Discrete Particle Simulation Research Articles

Mechanics and Morphology of Proliferating Cell Collectives with Self-Inhibiting Growth.

We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring patterns in cell size whose spatiotemporal structure is closely tied to the individual cell's stress response. Motivated by these observations, we derive a multiscale continuum theory whose parameters map directly to the discrete model. Analytical solutions of this theory show the concentric patterns arise from anisotropically accumulated resistance to growth over many cell cycles. This Letter shows how purely mechanical processes can affect the internal patterning and morphology of cell collectives, and provides a concise theoretical framework for connecting the micro- to macroscopic dynamics of proliferating matter.

A continuum model of discrete granular avalanches

A simple continuum model is proposed for discrete granular avalanches, as observed in slowly rotating drums. Subject to granular transfer across the basal interface, the model evolves the transient surface inclination and mid-slope velocity profile of the avalanches, from failure to arrest. This is done using new boundary conditions that allow entrainment or detrainment contingent on the basal shear rate. For entrainment to occur, the basal shear stress must overcome the erosion resistance of the jammed deposit, while for detrainment to take place the basal shear rate must vanish. The resulting avalanche dynamics is controlled by a single dimensionless number, the ratio of excess slope at failure to excess resistance to erosion, that can be determined from inclination history data. This number provides a measure of slope brittleness, from which the peak flow rate and arrest inclination can be predicted. Analytical techniques are used to derive model solutions, and clarify the resulting behaviour. Finally, the model is tested by comparing solutions with laboratory experiments and discrete particle simulations.

The role of flexural particles in the shear flow of pine residue biomass: An experiment-informed DEM simulation study

An experiment-informed discrete particle simulation study was performed to investigate the role of flexural particles in the shear flow of milled pine residues. Physical pine anatomical fraction samples were tested in an FT4 powder rheometer. A chip model for bark/stem chips and a fiber model for needles were proposed for DEM. The FT4 simulations show mixed fibers/chips require higher force and torque to drive shear flow than pure chips or fibers. The mass fraction and flexibility of fibers reveal nonlinear inter-dependency on impacting the shear flow of mixed fibers/chips. Polydisperse fibers well match the needle-rich samples on the flow attributes, while polydisperse mixed fibers/chips agree reasonably with the bark/stem-rich samples. The DEM study indicates that the flowability of pine residue biomass is determined collectively by various material attributes of the anatomical fractions, which must be considered when developing preprocessing methods for conversion-ready biomass with adequate material handling performance.

Order-disorder transition during shear thickening in bidisperse dense suspensions

Shear thickening of multimodal suspensions has proven difficult to understand because the rheology depends largely on the microscopic details of stress-induced frictional contacts at different particle size distributions (PSDs). Our discrete particle simulations below a critical volume fraction ϕc over a broad range of shear rates and PSDs elucidate the basic mechanism of order–disorder transition. Around the theoretical optimal PSD (relative content of small particles ζ1= 0.26), particles order into a layered structure in the Newtonian regime. At the onset of shear thickening, this layered structure transforms to a disordered one, accompanied by an abrupt viscosity jump. Minor increase in large-large particle contacts after the order–disorder transition causes apparent increase in radial force along the compressional axis. Bidisperse suspensions with less regular but stable layered structure at ζ1= 0.50 show good fluidity in the shear thickening regime. This work shows that in inertial flows where particle collisions dominate, order–disorder transition could play an essential role in shear thickening for bidisperse suspensions.

Numerical study of gas–solid transport characteristics within vortex region induced by porous media using lattice-Boltzmann based discrete particle simulation

Porous media, as delivery carriers, holds great potential application in various fields particular in drug delivery. A comprehensive understanding of gas–solid transport characteristics within porous media is significant and regulating retention and release of drug particles. A combined approach of lattice Boltzmann method and time-driven hard-sphere model (LBM-TDHS) was used to investigate particle transport process in porous media. The vortex induced by porous structures was observed. Particle trajectories with different connectivity of the vortex region and inlet flow angles was conducted. This study revealed that fluid velocity between connected regions significantly affects the gas streamlines’ shape and particle trajectories. Different inlet flow angles lead to five modes of particle trajectories in vortex regions. Finally, some modifications were performed in general irregular porous structure to control particle trajectories. LBM-TDHS successfully investigated particle dynamics in vortex regions within porous media, demonstrating potential applicationin optimizing the structure of drug delivery carriers.

Structured bubbling in vibrated gas-fluidized beds of binary granular particles: experiments and simulations.

