We investigate the drag forces acting on large objects moving through a granular packing immersed in water. In this aim, we conducted uplift experiments involving pulling out horizontal plates at a prescribed velocity vertically. During these tests, we observed that the drag force reaches to peak at a low displacement and then decays. Results show that the peak drag force strongly increases with the velocity and depends on the plate size and grain diameter. We identify empirical scaling laws for these properties and introduce a Darcy-flow mechanism that can explain them. Furthermore, we conducted tests involving suddenly stopping the motion of the plate, which evidenced a progressive relaxation of the drag force in time. We discuss how a visco-elasto-plastic mechanical analogue can reproduce these dynamics. These results and analyses highlight fundamental differences in drag force between dry and immersed granular materials.
We report the formation of a crater at the free surface of an immersed granular bed,locally crossed by an ascending gas flow. In two dimensions, the crater consists of two piles which develop around the location of the gas emission. We observe that the typical size of the crater increases logarithmically with time, independently of the gas emission dynamics. We describe the related granular flows and give an account of the influence of the experimental parameters, especially of the grain size and of the gas flow.
Like in liquids, objects moving in granular materials experience a drag force. We investigate here whether and how the object acceleration affect this drag force. The study is based on simulations of a canonical drag test, which involves vertically uplifting a plate through a granular packing with a prescribed acceleration pattern. Depending on the plate size, plate depth and acceleration pattern, results evidence a rate-independent regime and an inertial regime where the object acceleration strongly enhances the drag force. We introduce an elasto-inertial drag force model that captures the me…
We study the mobility of objects embedded in an immersed granular packing and subjected to cyclic loadings. In this aim, we conducted experiments using glass beads immersed in water and a horizontal plate subjected to a cyclic uplift force. Tests performed at different cyclic force frequencies and amplitudes evidence the development of three mobility regimes whereby the plate stays virtually immobile, moves up steadily or slowly creeps upwards. Results show that steady plate uplift can occur at lower force magnitudes when the frequency is increased. We propose an interpretation of this frequen…
The friction of a sliding plate on a thin immersed granular layer obeys Amonton-Coulomb law. We bring to the fore a large set of experimental results which indicate that, over a few decades of values, the effective dynamical friction-coefficient depends neither on the viscosity of the interstitial fluid nor on the size of beads in the sheared layer, which bears out the analogy with the solid-solid friction in a wide range of experimental parameters. We accurately determine the granular-layer dilatancy, which dependance on the grain size and slider velocity can be qualitatively accounted by con…
Impact dynamics is measured for spherical and cylindrical projectiles of many different densities dropped onto a variety non-cohesive granular media. The results are analyzed in terms of the material-dependent scaling of the inertial and frictional drag contributions to the total stopping force. The inertial drag force scales similar to that in fluids, except that it depends on the internal friction coefficient. The frictional drag force scales as the square-root of the density of granular medium and projectile, and hence cannot be explained by the combination of granular hydrostatic pressure …
We probe the dependence of the low velocity drag force in granular materials on the effective gravitational acceleration (geff) through studies of spherical granular materials saturated within fluids of varying density. We vary geff by a factor of 20, and we find that the granular drag is proportional to geff, i.e., that the granular drag follows the expected relation Fprobe = η ρgrain geff dprobe hprobe^2 for the drag force, Fprobe on a vertical cylinder with depth of insertion, hprobe, diameter dprobe, moving through grains of density ρgrain, and where η is a dimensionless constant. This dim…
The drag force law acting on a moving circular disk in a two-dimensional granular medium is analyzed based on the discrete element method (DEM). It is remarkable that the drag force on the moving disk in moderate dense and pure two-dimensional granular medium can be well reproduced by a perfect fluid with separation from the surface of the tracer. A yield force, being independent of the moving speed of the disk, appears if a dry friction between the granular disks and the bottom plate exists. The perfect fluidity is violated in this case. The yield force and the drag force diverge at the jammi…
Predicting the force exerted on an object as it penetrates a granular medium is of interest in engineering, locomotive, and geotechnical applications. Current models of granular drag, however, vary widely in applicability and parameterization, and the physical origin of the granular resistive force itself is a subject of debate. Here we perform constant speed penetration experiments, combined with calibrated, large-scale molecular dynamics simulations, at velocities up to 2 m/s to test the effect of impact velocity on the depth dependent `hydrostatic' drag force. We discover that the evolution…
We investigate the conditions leading to large drag force fluctuations in granular materials. The study is based on a set of experimental drag tests, which involve pulling a plate vertically through a cohesionless granular material. In agreement with previous observations, drag force exhibits significant and sudden drops -up to 60%- when the plate is pulled out at low velocities. We further find that this instability vanishes at higher pullout velocities and near the surface. We empirically characterise the frequency and amplitude of these fluctuations and find that these properties are not co…
