We present 3D DEM simulations of bidisperse granular packings to investigate their jamming densities, $ϕ_J$, and dimensionless bulk moduli, $K$, as a function of the size ratio, $δ$, and the concentration of small particles, $X_{\mathrm S}$. We determine the partial and total bulk moduli for each packing and report the jamming transition diagram, i.e., the density or volume fraction marking both the first and second transitions of the system. At a large enough size difference, e.g., $δ\le 0.22$, $X^{*}_{\mathrm S}$ divides the diagram with most small particles either non-jammed or jammed jointly with large ones. We find that the bulk modulus $K$ jumps at $X^{*}_{\mathrm S}(δ= 0.15) \approx 0.21$, at the maximum jamming density, where both particle species mix most efficiently, while for $X_{\mathrm S} < X^{*}_{\mathrm S}$ $K$ is decoupled in two scenarios as a result of the first and second jamming transition. Along the second transition, $K$ rises relative to the values found at the first transition, however, is still small compared to $K$ at $X^{*}_{\mathrm S}$. While the first transition is sharp, the second is smooth, carried by small-large interactions, while the small-small contacts display a transition. This demonstrates that for low enough $δ$ and $X_{\mathrm S}$, the jamming of small particles indeed impacts the internal resistance of the system. Our new results will allow tuning the bulk modulus $K$ or other properties, such as the wave speed, by choosing specific sizes and concentrations based on a better understanding of whether small particles contribute to the jammed structure or not, and how the micromechanical structure behaves at either transition.
We systematically map out the jamming transition of all 2D bidisperse mixtures of frictionless disks in the hard particle limit. The critical volume fraction, mean coordination number, number of rattlers, structural order parameters, and bulk modulus each show a rich variation with mixture composition and particle size ratio, and can therefore be tuned by choosing certain mixtures. We identify two local minima in the critical volume fraction, both of which have low structural order; one minimum is close to the widely studied 50:50 mixture of particles with a ratio of radii of 1:1.4. We also id…
By generalizing a geometric argument for frictionless spheres, a model is proposed for the jamming density $ϕ_J$ of mechanically stable packings of bidisperse, frictional spheres. The monodisperse, $μ_s$-dependent jamming density $ϕ_J^{\mathrm{mono}}(μ_s)$ is the only input required in the model, where $μ_s$ is the coefficient of friction. The predictions of the model are validated by robust estimates of $ϕ_J$ obtained from computer simulations of up to $10^7$ particles for a wide range of $μ_s$, and size ratios up to 40:1. Although $ϕ_J$ varies nonmonotonically with the volume fraction of sma…
We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or a higher fill fraction when the smaller particles are accomodated in the interstices of the larger spheres. Variation in the packing fraction is explained by a percolation transition, as chains of defects or scars previously discovered in the monodispersed case grow and eventually disconnect the neighbor graph.
We present numerical evidence for an additional discontinuous transition inside the jammed regime for an asymmetric bidisperse granular packing upon compression. This additional transition line separates jammed states with networks of predominantly large particles from jammed networks formed by both large and small particles, and the transition is indicated by a discontinuity in the number of particles contributing to the jammed network. The additional transition line emerges from the curves of jamming transitions and terminates in an end-point where the discontinuity vanishes. The additional …
By minimizing the enthalpy of packings of frictionless particles, we obtain jammed solids at desired pressures and hence investigate the jamming transition with and without shear. Typical scaling relations of the jamming transition are recovered in both cases. In contrast to systems without shear, shear-driven jamming transition occurs at a higher packing fraction and the jammed solids are more rigid with an anisotropic force network. Furthermore, by introducing the macro-friction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixe…
We study the rheology of monodisperse and bidisperse emulsions with various droplet sizes (1 $μ$m -- 2 $μ$m diameter). Above a critical volume fraction $ϕ_c$, these systems exhibit solid-like behavior and a yield stress can be detected. Previous experiments suggest that for small thermal particles, rheology will see a glass transition at $ϕ_c = ϕ_g =0.58$; for large athermal systems, rheology will see a jamming transition at $ϕ_c = ϕ_J =0.64$. However, simulations point out that at the crossover of thermal and athermal regimes, the glass and jamming transitions may both be observed in the same…
We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via purely repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to induce jamming in initially unjammed packings from th…
The formation of self-organised structures that resist shear deformation have been discussed in the context of shear jamming and thickening[1-3], with frictional forces playing a key role. However, shear induces geometric features necessary for jamming even in frictionless packings[4]. We analyse conditions for jamming in such assemblies by solving force and torque balance conditions for their contact geometry. We demonstrate, and validate with frictional simulations, that the isostatic condition for mean contact number Z = D + 1 (for spatial dimension D = 2, 3) holds at jamming for both finit…
Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined, and can be characterized as a random instantiation within the space of the force network ensemble. In this work, we show that by examining the boundaries of this space of allowed force networks, defect contacts which are not necessary for stability of the system can be uniquely identified. We further show that in the near jamming limit, this identification is nearly always correct and…
Jammed particulate systems composed of various shapes of particles undergo the jamming transition as they are compressed or decompressed. To date, sphere packings have been extensively studied in many previous works, where isostaticity at the transition and scaling laws with the pressure of various quantities, including the contact number and the vibrational density of states, have been established. Additionally, much attention has been paid to nonspherical packings, and particularly recent work has made progress in understanding ellipsoidal packings. In the present work, we study the dimer pa…
