Meheboob Alam

Rheology of bidisperse granular mixtures via event-driven simulations

The bulk rheology of bidisperse mixtures of granular materials is examined under homogeneous shear flow conditions using the event-driven simulation method. The granular material is modelled as a system of smooth inelastic disks, interacting via the hard-core potential. In order to understand the effect of size and mass disparities, two cases were examined separately, namely, a mixture of different sized particles with particles having either the same mass or the same material density. The relevant macroscopic quantities are the pressure, the shear viscosity, the granular energy (fluctuating kinetic energy) and the first normal stress difference. Numerical results for pressure, viscosity and granular energy are compared with a kinetic-theory constitutive model with excellent agreement in the low dissipation limit even at large size disparities. Systematic quantitative deviations occur for stronger dissipations

First normal stress difference and crystallization in a dense sheared granular fluid

The first normal stress difference (N1) and the microstructure in a dense sheared granular fluid of smooth inelastic hard-disks are probed using event-driven simulations. While the anisotropy in the second moment of fluctuation velocity, which is a Burnett-order effect, is known to be the progenitor of normal stress differences in dilute granular fluids, we show here that the collisional anisotropies are responsible for the normal stress behavior in the dense limit. As in the elastic hard-sphere fluids, N1 remains positive (if the stress is defined in the compressive sense) for dilute and moderately dense flows, but becomes negative above a critical density, depending on the restitution coefficient. This sign-reversal of N1 occurs due to the microstructural reorganization of the particles, which can be correlated with a preferred value of the average collision angle θav=π/4±π/2 in the direction opposing the shear. We also report on the shear-induced crystal-formation, signaling the onset of fluid–solid co...

Segregation in a fluidized binary granular mixture: Competition between buoyancy and geometric forces

Starting from hydrodynamic equations of binary granular mixtures, we derive an evolution equation for the relative velocity of the intruders, which is shown to be coupled to the inertia of the smaller particles. The onset of Brazil nut segregation is explained as a competition between the buoyancy and geometric forces: the Archimedean buoyancy force, a buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other one tensile in nature, due to the size difference. We show that inelastic dissipation strongly affects the phase diagram of the Brazil nut phenomenon and our model is able to explain the experimental results of Breu et al. (Phys. Rev. Lett. 90 (2003) 014302).

Kinetic theory of a binary mixture of nearly elastic disks with size and mass disparity

Corrections are provided for two transport coefficients derived by Willits and Arnarson [Phys. Fluids 11, 3116 (1999)] for a binary mixture of nearly elastic, circular disks using the revised Enskog theory. The corrected viscosity coefficient is compared to the shear viscosity obtained from simulation results of a bidisperse mixture of inelastic, hard disks, undergoing uniform shear flow. The agreement is good for a wide range of sizes and masses.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Observations on transition in plane bubble plumes

Flow visualization studies of plane laminar bubble plumes have been conducted to yield quantitative data on transition height, wavelength and wave velocity of the most unstable disturbance leading to transition. These are believed to be the first results of this kind. Most earlier studies are restricted to turbulent bubble plumes. In the present study, the bubble plumes were generated by electrolysis of water and hence very fine control over bubble size distribution and gas flow rate was possible to enable studies with laminar bubble plumes. Present observations show that (a) the dominant mode of instability in plane bubble plumes is the sinuous mode, (b) transition height and wavelength are related linearly with the proportionality constant being about 4, (c) wave velocity is about 40 % of the mean plume velocity, and (d) normalized transition height data correlate very well with a source Grashof number. Some agreement and some differences in transition characteristics of bubble plumes have been observed compared to those for similar single-phase flows.

Energy nonequipartition, rheology, and microstructure in sheared bidisperse granular mixtures

Event-driven simulations of smooth inelastic hard disks are used to probe the transport properties and the microstructure of bidisperse granular mixtures. A generic feature of such mixtures is that the two species have different levels of fluctuation kinetic energy (Tl≠Ts) in contrast with their elastic counterpart. The microscopic mechanism for this energy nonequipartition is shown to be directly tied to the asymmetric nature of collisional probabilities between the heavier and lighter species, compared to their purely elastic counterpart. The degree of collisional asymmetry increases with both increasing inelasticity and mass disparity, thereby increasing the energy ratio Tl∕Ts in the same limit. A phenomenological constitutive model, that incorporates energy nonequipartition, captures the nonmonotonic behavior of the transport coefficients, in agreement with the simulation results, whereas the standard constitutive model with equipartition assumption predicts monotonic variations. The sheared granular ...

Universality of shear-banding instability and crystallization in sheared granular fluid

The linear stability analysis of an uniform shear flow of granular materials is revisited using several cases of a Navier–Stokes-level constitutive model in which we incorporate the global equation of states for pressure and thermal conductivity (which are accurate up to the maximum packing density νm) and the shear viscosity is allowed to diverge at a density νμ (<νm), with all other transport coefficients diverging at νm. It is shown that the emergence of shear-banding instabilities (for perturbations having no variation along the streamwise direction), that lead to shear-band formation along the gradient direction, depends crucially on the choice of the constitutive model. In the framework of a dense constitutive model that incorporates only collisional transport mechanism, it is shown that an accurate global equation of state for pressure or a viscosity divergence at a lower density or a stronger viscosity divergence (with other transport coefficients being given by respective Enskog values that diverge at νm) can induce shear-banding instabilities, even though the original dense Enskog model is stable to such shear-banding instabilities. For any constitutive model, the onset of this shear-banding instability is tied to a universal criterion in terms of constitutive relations for viscosity and pressure, and the sheared granular flow evolves toward a state of lower ‘dynamic’ friction, leading to the shear-induced band formation, as it cannot sustain increasing dynamic friction with increasing density to stay in the homogeneous state. A similar criterion of a lower viscosity or a lower viscous-dissipation is responsible for the shear-banding state in many complex fluids.

Streamwise structures and density patterns in rapid granular Couette flow : a linear stability analysis

A three-dimensional linear stability analysis has been carried out to understand the origin of vortices and related density patterns in bounded uniform-shear flow of granular materials, using a kinetic-theory constitutive model. This flow is found to be unstable to pure spanwise stationary perturbations (

Isostaticity of constraints in amorphous jammed systems of soft frictionless Platonic solids.

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