Various order parameters, different types of contacts and clusters composed of face-contacting cubes, as well as the free volume regions in which each cube can move freely have been analyzed systematically to quantify the ordering process and the underlying mechanism of this granular self-assembly. The compaction process is featured by a first rapid formation of orientationally ordered local structures with faceted contacts, followed by further densification driven by free-volume maximization with an almost saturated degree of order. The ordered structures are strongly anisotropic with contacting ordered layers in the vertical direction while remaining liquid-like in the horizontal directions. Therefore, the constraint of mechanical stability for granular packings and the thermodynamic principle of entropy maximization are both effective in this system, which we propose can be reconciled by considering different depths of supercooling associated with various degrees of freedom.

Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness, giving therefore the first experimental evidence that the concept of effective temperature is valid in driven frictional granular systems.