Unified torque scaling in counter-rotating suspension Taylor-Couette flow.

Torque measurements are reported for the Taylor-Couette flow of a neutrally buoyant non-colloidal suspension in the counter-rotation regime up to a particle volume fraction of [Formula: see text]. A unified scaling relation for the dimensionless torque (the pseudo-Nusselt number) of the form [Formula: see text] is shown to hold over a range of Taylor numbers [Formula: see text] that covers primary, secondary and tertiary bifurcating states; here, [Formula: see text] is the reduced Taylor number, [Formula: see text] is the critical Taylor number at primary bifurcation and [Formula: see text] is the relative viscosity of the suspension. Possible effects of flow transitions and inhomogeneous distribution of particles on torque scaling are discussed.

Asymptotic expansion and Padé approximants for acceleration-driven Poiseuille flow of a rarefied gas: Bulk hydrodynamics and rheology.

The perturbation expansion technique is employed to solve the Boltzmann equation for the acceleration-driven steady Poiseuille flow of a dilute molecular gas flowing through a planar channel. Neglecting wall effects and focusing only on the bulk hydrodynamics and rheology, the perturbation solution is sought around the channel centerline in powers of the strength of acceleration. To make analytical progress, the collision term has been approximated by the Bhatnagar-Gross-Krook kinetic model for hard spheres, and the related problem for Maxwell molecules was analyzed previously by Tij and Santos [J.

Phase-coexisting patterns, horizontal segregation, and controlled convection in vertically vibrated binary granular mixtures.

We report patterns consisting of coexistence of synchronous and asynchronous states [for example, a granular gas co-existing with (i) bouncing bed, (ii) undulatory subharmonic waves, and (iii) Leidenfrost-like states] in experiments on vertically vibrated binary granular mixtures in a Hele-Shaw cell. Most experiments have been carried out with equimolar binary mixtures of glass and steel balls of same diameter by varying the total layer height (F) for a range of shaking acceleration (Γ). All patterns as well as the related phase diagram in the (Γ,F) plane have been reproduced via molecular dynamics simulations of the same system.

Disentangling the role of athermal walls on the Knudsen paradox in molecular and granular gases.

The nature of particle-wall interactions is shown to have a profound impact on the well-known "Knudsen paradox" [or the "Knudsen minimum" effect, which refers to the decrease of the mass-flow rate of a gas with increasing Knudsen number Kn, reaching a minimum at Kn∼O(1) and increasing logarithmically with Kn as Kn→∞] in the acceleration-driven Poiseuille flow of rarefied gases. The nonmonotonic variation of the flow rate with Kn occurs even in a granular or dissipative gas in contact with thermal walls. The latter result is in contradiction with recent work [Alam et al.

Hydrodynamics, wall-slip, and normal-stress differences in rarefied granular Poiseuille flow.

Hydrodynamic fields, macroscopic boundary conditions, and non-Newtonian rheology of the acceleration-driven Poiseuille flow of a dilute granular gas are probed using "direct simulation Monte Carlo" method for a range of Knudsen numbers (Kn, the ratio between the mean free path and the macroscopic length), spanning the rarefied regime of slip and transitional flows. It is shown that the "dissipation-induced clustering" (for 1-e_{n}>0, where e_{n} is the restitution coefficient), leading to inhomogeneous density profiles along the transverse direction, competes with "rarefaction-induced declustering" (for Kn>0) phenomenon, leaving seemingly "anomalous" footprints on several hydrodynamic and rheological quantities; one example is the well-known rarefaction-induced temperature bimodality, which could also result from inelastic dissipation that dominates in the continuum limit (Kn→0) as found recently [Alam et al., J.

Pattern transition, microstructure, and dynamics in a two-dimensional vibrofluidized granular bed.

Experiments are conducted in a two-dimensional monolayer vibrofluidized bed of glass beads, with a goal to understand the transition scenario and the underlying microstructure and dynamics in different patterned states. At small shaking accelerations (Γ=Aω^{2}/g<1, where A and ω=2πf are the amplitude and angular frequency of shaking and g is the gravitational acceleration), the particles remain attached to the base of the vibrating container; this is known as the solid bed (SB). With increasing Γ (at large enough shaking amplitude A/d) and/or with increasing A/d (at large enough Γ), the sequence of transitions/bifurcations unfolds as follows: SB ("solid bed") to BB ("bouncing bed") to LS ("Leidenfrost state") to "2-roll convection" to "1-roll convection" and finally to a gas-like state.

Higher-order effects on orientational correlation and relaxation dynamics in homogeneous cooling of a rough granular gas.

The orientational or angular correlation between the directions of the translational and rotational motions is analyzed theoretically for the homogeneous cooling state of a rough granular gas. The dynamical equations are derived using an approximate form of the single-particle distribution function that incorporates angular correlations. The goal is to assess the effects of higher-order angular corrections for which both quadratic- and quartic-order terms (in translational and rotational velocities of particles) are retained in the perturbation expansion of the distribution function.

Variable-cell method for stress-controlled jamming of athermal, frictionless grains.