Mixing and segregation of granular particles on the basis of size and density from vertical vibration or upward gas flow is critical to a wide range of industrial, agricultural and natural processes. Recently, combined vibration and gas flow under certain conditions has been shown to create periodically repeating structured bubbling patterns within a fluidized bed of spherical, monodisperse particles. Here, we demonstrate with experiments and simulations that structured bubbling can form in binary mixtures of particles with different size and density, but with similar minimum fluidization velocities. Structured bubbling leads to particles mixing regardless of initial particle configuration, while exciting particles with only gas flow produces smaller unstructured bubbles which act to segregate particles. Discrete particle simulations match the experimental results qualitatively and, in some regards quantitatively, while continuum particle simulations do not predict mixing in the case of structured bubbling, highlighting areas for future model improvement.

Rigid clumps in the MercuryDPM particle dynamics code

Discrete particle simulations have become the standard in science and industrial applications exploring the properties of particulate systems. Most of such simulations rely on the concept of interacting spherical particles to describe the properties of particulates, although, the correct representation of the nonspherical particle shape is crucial for a number of applications. In this work we describe the implementation of clumps, i.e. assemblies of rigidly connected spherical particles, which can approximate given nonspherical shapes, within the MercuryDPM particle dynamics code. MercuryDPM contact detection algorithm is particularly efficient for polydisperse particle systems, which is essential for multilevel clumps approximating complex surfaces. We employ the existing open-source CLUMP library to generate clump particles. We detail the pre-processing tools providing necessary initial data, as well as the necessary adjustments of the algorithms of contact detection, collision/migration and numerical time integration. The capabilities of our implementation are illustrated for a variety of examples.

An immersed moving boundary for fast discrete particle simulation with complex geometry

An immersed moving boundary (IMB) scheme in LBM-DEM is proposed for discrete particle simulation with arbitrarily complex geometry. Momentum exchange between fluid and unresolved particles can be exerted by a modified weighting function with drag force and a new solid operator in IMB, which can describe both particle–fluid interaction and complex geometry, and requires only local information in perspective of solution. Combined with stereolithography (STL) format for describing complex geometry, a GPU-based LBM-DEM-IMB is implemented, and its ability and accuracy for complex geometry from STL model is verified by simulating flow past a stationary sphere. Compared with CFD-DEM in discrete particle simulations of both fluidized bed with immersed tube and aerosol transporting in human nasal, proposed method has much higher efficiency and maintains comparable accuracy in dense and dilute particle–fluid systems with complex geometry, which demonstrates it to be a promising computational strategy for particle–fluid two-phase flows.

Modeling Charge Transport in Flowable Suspension Electrolytes

Flowable suspension electrolytes (FSEs) consist of electrically conductive, redox-active, and/or energy-storing particles suspended in aqueous or non-aqueous electrolyte solutions (supporting salt + solvent). These particles, which can range in size from nanometers to micrometers, are subjected to Brownian forces, hydrodynamic forces, hydrophobic interactions, and van der Walls interactions among others. FSEs may enable electrochemical processes where solid reactants can be integrate with flow cells potentially unlocking new approaches to materials processing (e.g., synthesis, extraction/recovery). For example, FSEs has been demonstrated in redox flow batteries, facilitating higher energy densities without sacrificing independent power and energy scaling However, understanding and controlling charge transport through the deformable particle microstructures, especially under shear, is key to enable desirable current distributions and thus effective electrode utilization.In this presentation, we investigate the impact of interparticle interactions, particle volume fractions, and applied shear rate on charge transport through FSEs. At sufficiently large volume fractions above the percolation threshold and stationary conditions, particle interactions in an FSE can drive the formation of networks that span the cell dimensions and provide electronic transport similar to stationary freestanding porous electrodes. However, under flowing conditions, shear forces can break these networks, hampering charge transport. Conversely, increasing attractive particle interactions or particle concentration can strengthen the particle networks and fortifying charge transport, albeit at the expense of fluid viscosity. To better understand these processes, we model the charge transport through these dynamic particle networks, using a combination of local charge transport models and discrete particle simulations, considering the Peclet number (ratio of shearing to Brownian forces) and Mason number (ratio of shearing to attractive forces). Our results contribute to the development of continuum models for charge transport in FSEs, which, in turn, can facilitate efficient and accurate system-level analysis. Acknowledgments This work was funded by the Skoltech – MIT Next Generation Program.