Self-organization, and transitions from reversible to irreversible behaviour, of interacting particle assemblies driven by externally imposed stresses or deformation is of interest in comprehending diverse phenomena in soft matter. They have been investigated in a wide range of systems, such as colloidal suspensions, glasses, and granular matter. In different density and driving regimes, such behaviour is related to yielding of amorphous solids, jamming, and memory formation, \emph{etc.} How these phenomena are related to each other has not, however, been much studied. In order to obtain a uni…
Discrete element method is conducted to investigate the bidisperse dense granular flow having big and small grains in a two dimensional hopper. A half-circular dynamical force arch is observed above the outlet and Beverloo's law is verified to describe the relationship between flow rate and outlet size. The bidisperse flow can reach the maximum flow rate when a small fraction of big grains is added into the monodisperse flow with only small grains. The distributions of contact force, packing fraction and grain velocity indicate that the flow properties in the hopper are closely related to the …
At the same solid volume fraction, bidisperse and polydisperse suspensions display lower viscosities, and weaker normal stress response, compared to monodisperse suspensions. The reduction of viscosity associated with size distribution can be explained by an increase of the maximum flowable, or jamming, solid fraction $ϕ_m$. In this work, dense suspensions are simulated under strong shearing, where thermal motion and repulsive forces are negligible, but we allow for particle contact with a mild frictional interaction with interparticle friction coefficient of $μ = 0.2$. Aspects of bidisperse s…
We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging…
By exploring the properties of the energy landscape of a bidisperse system of soft harmonic disks in two dimensions we determine the thermal jamming transition. To be specific, we study whether the ground state of the system where the particle do not overlap can be reached within a reasonable time. Starting with random initial configurations, the energy landscape is probed by energy minimization steps as in case of athermal jamming and in addition steps where an energy barrier can be crossed with a small but non-zero probability. For random initial conditions we find that as a function of pack…
We present a theoretical prediction on random close packing factor ϕ_RCP^b of binary granular packings based on the hard-sphere fluid theory. An unexplored regime is unravelled, where the packing fraction ϕ_RCP^b is smaller than that of the mono-sized one ϕ_RCP^m, i.e., the so-called loose jamming state. This is against our common perception that binary packings should always reach a denser packing than mono-sized packings at the jamming state. Numerical evidence further supports this prediction and confirms the regime location in the size ratio and mole fraction (R_r-X_s) space, where the siz…
We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction phi_J. For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction phi(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at phi_J. For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale, and that this length scale appears to remain finite as the s…
The glassy dynamics of soft harmonic spheres is often mapped onto the dynamics of hard spheres by considering an effective diameter for the soft particles and therefore an effective packing fraction. While in this approach the thermal fluctuations within valleys of the energy landscape are covered, the crossing of energy barriers from one valley into another usually is neglected. Here we argue - motivated by studies of the glass transition based on explorations of the energy landscape - that the crossing of energy barriers can be attributed by an effective decrease of the glass transition pack…
There are two main classes of physics-based models for two-dimensional cellular materials: packings of repulsive disks and the vertex model. These models have several disadvantages. For example, disk interactions are typically a function of particle overlap, yet the model assumes that the disks remain circular during overlap. The shapes of the cells can vary in the vertex model, however, the packing fraction is fixed at $ϕ=1$. Here, we describe the deformable particle model (DPM), where each particle is a polygon composed of a large number of vertices. The total energy includes three terms: tw…
Colloidal and other granular media experience a transition to rigidity known as jamming if the fill fraction is increased beyond a critical value. The resulting jammed structures are locally disordered, bear applied loads inhomogenously, possess the minimal number of contacts required for stability and elastic properties that scale differently with volume fraction to crystalline media. Here the jamming transition is studied on a curved ellipsoidal surface by computer simulation, where shape evolution leads to a reduction in area, crowding the particles and preventing further evolution of the s…
No known analytic framework precisely explains all the phenomena observed in jamming. The replica theory for glass and jamming is a mean field theory which attempts to do so by working in the limit of infinite dimensions, such that correlations between neighbors are negligible. As such, results from this mean field theory are not guaranteed to be observed in finite dimensions. However, many results in mean field for jamming have been shown to be exact or nearly exact in low dimensions. This suggests that the infinite dimensional limit is not necessary to obtain these results. In this paper, we…
Granular packings display the remarkable phenomenon of dilatancy [1], wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, as also the related phenomenon of shear-induced jamming, requires frictional interactions [2, 3]. Here, we investigate the occurrence of dilatancy and shear jamming in frictionless packings. We show that the existence of isotropic jamming densities ϕj above the minimal density, the J-point density ϕJ [4, 5], leads both to the emergence of shear-induced jamming and dilatancy. Packings at ϕJ form a significan…
The concept of jamming has attracted great research interest due to its broad relevance in soft matter such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to the sphere packing problem and optimization problems. Here we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with a help of an …
While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a f…