We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles. For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model. We take into account the effects of non-conservation of energy upon particle collision. We find an (approximate) analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition. We assess the accuracy of t…
This paper investigates the lift force exerted on an elliptical obstacle immersed in a granular flow through analytical calculations and computer simulations. The results are shown as a function of the obstacle size, orientation with respect to the flow direction (tilt angle), the restitution coefficient and ellipse eccentricity. The theoretical argument, based on the force exerted on the obstacle due to inelastic, frictionless collisions of a very dilute flow, captures the qualitative features of the lift, but fails to reproduce the data quantitatively. The reason behind this disagreement is …
Motivated by recent experiments on objects moved vertically through a bed a glass beads, a simple model to study granular drag is proposed. The model consists of dimers on a slanted two-dimensional lattice through which objects are dragged very slowly to obtain full relaxation between moves. Such an approach avoids complications due to static friction in more realistic off-lattice models, and provides for fast simulations at large system sizes. The upward motion of objects of various diameters embedded in the lattice is simulated and close resemblance with the experiments is found.
Laboratory experiments and numerical simulation reveal that a submerged intruder dragged horizontally at constant velocity within a granular medium experiences a lift force whose sign and magnitude depend on the intruder shape. Comparing the stress on a flat plate at varied inclination angle with the local surface stress on the intruders at regions with the same orientation demonstrates that intruder lift forces are well approximated as the sum of contributions from flat-plate elements. The plate stress is deduced from the force balance on the flowing media near the plate.
The drag of an elliptic intruder in a two-dimensional granular environment is numerically studied. The movement parallel to the major axis of the intruder is found to be unstable. The drag law is given by the sum of the yield force and the dynamic term, the latter of which is approximately reproduced by a simple collision model. The flow field around the intruder for sufficiently larger drag force is well fitted by the streamlines obtained from the perfect fluid. The stress fields around the intruder are also investigated when the movement of the intruder is balanced with interactions with the…
Frictional constitutive law for very slow vertical withdrawing of a thin rod from a granular bed is experimentally studied. Using a very precise creep meter, geometry-dependent granular frictional constitutive law is particularly examined. In some previous works, a dimensionless number $I=\dotγD_g/\sqrt{p/ρ_g}$ has been used to characterize granular frictional constitutive laws, where $\dotγ$, $D_g$, $p$, and $ρ_g$ are the shear strain rate, grain diameter, confining pressure, and bulk density of granular bed, respectively. It has been considered that granular frictional constitutive law expre…
We measure the torque acting on a rod rotated perpendicular to its axis in a granular bed, through which an upflow of gas is utilized to tune the hydrostatic loading between grains. At low rotation rates the torque is independent of speed, but scales quadratically with rod-length and linearly with depth; the proportionality approaches zero linearly as the upflow of gas is increased towards a critical value above which the grains are fluidized. At high rotation rates the torque exhibits quadratic rate- dependence and scales as the rod's length to the 4th power. The torque has no dependence on e…
This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated by an inertial drag term proportional to the intruder velocity squared. The primary focus here is on the microscopic force response of the granular material, and how the grain-scale effects give rise to this inertial drag term. We show that the inertial drag arises from intermittent collisions with force-chain-like structures. We construct a simple collisio…
We studied the drag and lift forces acting on an inclined plate while it is dragged on the surface of a granular media, both in experiment and numerical simulation. In particular, we investigated the influence of the horizontal velocity of the plate and its angle of attack. We show that a steady wedge of grains is moved in front of the plow and that the lift and drag forces are proportional to the weight of this wedge. These constants of proportionality vary with the angle of attack but not (or only weakly) on the velocity. We found a universal effective friction law which accounts for the dep…
Large objects, immersed in a homogeneous granular system, migrate when subjected to vibrations. Under certain conditions large heavy objects rise and similar light ones sink to the bottom. This is called reverse buoyancy. We report an experimental study of this singular behavior, for a large sphere immersed in a deep granular bed. A simple mechanism is proposed to describe the motion of a sphere, inside a vertically vibrated granular system. When reverse buoyancy is observed, the measured vertical velocity of the immersed object, as a function of its density, shows a simple behavior. With a on…
In this letter, we investigate the transient rheological behavior of immersed granular flows using both experiments of submerged granular column collapses and corresponding numerical simulations. The simulations are performed with the lattice-Boltzmann method (LBM) coupled with the discrete element method (DEM) and provide a significant amount of data of the stress and deformation conditions at different positions and times during the granular collapse. We derive a new dimensionless number $\mathcal{G}$ that can unify the rheology of transient granular flows in different regimes for all the si…