Linking dynamics between anchors and granular materials

The research quantitatively explores the linking properties between the circular plate anchor and the granular assembly during the failure process under the subject of a specified pullout force given to the anchor using three-dimensional discrete particle simulations. This circular anchor is created as a hard cluster of spherical grains and is initially buried at a depth in the granular assembly. The numerical method is constructed based on the frictional interaction force law. The linking dynamic is characterized by the variation of the drag force acting on such anchor due to interaction with grains at the bottom of the frustum which is formed during the uplifting movement of the anchor. The results show that the drag force acting on the anchor first reaches a nearly constant value corresponding to the loading phenomenon at small anchor movement, reflecting the plastic deformation of granular bed as a result of particle rearrangement, and then fluctuates in a wide range, this range increases with increasing the anchor movement as a result of the unloading/reloading events. These loading/unloading/reloading events provide evidence for the linking properties between the anchor movement and granular assembly, which are highlighted by the density and intensity of force network within the frustum.

A computational study of the influence of evaporation and molecular transport on temporally-evolving droplet-laden plane jets

Numerical simulations of temporally-evolving droplet-laden plane jets are performed in conditions relevant to rocket main engines fed with liquid oxygen (LOx) and gaseous methane (CH4). The computations are performed using a direct numerical simulation (DNS) solver with the liquid phase represented within the discrete particle simulation (DPS) framework. Considering the multiplicity of the physical phenomena that are involved in such conditions – e.g., atomization, dispersion, evaporation – a progressive and phenomenological methodology is retained to proceed with a complexity-increasing set of computations. Thus, the development of a purely gaseous jet is first studied with the corresponding set of data providing a reference or baseline condition. Then, other conditions are considered to analyze the influence of (i) liquid droplet evaporation and (ii) molecular mixing processes as described by two distinct multicomponent transport models. The analysis of the obtained results shows that both evaporation and molecular transport representation play a crucial role in the plane jet development and may drastically alter its characteristics before ignition and subsequent combustion stabilization may take place. Finally, the obtained results also unambiguously put into evidence the influence of the Lewis number onto the vaporization rate.

GPU-based unresolved LBM-DEM for fast simulation of gas–solid flows

A new discrete particle simulation algorithm, namely unresolved LBM-DEM method, is proposed. In this method, fluid phase and particle phase are calculated by lattice Boltzmann method (LBM) and discrete element method (DEM) respectively, and immersed moving boundary (IMB) is used for treating gas–solid coupling. The additional collision term in IMB is regarded as force source term, and grid equivalent drag force is introduced to modify the weighting function. Due to the intrinsic mesoscopic properties of LBM, unresolved LBM-DEM method is suitable for simulating the hydrodynamics of Geldart A particles. In addition, GPU parallel computation of unresolved LBM-DEM is implemented to improve computational efficiency. To validate GPU-based unresolved LBM-DEM, it is used to simulate three classical gas–solid fluidizations. It was found that the results predicted by GPU-based LBM-DEM are all in good agreement with experimental data. Meanwhile, GPU-based LBM-DEM method brings one to two orders of magnitude speed up ratio compared with CPU or CPU-GPU heterogeneous CFD-DEM algorithm. The proposed unresolved LBM-DEM method has significant advantages over the traditional CFD-DEM in resolution scale and computational efficiency, suggesting it to be a promising computational strategy for fluidization and multiphase flows.

Seepage failure prediction of breakwater using an unresolved ISPH-DEM coupling method enriched with Terzaghi’s critical hydraulic gradient

This study develops a new numerical simulation model for rubble mound failure prediction caused by piping destruction under seepage flows. The piping has been pointed out as a significant cause of breakwater failure during tsunamis. Once boiling and heaving occur on the mound surface, the piping suddenly propagates in the opposite direction of seepage flow. For the seepage failure prediction, a coupled fluid-soil-structure simulator is developed by combining the ISPH for fluid and the DEM for rubble mounds and caisson blocks. The ISPH, a Lagrangian particle method for incompressible fluids, can simulate seepage and violent flows such as tsunamis. The DEM has been applied for discrete particle and rigid body simulations that include discontinuous deformation, as in the rubble mounds failure and large displacement of the caisson block. ISPH-DEM coupling simulations have already been proposed as a technique for multi-phase flows. Still, the technique cannot reproduce the sudden onset of piping from a stable mound. Two simple assumptions are applied to reduce the numerical cost for the fluid-soil-structure simulators of a breakwater structure composed of a rubble mound and the caisson block. Firstly, each rubble is modeled as an idealized spherical DEM particle with the mean diameter of the rubble. The ISPH particle size is assumed to be the same size as the DEM particle. Under these assumptions, the unresolved coupling model between rubble mound particles and fluid, which obtains the interaction through empirical drag force, should be applied. At the same time, the interaction between the fluid and the caisson block is fully resolved with the spatial resolution with the ISPH and DEM particle size. Our new contribution in this paper is how to model the interaction as an unresolved coupling between seepage flow simulated by ISPH and rubble mound particle modeled with DEM. Our original seepage failure experiment is simulated using the proposed ISPH-DEM coupling simulator. We identified the conventional drag force models as the unresolved coupling model are insufficient to initiate the boiling and piping observed in the experiment. It may be due in one part to excessive averaging of flow velocities caused by unresolved coupling. Therefore, Terzaghi’s critical hydraulic gradient is introduced to initiate the boiling and heaving. Unstable DEM particles, judged by Terzaghi’s critical hydraulic gradient, gradually lose their mass to represent unresolved suspended fine rubble mound particles. Our models qualitatively reproduce the sand boiling and backward erosion in the opposite direction of the seepage flow, as shown in the experiment.

