arXiv subjects

Lu Jing

Publications and source records attributed to Lu Jing.

13 recordsLinked to original sources

arXiv2025

White-box machine learning for uncovering physically interpretable dimensionless governing equations for granular materials

Granular material has significant implications for industrial and geophysical processes. A long-lasting challenge, however, is seeking a unified rheology for its solid- and liquid-like behaviors under quasi-static, inertial, and even unsteady shear conditions. Here, we present a data-driven framework to discover the hidden governing equation of sheared granular materials. The framework, PINNSR-DA, addresses noisy discrete particle data via physics-informed neural networks with sparse regression (PINNSR) and ensures dimensional consistency via machine learning-based dimensional analysis (DA). Applying PINNSR-DA to our discrete element method simulations of oscillatory shear flow, a general differential equation is found to govern the effective friction across steady and transient states. The equation consists of three interpretable terms, accounting respectively for linear response, nonlinear response and energy dissipation of the granular system, and the coefficients depends primarily on a dimensionless relaxation time, which is shorter for stiffer particles and thicker flow layers. This work pioneers a pathway for discovering physically interpretable governing laws in granular systems and can be readily extended to more complex scenarios involving jamming, segregation, and fluid-particle interactions.

cond-mat.soft↗

arXiv2025

Basal layer of granular flow down smooth and rough inclines: kinematics, slip laws and rheology

Granular flow down an inclined plane is ubiquitous in geophysical and industrial applications. On rough inclines, the flow exhibits Bagnold's velocity profile and follows the so-called $\mu(I)$ local rheology. On insufficiently rough or smooth inclines, however, velocity slip occurs at the bottom and a basal layer with strong agitation emerges below the bulk, which is not predicted by the local rheology. Here, we use discrete element method simulations to study detailed dynamics of the basal layer in granular flows down both smooth and rough inclines. We control the roughness via a dimensionless parameter, $R_a$, varied systematically from 0 (flat, frictional plane) to near 1 (very rough plane). Three flow regimes are identified: a slip regime ($R_a \lesssim 0.45$) where a dilated basal layer appears, a no-slip regime ($R_a \gtrsim 0.6$) and an intermediate transition regime. In the slip regime, the kinematics profiles (velocity, shear rate and granular temperature) of the basal layer strongly deviate from Bagnold's profiles. General basal slip laws are developed which express the slip velocity as a function of the local shear rate (or granular temperature), base roughness and slope angle. Moreover, the basal layer thickness is insensitive to flow conditions but depends somewhat on the inter-particle coefficient of restitution. Finally, we show that the rheological properties of the basal layer do not follow the $\mu(I)$ rheology, but are captured by Bagnold's stress scaling and an extended kinetic theory for granular flows. Our findings can help develop more predictive granular flow models in the future.

physics.flu-dyn↗

arXiv2025

Enhancing semi-resolved CFD-DEM for dilute to dense particle-fluid systems: A point cloud based, two-step mapping strategy via coarse graining

Computational fluid dynamics and discrete element method (CFD-DEM) coupling is an efficient and powerful tool to simulate particle-fluid systems. However, current volume-averaged CFD-DEM relying on direct grid-based mapping between the fluid and particle phases can exhibit a strong dependence on the fluid grid resolution, becoming unstable as particles move across fluid grids, and can fail to capture pore fluid pressure effects in very dense granular systems. Here we propose a two-step mapping CFD-DEM which uses a point-based coarse graining technique for intermediate smoothing to overcome these limitations. The discrete particles are first converted into smooth, coarse-grained continuum fields via a multi-layer Fibonacci point cloud, independent of the fluid grids. Then, accurate coupling is achieved between the coarse-grained, point cloud fields and the fluid grid-based variables. The algorithm is validated in various configurations, including weight allocation of a static particle on one-dimensional grids and a falling particle on two-dimensional grids, sedimentation of a sphere in a viscous fluid, size-bidisperse fluidized beds, Ergun's pressure drop test, and immersed granular column collapse. The proposed CFD-DEM represents a novel strategy to accurately simulate fluid-particle interactions for a wide range of grid-to-particle size ratios and solid concentrations, which is of potential use in many industrial and geophysical applications.

physics.flu-dyn↗

arXiv2025

Effects of particle elongation on dense granular flows down a rough inclined plane