The drag of two cylindrical intruders in a two-dimensional granular environment is numerically studied by the discrete element method. We find the yield force, below which the intruders cannot move because of interactions with the surrounding particles. Above the yield force, on the other hand, the intruders can move at a constant speed. We investigate the relationship between the drag force and the steady speed of the intruders, where the speed becomes higher as the distance between the intruders decreases. We confirm that the origin of the yield is the Coulombic friction between the particle…
The transport coefficients of a dilute gas of inelastic hard spheres immersed in a molecular gas are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the latter is not affected by the presence of solid particles. In this situation, the molecular gas may be treated as a thermostat (or bath) of elastic hard spheres at a fixed temperature. This system (granular gas thermostated by a bath of elastic hard spheres) can be considered as a reliable model for describing the dynamic properties of particle-laden suspensi…
Making use of the system of pulling a spherical intruder in static three-dimensional granular media, we numerically study the scaling law for the drag force $F_{\rm drag}$ acting on the moving intruder under the influence of the gravity. Suppose if the intruder of diameter $D$ immersed in a granular medium consisting of grains of average diameter $d$ is located at a depth $h$ and moves with a speed $V$, we find that $F_{\rm drag}$ can be scaled as $(D+d)^{ϕ_μ} h^{α_μ}$ with two exponents $ϕ_μ$ and $α_μ$, which depend on the friction coefficient $μ$ and satisfy an approximate sum rule $ϕ_μ+α_μ\…
We report experiments on the overall phase diagram of granular flows on an incline with emphasis on high inclination angles where the mean layer velocity approaches the terminal velocity of a single particle free falling in air. The granular flow was characterized by measurements of the surface velocity, the average layer height, and the mean density of the layer as functions of the hopper opening, the plane inclination angle and the downstream distance x of the flow. At high inclination angles the flow does not reach an x-invariant steady state over the length of the inclined plane. For low v…
We examine the drag experienced by a pair of vertical rods moving in tandem through a granular bed immersed in a fluid as a function of their separation distance and speed. As in Newtonian fluids, the net drag experienced by the rods initially increases with distance from the value for a single rod before plateauing to twice the value. However, the drag acting on the two rods is remarkably different, with the leading rod experiencing roughly similar drag compared to a solitary rod, while the following rod experiences far less drag. The anomalous relationship of drag and the distance between th…
When a solid projectile impacts a granular target, it experiences a drag force and abruptly comes to rest as its momentum transfers to the grains. An empirical drag force law successfully describes the force experienced by the projectile, and the corresponding grain-scale mechanisms have been deciphered for normal impacts. However, there is little work exploring non-normal impacts. Accordingly, we extend studies to explore oblique impact, in which a significant horizontal component of the drag force is present. In our experiments, a projectile impacts a quasi-two-dimensional bed of bidisperse …
Impact of a solid object onto a small-body surface can be modeled by the solid impact onto a hierarchically structured granular target. Impact drag force model for the hierarchically structured granular target is developed based on the experiment. We perform a set of granular impact experiments in which mechanical strength and porosity of target grains are systematically varied. Tiny glass beads ($5$~$μ$m in diameter) are agglomerated to form porous grains of $2$--$4$~mm in diameter. Then, the grains are sintered to control their strength. A polyethylene sphere ($12.7$~mm in diameter) is dropp…
We use numerical simulation to investigate the effect an intruder's shape has on the drag and lift forces that it experiences while moving through a granular medium composed of polydisperse disks of mean diameter d. The intruder velocity,v, was varied from 0.1 \sqrt(dg) to 20 \sqrt(dg). For frictionless particles (μ= 0.0)there is a gradual increase in drag force with increasing v, whereas for frictional systems (μ= 0.1,0.5) a constant drag regime appears at low velocities. The drag force depends weakly on the shape of the object provided that the cross-section is same. The drag force depends l…
Bulldozing an immersed granular material in a confined channel
University of Oxford（牛津大学）；The Australian National University（澳大利亚国立大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Bristol（布里斯托大学）；University of Cambridge（剑桥大学）；Swansea University（斯旺西大学）
The drag acting on an intruder in a three-dimensional frictionless dry granular environment is numerically studied. It is found the followings: (i) There is no yield force for the motion of the intruder without the gravity. (ii) The drag is proportional to the cross section of the moving intruder. (iii) If the intruder is larger than surrounding grains, the drag is proportional to the moving speed $V$ of the intruder for dense systems, but it exhibits a crossover from quadratic to linear dependences of the moving speed when the volume fraction of the surrounding grains is much lower than the j…
The drag force exerted on an object intruding into granular media can depend on the object's velocity as well as the depth penetrated. We report on intrusion experiments at constant speed over four orders in magnitude together with systematic molecular dynamics simulations well beyond the quasi-static regime. We find that velocity dependence crosses over to depth dependence at a characteristic time after initial impact. This crossover time scale, which depends on penetration speed, depth, gravity and intruder geometry, challenges current models that assume additive contributions to the drag.
