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Register a new userIntruder in a two-dimensional granular system: Effects of dynamic and static basal friction on stick-slip and clogging dynamics
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We discuss the results of simulations of an intruder pulled through a two-dimensional granular system by a spring, using a model designed to lend insight into the experimental findings described by Kozlowski et al. [Phys. Rev. E, 100, 032905 (2019)]. In that previous study the presence of basal friction between the grains and the base was observed to change the intruder dynamics from clogging to stick-slip. Here we first show that our simulation results are in excellent agreement with the experimental data for a variety of experimentally accessible friction coefficients governing interactions of particles with each other and with boundaries. Then, we use simulations to explore a broader range of parameter space, focusing on the friction between the particles and the base. We consider a range of both static and dynamic basal friction coefficients, which are difficult to vary smoothly in experiments. The simulations show that dynamic friction strongly affects the stick-slip behaviour when the coefficient is decreased below 0.1, while static friction plays only a marginal role in the intruder dynamics.
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We report on a series of experiments in which a grain-sized intruder is pushed by a spring through a 2D granular material comprised of photoelastic disks in a Couette geometry. We study the intruder dynamics as a function of packing fraction for two types of supporting substrates: a frictional glass plate and a layer of water for which basal friction forces are negligible. We observe two dynamical regimes: intermittent flow, in which the intruder moves freely most of the time but occasionally gets stuck, and stick-slip dynamics, in which the intruder advances via a sequence of distinct, rapid events. When basal friction is present, we observe a smooth crossover between the two regimes as a function of packing fraction, and we find that reducing the interparticle friction coefficient causes the stick-slip regime to shift to higher packing fractions. When basal friction is eliminated, we observe intermittent flow at all accessible packing fractions. For all cases, we present results for the statistics of stick events, the intruder velocity, and the force exerted on the intruder by the grains. Our results indicate the qualitative importance of basal friction at high packing fractions and suggest a possible connection between intruder dynamics in a static material and clogging dynamics in granular flows.
We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs, when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear viscous friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first order phase transitions we discuss a ``soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as function of the driving velocity. The relevance of our results to recent experiments is discussed.
The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental results which suggest a wave-like (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Numerical simulations of two-dimensional granular systems subject to a localized external force are employed to examine the nature of stress transmission in these systems as a function of the magnitude of the applied force, the frictional parameters and the disorder (polydispersity). The results indicate that in large systems (typically considered by engineers), the response is close to that predicted by isotropic elasticity whereas the response of small systems (or when sufficiently large forces are applied) is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding. The larger the coefficient of static friction, the more extended is the range of forces for which the response is elastic and the smaller the anisotropy. Increasing the degree of polydispersity (for the range studied, up to 25%) decreases the range of elastic response. This article is an extension of a previously published letter [1].
Granular flows through narrow outlets may be interrupted by the formation of arches or vaults that clog the exit. These clogs may be destroyed by vibrations. A feature which remains elusive is the broad distribution $p(tau)$ of clog lifetimes $tau$ measured under constant vibrations. Here, we propose a simple model for arch-breaking, in which the vibrations are formally equivalent to thermal fluctuations in a Langevin equation; the rupture of an arch corresponds to the escape from an energy trap. We infer the distribution of trap depths from experiments and, using this distribution, we show that the model captures the empirically observed heavy tails in $p(tau)$. These heavy tails flatten at large $tau$, consistently with experimental observations under weak vibrations, but this flattening is found to be systematic, thus questioning the ability of gentle vibrations to restore a finite outflow forever. The trap model also replicates recent results on the effect of increasing gravity on the statistics of clog formation in a static silo. Therefore, the proposed framework points to a common physical underpinning to the processes of clogging and unclogging, despite their different statistics.
The growth dynamics of an air finger injected in a visco-elastic gel (a PVA/borax aqueous solution) is studied in a linear Hele-Shaw cell. Besides the standard Saffmann-Taylor instability, we observe - with increasing finger velocities - the existence of two new regimes: (a) a stick-slip regime for which the finger tip velocity oscillates between 2 different values, producing local pinching of the finger at regular intervals, (b) a ``tadpole regime where a fracture-type propagation is observed. A scaling argument is proposed to interpret the dependence of the stick-slip frequency with the measured rheological properties of the gel.
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