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Register a new userHydrodynamics of fluid-solid coexistence in dense shear granular flow
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Evgeniy Khain
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We consider dense rapid shear flow of inelastically colliding hard disks. Navier-Stokes granular hydrodynamics is applied accounting for the recent finding cite{Luding,Khain} that shear viscosity diverges at a lower density than the rest of constitutive relations. New interpolation formulas for constitutive relations between dilute and dense cases are proposed and justified in molecular dynamics (MD) simulations. A linear stability analysis of the uniform shear flow is performed and the full phase diagram is presented. It is shown that when the inelasticity of particle collision becomes large enough, the uniform sheared flow gives way to a two-phase flow, where a dense solid-like striped cluster is surrounded by two fluid layers. The results of the analysis are verified in event-driven MD simulations, and a good agreement is observed.
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We study in this work a steady shearing laminar flow with null heat flux (usually called uniform shear flow) in a gas-solid suspension at low density. The solid particles are modeled as a gas of smooth hard spheres with inelastic collisions while the influence of the surrounding interstitial fluid on the dynamics of grains is modeled by means of a volume drag force, in the context of a rheological model for suspensions. The model is solved by means of three different but complementary routes, two of them being theoretical (Grads moment method applied to the corresponding Boltzmann equation and an exact solution of a kinetic model adapted to granular suspensions) and the other being computational (Monte Carlo simulations of the Boltzmann equation). Unlike in previous studies on granular sheared suspensions, we include in our Grads solution nonlinear terms in the stress tensor in the collisional moment associated with the momentum transfer. This theoretical enhancement allows us for the detection and evaluation of the normal stress differences in the plane normal to the laminar flow. In addition, the exact solution of the kinetic model gives the explicit form of the velocity moments of the velocity distribution function. Comparison between our theoretical and numerical results shows in general a good agreement for the non-Newtonian rheological properties, the kurtosis (fourth velocity moment of the distribution function) and the velocity distribution of the kinetic model for quite strong inelasticity and not too large values of the (scaled) friction coefficient characterizing the viscous drag force. This shows the accuracy of our analytical results that allows us to describe in detail the flow dynamics of the granular suspension with zero heat flux throughout the paper.
Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5]. Since shear bands mark areas of flow, material failure and energy dissipation, they play a crucial role for many industrial, civil engineering and geophysical processes[6]. They also appear in related contexts, such as in lubricating fluids confined to ultra-thin molecular layers[7]. Detailed information on motion within a shear band in a three-dimensional geometry, including the degree of particle rotation and inter-particle slip, is lacking. Similarly, only little is known about how properties of the individual grains - their microstructure - affect movement in densely packed material[5]. Combining magnetic resonance imaging, x-ray tomography, and high-speed video particle tracking, we obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.
We experimentally investigate the rheology and stress fluctuations of granules densely suspended in silicone oil. We find that both thickening strength and stress fluctuations significantly weaken with oil viscosity $eta_0$. Comparison of our rheological results to the Wyart-Cates model for describing different dynamic jamming states suggests a transition from frictional contacts to lubrication interactions as $eta_0$ increases. To clarify the contribution from viscous interactions to the rheology, we systematically measure stress fluctuations in various flow states. Reduction of stress fluctuations with $eta_0$ indicates that a strong lubrication layer greatly inhibits force correlations among particles. Measuring stress fluctuations in the strong shear thickening regime, we observe a crossover from asymmetric Gamma to symmetric Gaussian distributions and associated with it a decrease of lateral (radial) correlation length $xi$ with increasing shear rate.
We perform three-dimensional simulations of a granular jet impact for both frictional and frictionless grains. Small shear stress observed in the experiment[X. Cheng et al., Phys. Rev. Lett. 99, 188001 (2007) ] is reproduced through our simulation. However, the fluid state after the impact is far from a perfect fluid, and thus, similarity between granular jets and quark gluon plasma is superficial, because the observed viscosity is finite and its value is consistent with the prediction of the kinetic theory.
Experimental measurements of particle dynamics on the lower surface of a 3D Couette cell containing monodisperse spheres are reported. The average radial density and velocity profiles are similar to those previously measured within the bulk and on the lower surface of the 3D cell filled with mustard seeds. Observations of the evolution of particle velocities over time reveal distinct motion events, intervals where previously stationary particles move for a short duration before jamming again. The cross-correlation between the velocities of two particles at a given distance $r$ from the moving wall reveals a characteristic lengthscale over which the particles are correlated. The autocorrelation of a single particles velocity reveals a characteristic timescale $tau$ which decreases with distance from the inner moving wall. This may be attributed to the increasing rarity at which the discrete motion events occur and the reduced duration of those events at large $r$. The relationship between the RMS azimuthal velocity fluctuations, $delta v_theta(r)$, and average shear rate, $dotgamma(r)$, was found to be $delta v_theta propto dotgamma^alpha$ with $alpha = 0.52 pm 0.04$. These observations are compared with other recent experiments and with the modified hydrodynamic model recently introduced by Bocquet et al.
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