Arched footprints preserve the motions of fossil hominin feet.

The longitudinal arch of the human foot is viewed as a pivotal adaptation for bipedal walking and running. Fossil footprints from Laetoli, Tanzania, and Ileret, Kenya, are believed to provide direct evidence of longitudinally arched feet in hominins from the Pliocene and Pleistocene, respectively. We studied the dynamics of track formation using biplanar X-ray, three-dimensional animation and discrete element particle simulation. Here, we demonstrate that longitudinally arched footprints are false indicators of foot anatomy; instead they are generated through a specific pattern of foot kinematics that is characteristic of human walking. Analyses of fossil hominin tracks from Laetoli show only partial evidence of this walking style, with a similar heel strike but a different pattern of propulsion. The earliest known evidence for fully modern human-like bipedal kinematics comes from the early Pleistocene Ileret tracks, which were presumably made by members of the genus Homo. This result signals important differences in the foot kinematics recorded at Laetoli and Ileret and underscores an emerging picture of locomotor diversity within the hominin clade.

Shear thickening in dense bidisperse suspensions

Discrete-particle simulations of bidisperse shear thickening suspensions are reported. The work considers two packing parameters, the large-to-small particle radius ratio ranging from δ=1.4 (nearly monodisperse) to δ=4, and the large particle fraction of the total solid loading with values ζ=0.15, 0.5, and 0.85. Particle-scale simulations are performed over a broad range of shear stresses using a simulation model for spherical particles accounting for short-range lubrication forces, frictional interaction, and repulsion between particles. The variation of rheological properties and the maximum packing fraction ϕJ with shear stress σ are reported. At a fixed volume fraction ϕ, bidispersity decreases the suspension relative viscosity ηr=ηs/η0, where ηs is the suspension viscosity and η0 is the suspending fluid viscosity, over the entire range of shear stresses studied. However, under low shear stress conditions, the suspension exhibits an unusual rheological behavior: the minimum viscosity does not occur as expected at ζ≈0.5, but instead decreases with further increase of ζ to 0.85. The second normal stress difference N2 acts similarly. This behavior is caused by particles ordering into a layered structure, as is also reflected by the zero slope with respect to time of the mean-square displacement in the velocity gradient direction. The relative viscosity ηr of bidisperse rate-dependent suspensions can be predicted by a power law linking it to ϕJ, ηr=(1−ϕ/ϕJ)−2 in both low and high shear stress regimes. The agreement between the power law and experimental data from literature demonstrates that the model captures well the effect of particle size distribution, showing that viscosity roughly collapses onto a single master curve when plotted against the reduced volume fraction ϕ/ϕJ.

An inertial number regulated stress model for gas-particle flows with particle friction and volume fraction gradient

In this study, a solid stress model that can be used in both dilute and dense regimes for simulation of gas-particle flows with comprehensive considerations of friction and the effect of local solid volume fraction gradient is proposed. In the dilute regime, solid stress is closed by a modified kinetic theory that accounts for the effect of particle friction and volume fraction gradient. In the dense regime, solid stress is closed by the inertial number model. The transition from dilute to dense regimes is realized by using a dimensionless parameter χ , which is a function of the inertial number I s . This new model is validated with experimental data and discrete particle simulation from spout-fluid bed and bubbling fluidized bed. When compared with the traditional kinetic-frictional stress model, this new model improves the transition from dilute to dense regimes and the particle velocity predictions in both beds. • A solid stress model is proposed in both dilute and dense regimes for gas-solid flow. • The model comprehensively considers the effect of friction and volume fraction gradient. • The expression of excluded volume is derived from the generalized van der Waals theory. • The model gives a better prediction of spout-fluid bed and bubbling fluidized bed.