Granular materials in nature are nearly always non-spherical, but particle shape effects in granular flow remain largely elusive. This study uses discrete element method simulations to investigate how elongated particle shapes affect the mobility of dense granular flows down a rough incline. For a range of systematically varied particle length-to-diameter aspect ratios (AR), we run simulations with various flow thicknesses $h$ and slope angles $\theta$ to extract the well-known $h_\textrm{stop}(\theta)$ curves (below which the flow ceases) and the $Fr$-$h/h_\textrm{stop}$ relations following Pouliquen's approach, where $Fr=u/\sqrt{gh}$ is the Froude number, $u$ is the mean flow velocity, and $g$ is the gravitational acceleration. The slope $\beta$ of the $Fr$-$h/h_\textrm{stop}$ relations shows an intriguing S-shaped dependence on AR, with two plateaus at small and large AR, respectively, transitioning with a sharp increase. We understand this S-shaped dependence by examining statistics of particle orientation, alignment, and hindered rotation. We find that the rotation ability of weakly elongated particles ($\textrm{AR}\lesssim1.3$) remains similar to spheres, leading to the first plateau in the $\beta$-AR relation, whereas the effects of particle orientation saturates beyond $\textrm{AR}\approx2.0$, explaining the second plateau. An empirical sigmoidal function is proposed to capture this non-linear dependence. The findings are expected to enhance our understanding of how particle shape affects the flow of granular materials from both the flow- and particle-scale perspectives.

cond-mat.soft↗

arXiv2025

Unified Flow Rule of Undeveloped and Fully Developed Dense Granular Flows Down Rough Inclines

We report on chute measurements of the free-surface velocity $v$ in dense flows of spheres and diverse sands and spheres-sand mixtures down rough inclines. These and previous measurements are inconsistent with standard flow rules, in which the Froude number $v/\sqrt{gh}$ scales linearly with $h/h_s$ or $(\tan\theta/\mu_r)^2h/h_s$, where $\mu_r$ is the dynamic friction coefficient, $h$ the flow thickness, and $h_s(\theta)$ its smallest value that permits a steady, uniform dense flow state at a given inclination angle $\theta$. This is because the characteristic length $L$ a flow needs to fully develop can exceed the chute or travel length $l$ and because neither rule is universal for fully developed flows across granular materials. We use a dimensional analysis motivated by a recent unification of sediment transport to derive a flow rule that solves both problems in accordance with our and previous measurements: $v=v_\infty[1-\exp(-l/L)]^{1/2}$, with $v_\infty\propto\mu_r^{3/2}\left[(\tan\theta-\mu_r)h\right]^{4/3}$ and $L\propto\mu_r^3\left[(\tan\theta-\mu_r)h\right]^{5/3}h$.

cond-mat.soft↗

arXiv2024

Granular segregation across flow geometries: a closure model for the particle segregation velocity

Predicting particle segregation has remained challenging due to the lack of a general model for the segregation velocity that is applicable across a range of granular flow geometries. Here, a segregation velocity model for dense granular flows is developed by exploiting momentum balance and recent advances in particle-scale modelling of the segregation driving and drag forces over a wide range of particle concentrations, size and density ratios, and flow conditions. This model is shown to correctly predict particle segregation velocity in a diverse set of idealized and natural granular flow geometries simulated using the discrete element method. When incorporated in the well-established advection-diffusion-segregation formulation, the model has the potential to accurately capture segregation phenomena in many relevant industrial application and geophysical settings.

cond-mat.soft↗

arXiv2023

General model for segregation forces in flowing granular mixtures

Particle segregation in dense flowing size-disperse granular mixtures is driven by gravity and shear, but predicting the associated segregation force due to both effects has remained an unresolved challenge. Here, a model of the combined gravity- and kinematics-induced segregation force on a single intruder particle is integrated with a model of the concentration dependence of the gravity-induced segregation force. The result is a general model of the net particle segregation force in flowing size-bidisperse granular mixtures. Using discrete element method simulations for comparison, the model correctly predicts the segregation force for a variety of mixture concentrations and flow conditions in both idealized and natural shear flows.

cond-mat.soft↗

arXiv2021

Image-based study of granular column collapse over controlled-roughness surfaces

Basal effects have important implications for the high mobility and long runout of granular flows such as rock avalanches and landslides. However, fundamental understanding of the basal effect in granular flows remains challenging due to the complex forms of base roughness and the multiscale nature of flow-bed interactions. Here we experimentally investigate the basal effect in granular column collapse over controlled-roughness bases. Image processing methods are developed to obtain robust measurements of base roughness, runout distance and deposit morphology. A geometric roughness parameter Ra is applied to consider both the size and spatial distribution of base particles, which enables systematic analysis of the basal effect. The results indicate that the runout distance can be characterized as a function of Ra, regardless of the variations in the base particle size and spacing, and the roughness has a major influence on the frontal region of the granular flow, as well as the overall profile of the granular deposit. When Ra is increased beyond a threshold value (Ra > 0.62), flow characteristics show minor changes, which coinsides with a previous phase diagram for the transition between slip and non-slip boundary conditions from steady state granular flow simulations.