A method is introduced to simulate jamming of polyhedral grains under controlled stress that incorporates global degrees of freedom through the metric tensor of a periodic cell containing grains. Jamming under hydrostatic (isotropic) stress and athermal conditions leads to a precise definition of the ideal jamming point at zero shear stress. The structures of tetrahedra jammed hydrostatically exhibit less translational order and lower jamming-point density than previously described maximally random jammed hard tetrahedra.

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

The average number of constraints per particle in mechanically stable amorphous systems of Platonic solids approaches the isostatic limit at the jamming point (→12), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming, chainlike face-face clusters form with finite extent--a signature of amorphous jammed systems.

Effect of Coulomb friction on orientational correlation and velocity distribution functions in a sheared dilute granular gas.

From particle simulations of a sheared frictional granular gas, we show that the Coulomb friction can have dramatic effects on orientational correlation as well as on both the translational and angular velocity distribution functions even in the Boltzmann (dilute) limit. The dependence of orientational correlation on friction coefficient (μ) is found to be nonmonotonic, and the Coulomb friction plays a dual role of enhancing or diminishing the orientational correlation, depending on the value of the tangential restitution coefficient (which characterizes the roughness of particles). From the sticking limit (i.

Athermal jamming of soft frictionless Platonic solids.

A mechanically based structural optimization method is utilized to explore the phenomena of jamming for assemblies of frictionless Platonic solids. Systems of these regular convex polyhedra exhibit mechanically stable phases with density substantially less than optimal for a given shape, revealing that thermal motion is necessary to access high-density phases. We confirm that the large system jamming threshold of 0.

Onset of convection in strongly shaken granular matter.

Strongly vertically shaken granular matter can display a density inversion: A high-density cluster of beads is elevated by a dilute gaslike layer of fast beads underneath ("granular Leidenfrost effect"). For even stronger shaking the granular Leidenfrost state becomes unstable and granular convection rolls emerge. This transition resembles the classical onset of convection in fluid heated from below at some critical Rayleigh number.

Landau-type order parameter equation for shear banding in granular Couette flow.

We show that a Landau-type "order-parameter" equation describes the onset of shear-band formation in granular plane Couette flow wherein the flow undergoes an ordering transition into alternate layers of dense and dilute regions of low and high shear rates, respectively, parallel to the flow direction. Even though the linear theory predicts the stability of the homogeneous shear solution in dilute flows, our analytical bifurcation theory suggests that there is a subcritical finite-amplitude instability that is likely to lead to shear-band formation in dilute flows, which is in agreement with previous numerical simulations.

Slip velocity and stresses in granular Poiseuille flow via event-driven simulation.

Event-driven simulations of inelastic smooth hard disks are used to probe the slip velocity and rheology in gravity-driven granular Poiseuille flow. It is shown that both the slip velocity (U(w)) and its gradient (dU(w)/dy) depend crucially on the mean density, wall roughness, and inelastic dissipation. While the gradient of slip velocity follows a single power-law relation with Knudsen number, the variation in U(w) with Kn shows three distinct regimes in terms of Knudsen number.

Instabilities and patterns in horizontally oscillating particulate suspension.

The mean flow and the linear stability characteristics of a two-dimensional particulate suspension, driven horizontally via harmonic oscillation, are analyzed. A constitutive model based on the kinetic theory of granular materials, which takes into account the dissipative collisional interactions among particles as well as their interactions with the interstitial fluid, is used; the effects of the interstitial fluid are incorporated in the balance equations for the particle phase. Assuming that the suspension is thin along the vertical direction, the effects of driving are incorporated into the governing equations in a mean-field manner.

Linear stability, transient energy growth, and the role of viscosity stratification in compressible plane Couette flow.

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M , the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, alpha ) of each mean flow belongs to different modes for a range of supersonic M .

Orientational correlation and velocity distributions in uniform shear flow of a dilute granular gas.

Using particle simulations of the uniform shear flow of a rough dilute granular gas, we show that the translational and rotational velocities are strongly correlated in direction, but there is no orientational correlation-induced singularity at perfectly smooth (beta=-1) and rough (beta=1) limits for elastic collisions (e=1); both the translational and rotational velocity distribution functions remain close to a Gaussian for these two limiting cases. Away from these two limits, the orientational as well as spatial velocity correlations are responsible for the emergence of non-Gaussian high-velocity tails. The tails of both distribution functions follow stretched exponentials, with the exponents depending on normal (e) and tangential (beta) restitution coefficients.

Velocity distribution and the effect of wall roughness in granular Poiseuille flow.

From event-driven simulations of a gravity-driven channel flow of inelastic hard disks, we show that the velocity distribution function remains close to a Gaussian for a wide range densities (even when the Knudsen number is of order 1) if the walls are smooth and the particle collisions are nearly elastic. For dense flows, a transition from a Gaussian to a power-law distribution for the high-velocity tails occurs with increasing dissipation in the center of the channel, irrespective of wall roughness. For a rough wall, the near-wall distribution functions are distinctly different from those in the bulk, even in the quasielastic limit.