We study the drag force experienced by an object slowly moving at constant velocity through a 2D granular material consisting of bidisperse disks. The drag force is dominated by force chain structures in the bulk of the system, thus showing strong fluctuations. We consider the effect of three important control parameters for the system: the packing fraction, the drag velocity and the size of the tracer particle. We find that the mean drag force increases as a power-law (exponent of 1.5) in the reduced packing fraction, $(γ- γ_c)/γ_c$, as $γ$ passes through a critical packing fraction, $γ_c$. B…
We report experimental measurements on the rheology of a dry granular material under a weak level of vibration generated by sound injection. First, we measure the drag force exerted on a wire moving in the bulk. We show that when the driving vibration energy is increased, the effective rheology changes drastically: going from a non-linear dynamical friction behavior - weakly increasing with the velocity- up to a linear force-velocity regime. We present a simple heuristic model to account for the vanishing of the stress dynamical threshold at a finite vibration intensity and the onset of a line…
Transport properties of a suspension of solid particles in a viscous gas are studied. The dissipation in such systems arises from two sources: inelasticity in particle collisions and viscous dissipation due to the effect of the gas phase on the particles. Here, we consider a simplified case in which the mean relative velocity between the gas and solid phases is taken to be zero, such that "thermal drag" is the only remaining gas-solid interaction. Unlike the previous more general treatment of the drag force [Garzó \emph{et al.}, J. Fluid Mech. \textbf{712}, 129 (2012)], here we take into accou…
We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog--Fokker--Planck equation for the one-particle velocity distribution function. To get explicit results of the temper…
Recently, experiments showed that forces on intruders dragged horizontally through dense, hydrostatic granular packings mainly depend on the local surface orientation and can be seen as the sum of the forces exerted on small surface elements. In order to understand such forces more deeply, we perform 2D soft-sphere molecular dynamics simulation, on similar set up, of an intruder dragged through a 50-50 bi-disperse granular packing, with diameters 0.30 and 0.34 cm. We measure, for both circular and half-circle shapes, the forces parallel (drag) and perpendicular (lift) to the drag direction as …
We study velocity statistics of electrostatically driven granular gases. For two different experiments: (i) non-magnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(v) ~ exp(-|v|). This behavior is consistent with kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gas…
Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients f…
Velocity-squared drag forces are common in describing an object moving through a granular material. The resulting force law is a nonlinear differential equation, and closed-form solutions of the dynamics are typically obtained by making simplifying assumptions. Here, we consider a generalized version of such a force law which has been used in many studies of granular impact. We show that recasting the force law into an equation for the kinetic energy versus depth, K(z), yields a linear differential equation, and thus general closed-form solutions for the velocity versus depth. This approach al…
When pulling a particle in a driven granular fluid with constant force $F_{ex}$, the probe particle approaches a steady-state average velocity $v$. This velocity and the corresponding friction coefficient of the probe $ζ=F_{ex}/v$ are obtained within a schematic model of mode-coupling theory and compared to results from event-driven simulations. For small and moderate drag forces, the model describes the simulation results successfully for both the linear as well as the nonlinear region: The linear response regime (constant friction) for small drag forces is followed by shear thinning (decreas…
Stressed soft materials commonly present viscoelastic signatures in the form of power-law or exponential decay. Understanding the origins of such rheologic behaviors is crucial to find proper technological applications. Using an elastic network model of macromolecules immersed in a viscous fluid, we numerically reproduce those characteristic viscoelastic relaxations and show how the microscopic interactions determine the rheologic response. We find that exponential relaxations are indeed the most common behavior. However, power laws may arise when drag forces between the macromolecules and the…
Projectile impact into a light granular material composed of expanded polypropylene (EPP) particles is investigated systematically with various impact velocities. Experimentally, the trajectory of an intruder moving inside the granular material is monitored with a recently developed non-invasive microwave radar system. Numerically, discrete element simulations together with coarse-graining techniques are employed to address both dynamics of the intruder and response of the granular bed. Our experimental and numerical results of the intruder dynamics agree with each other quantitatively and are…
We consider a dilute system of small hard beads or hard fibers immersed in a very soft gel able to withstand large elastic deformations. Because of its low to very low shear modulus, this system is very sensitive to small forces. We calculate the local deformation induced by a constant volume force, the inclusion weight. We explain how this deformation could be put in evidence by using techniques similar to the PIV method (particle image velocimetry) used to show complex velocity fields in transparent fluids.