Assessment of kinetic theory for gas–solid flows using discrete particle method

Kinetic theory is a common choice for closing the solid phase stress in the continuum theory for dilute and moderate dense gas–solid flows. In this article, methods are proposed for postprocessing the data obtained from discrete particle simulations, and the results are then used to critically assess the fundamental assumptions of kinetic theory. It is shown that (i) the fundamental assumptions and predictions of kinetic theory are, respectively, valid and accurate in homogeneous granular flows, as expected. Those results prove that the methods for data postprocessing are effective; (ii) in the case of nonequilibrium and heterogeneous gas–solid flows, nearly all fundamental assumptions get challenged, and the predictions of kinetic theory, in terms of collision frequency and particle pressure, deviate significantly from the statistical results of discrete particle simulation. Therefore, the standard kinetic theory is insufficient to provide the constitutive laws for continuum modeling of heterogeneous gas–solid flows.

Scaling Analysis of Shear Thickening Suspensions

Dense suspensions of particles in viscous liquid often demonstrate the striking phenomenon of abrupt shear thickening, where their viscosity increases strongly with increase of the imposed stress or shear rate. In this work, discrete-particle simulations accounting for short-range hydrodynamic, repulsive, and contact forces are performed to simulate flow of shear thickening bidisperse suspensions, with the packing parameters of large-to-small particle radius ratio δ = 3 and large particle fraction ζ = 0.15, 0.50, and 0.85. The simulations are carried out for volume fractions 0.54 ≤ ϕ ≤ 0.60 and a wide range of shear stresses. The repulsive forces, of magnitude FR, model the effects of surface charge and electric double-layer overlap, and result in shear thinning at small stress, with shear thickening beginning at stresses σ ∼ FRa−2. A crossover scaling analysis used to describe systems with more than one thermodynamic critical point has recently been shown to successfully describe the experimentally-observed shear thickening behavior in suspensions. The scaling theory is tested here on simulated shear thickening data of the bidisperse mixtures, and also on nearly monodisperse suspensions with δ = 1.4 and ζ = 0.50. Presenting the viscosity in terms of a universal crossover scaling function between the frictionless and frictional maximum packing fractions collapses the viscosity for most of the suspensions studied. Two scaling regimes having different exponents are observed. The scaling analysis shows that the second normal stress difference N2 and the particle pressure Π also collapse on their respective curves, with the latter featuring a different exponent from the viscosity and normal stress difference. The influence of the fraction of frictional contacts, one of the parameters of the scaling analysis, and its dependence on the packing parameters are also presented.

Computing equilibrium measures with power law kernels

We introduce a method to numerically compute equilibrium measures for problems with attractive-repulsive power law kernels of the form K ( x − y ) = | x − y | α α − | x − y | β β K(x-y) = \frac {|x-y|^\alpha }{\alpha }-\frac {|x-y|^\beta }{\beta } using recursively generated banded and approximately banded operators acting on expansions in ultraspherical polynomial bases. The proposed method reduces what is naïvely a difficult to approach optimization problem over a measure space to a straightforward optimization problem over one or two variables fixing the support of the equilibrium measure. The structure and rapid convergence properties of the obtained operators result in high computational efficiency in the individual optimization steps. We discuss stability and convergence of the method under a Tikhonov regularization and use an implementation to showcase comparisons with analytically known solutions as well as discrete particle simulations. Finally, we numerically explore open questions with respect to existence and uniqueness of equilibrium measures as well as gap forming behaviour in parameter ranges of interest for power law kernels, where the support of the equilibrium measure splits into two intervals.

Discrete particle simulation for mixing of granular materials in ribbon mixers: A scale-up study

This work presents a numerical study of particle mixing and scale-up of ribbon mixers with four sizes (mixer A - 5.62 L, mixer B - 49.02 L, mixer C - 142.91 L, and mixer D - 482.32 L). The results show that the mixing performance becomes worse with the mixer size increasing. A correlation is proposed to predict the mixing rate as a function of the scale-up ratio and Froude number. The top-bottom initial loading condition of granular materials mix much faster than the side-side and front-back loading conditions. With the mixer size becoming larger, the total mixing time increases significantly. The power consumption per unit mass for the four mixers is in this order: mixer A > mixer D > mixer C > mixer B. The results suggest that scale-up is necessary to save mixing time and power consumption and reduce additional operating costs such as labour and down-time.