physics.geo-ph↗

arXiv2021

Segregation forces in dense granular flows: Closing the gap from single intruders to mixtures

Using simulations and a virtual-spring-based approach, we measure the segregation force, Fseg, over a range of size-bidisperse mixture concentrations, particle size ratios, and shear rates to develop a model for Fseg that extends its applicability from the well-studied non-interacting intruders regime to finite-concentration mixtures where cooperative phenomena occur. The model predicts the concentration below which the single intruder assumption applies and provides an accurate description of the pressure partitioning between species.

cond-mat.soft↗

arXiv2021

A unified description of gravity- and kinematics-induced segregation forces in dense granular flows

Particle segregation is common in natural and industrial processes involving flowing granular materials. Complex, and seemingly contradictory, segregation phenomena have been observed for different boundary conditions and forcing. Using discrete element method simulations, we show that segregation of a single particle intruder can be described in a unified manner across different flow configurations. A scaling relation for the net segregation force is obtained by measuring forces on an intruder particle in controlled-velocity flows where gravity and flow kinematics are varied independently. The scaling law consists of two additive terms: a buoyancy-like gravity-induced pressure gradient term and a shear rate gradient term, both of which depend on the particle size ratio. The shear rate gradient term reflects a kinematics-driven mechanism whereby larger (smaller) intruders are pushed toward higher (lower) shear rate regions. The scaling is validated, without refitting, in wall-driven flows, inclined wall-driven flows, vertical silo flows, and free surface flows down inclines. Comparing the segregation force to the intruder weight results in predictions of the segregation direction that match experimental and computational results for various flow configurations.

cond-mat.soft↗

arXiv2019

Modified Archimedes' principle predicts rising and sinking of intruders in sheared granular flows

We computationally determine the force on single spherical intruder particles in sheared granular flows as a function of particle size, particle density, shear rate, overburden pressure, and gravitational acceleration. The force scales similarly to, but deviates from, the buoyancy force predicted by Archimedes' principle. The deviation depends only on the intruder to bed particle size ratio, but not the density ratio or flow conditions. We propose a simple force model that successfully predicts whether intruders rise or sink, knowing only the size and density ratios, for a variety of flow configurations in physical experiments.

cond-mat.soft↗

arXiv2016

Characterization of base roughness for granular chute flows

Base roughness plays an important role to the dynamics of granular flows but is yet poorly understood due to the difficulty of its quantification. For a bumpy base made by spheres, at least two factors should be considered to characterize its geometric roughness, namely the size ratio of base- to flow-particles and the packing of base particles. In this paper, we propose a definition of base roughness, Ra, which is a function of both the size ratio and the packing arrangement of base particles. The function is generalized for random and regular packing of multi-layered spheres, where the range of possible values of Ra is studied, along with the optimal values to create maximum base roughness. The new definition is applied to granular flows down chute in both two- and three-dimensional configurations. It is proven to be a good indicator of slip condi- tion, and a transition occurs from slip to non-slip condition as Ra increases. Critical values of Ra are identified for the construction of a non-slip base. The effects of contact parameters on base velocity are studied, and it is shown that while the coefficient of friction is less influential, normal damping has more profound effect on base velocity at lower values of Ra. The application of present definition to other base geometries is also discussed.

physics.flu-dyn↗

arXiv2016

Squeeze expulsion in grain size segregation

Grain segregation occurs under various conditions, such as vibration, shear and mixing. In the gravity-driven shear flow, size segregation is triggered by the percolation of small particles through the opened voids (kinetic sieving), and large particles are accumulated in the upper layer. One hypothesis for the upward migration of large particles is the squeeze expulsion mechanism, which remains yet ambiguous due to limited evidences from either physical or numerical experiments. Here we show statistically how the percolation of small particles facilitates the upward movement of large particles. We found that in large particles, the mechanical anisotropy (strong force network) coincides with the geometric anisotropy (contact network), which indicates squeeze, and the connectivity of large particles is much higher when they are squeezed through small particles. The presence of small particles filling the voids hinders the downward movements and provides dynamic steps for the climbing large particles. Furthermore, increasing the coefficient of friction promotes rotation and empowers more large particles to reach the top layer, implying that the climbing particles tend to rotate relative to their neighbors. Our findings of the microstructure and movement pattern of individual particles add new evidences to the mechanism of squeeze expulsion and provide new perspective for the study of segregation.

nlin.AO↗