We study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_\perp$ and parallel $F_\parallel$ to its axis as a function of speed $U$ from the quasi-static to the rate-dependent regime. We find that the drag anisotropy $ξ= F_\perp/F_\parallel$ is…
We use plate drag to study the response of granular media to localized forcing as a function of volume fraction, $ϕ$. A bifurcation in the force and flow occurs at the onset of dilatancy, $ϕ_c.$ Below $ϕ_c$ rapid fluctuations in the drag force, $F_D,$ are observed. Above $ϕ_c$ fluctuations in $F_D$ are periodic and increase with $ϕ$. Velocity field measurements indicate that the bifurcation in $F_D$ results from the formation of stable shear bands above $ϕ_c$ which are created and destroyed periodically during drag. A friction-based model captures the dynamics for $ϕ>ϕ_c$.
We present in this Letter experimental results on the bidimensional flow field around a cylinder penetrating into dense granular matter together with drag force measurements. A hydrodynamic model based on extended kinetic theory for dense granular flow reproduces well the flow localization close to the cylinder and the corresponding scalings of the drag force, which is found to not depend on velocity, but linearly on the pressure and on the cylinder diameter and weakly on the grain size. Such a regime is found to be valid at a low enough "granular" Reynolds number.
We report on experimentally measured drag force experienced by a solid cylinder penetrating a granular bed of glass beads including, specifically, a highly polydisperse sample with grain sizes in the range 1-100 μm. We consider both cases of lateral and axial intrusion in which the long axis of the cylinder is held horizontally and vertically, respectively. We explore different regimes of behavior for the drag force as a function of the penetration depth. In lateral intrusion, where the motion is effectively quasi-two-dimensional, we establish quantitative comparisons with existing theoretical…
We measure the drag encountered by a vertically oriented rod moving across a sedimented granular bed immersed in a fluid under steady-state conditions. At low rod speeds, the presence of the fluid leads to a lower drag because of buoyancy, whereas a significantly higher drag is observed with increasing speeds. The drag as a function of depth is observed to decrease from being quadratic at low speeds to appearing more linear at higher speeds. By scaling the drag with the average weight of the grains acting on the rod, we obtain the effective friction $μ_e$ encountered over six orders of magnitu…
The local flow field and seepage induced drag obtained from Pore Network Models (PNM) is compared to Immersed Boundary Method (IBM) simulations, for a range of linear graded and bimodal samples. PNM were generated using a weighted Delaunay Tessellation (DT), along with the Modified Delaunay Tessellation (MDT) which considers the merging of tetrahedral Delaunay cells. The local pressure field was very accurately captured in all linear graded and bimodal samples. Local flux (flow rate) exhibited more scatter, but the PNM based on the MDT clearly provided a better correlation with the IBM. There …
The "free" water surface is generally prone to contamination with surface impurities be they surfactants, particles or other surface active agents. The presence of such impurities can modify flow boundary near such interfaces in a drastic manner. Here we show that vibrating a small sphere mounted on an AFM cantilever near a gas bubble immersed in water, is an excellent probe of surface contamination. Both viscous and elastic forces are exerted by an air-water interface on the vibrating sphere even when very low doses of contaminants are present. The viscous drag forces show a cross-over from n…
Non-cohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material. We find a crossover from nearly incompressible, fluid-like behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated. We discuss these results in light of recent proposals fo…
