Density inhomogeneities in granular flows can dramatically influence microscopic and macroscopic properties. Here, we numerically examine dilute rapid granular flows in the Couette geometry via large-scale particle-dynamic simulations, and characterize development of nonuniform particle distributions. For monodisperse grains we observe density waves in two-and three-dimensional computational domains of varying aspect ratios. Both fully developed and transient states are quantified using Fourier methods. For inelastic, planar ͑two-dimensional͒ flows exceeding a minimum solids fraction, one-dimensional, high-density clusters-well-known features of inelastic materials-align parallel to the walls. Above a critical streamwise length, these are destabilized by two-dimensional antisymmetric modes with wavelength ϳ100 particle diameters. We relate oscillatory behavior to an underlying physical mechanism of the slow drift of clusters towards walls and their subsequent bursting. Further streamwise or spanwise expansions permit additional wave numbers to be expressed in these directions. In ''shallow'' three-dimensional flows, the planar wave types initially survive. As depth is increased above a critical value, cross-stream invariance experiences symmetry preserving instabilities to form coherent structures resembling steady and wavy Taylor-Couette fluid vortices. Their presence strongly impacts macroscopic behavior, as regions of sustained vorticity develop, and stresses and granular temperatures deviate by up to an order of magnitude from mean values. The influence of solids fraction, particle size, material elasticity, surface friction, polydispersity, and gravity are considered, and instabilities are found to intensify as collisional dissipation rises. For planar flows, transient and fully developed density distributions share many parametric responses with previous continuum results using kinetic theory.
Fluids sheared between concentric rotating cylinders undergo a series of three-dimensional instabilities. Since Taylor's archetypal 1923 study, these have proved pivotal to understanding how fluid flows become unstable and eventually undergo transitions to chaotic or turbulent states. In contrast, predicting the dynamics of granular systems--from nano-sized particles to debris flows--is far less reliable. Under shear these materials resemble fluids, but solid-like responses, non-equilibrium structures and segregation patterns develop unexpectedly. As a result, the analysis of geophysical events and the performance of largely empirical particle technologies might suffer. Here, using gas fluidization to overcome jamming, we show experimentally that granular materials develop vortices consistent with the primary Taylor instability in fluids. However, the vortices observed in our fluidized granular bed are unlike those in fluids in that they are accompanied by novel mixing-segregation transitions. The vortices seem to alleviate increased strain by spawning new vortices, directly modifying the scale of kinetic interactions. Our observations provide insights into the mechanisms of shear transmission by particles and their consequent convective mixing.
In contrast to [Cp(2)MoH(3)](+), which is a thermally stable trihydride complex, the ansa-bridged analogue [(eta-C(5)H(4))(2)CMe(2)MoH(H(2))](+) (1) is a thermally labile dihydrogen/hydride complex. Partial deuteration of the hydride ligands allows observation of J(H)(-)(D) = 11.9 Hz in 1-d(1) and 9.9 Hz in 1-d(2) (245 K), indicative of a dihydrogen/hydride structure. There is a slight preference for deuterium to concentrate in the dihydrogen ligand. A rapid dynamic process interchanges the hydride and dihydrogen moieties in complex 1. Low temperature (1)H NMR spectra of 1 give a single hydride resonance, which broadens at very low temperature due to rapid dipole-dipole relaxation (T(1) = 23 ms (750 MHz, 175 K) for the hydride resonance in 1). Low temperature (1)H NMR spectra of 1-d(2) allow the observation of decoalescence at 180 K into two resonances. The bound dihydrogen ligand exhibits hindered rotation with DeltaG(150) = 7.4 kcal/mol, but H atom exchange is still rapid at all accessible temperatures (down to 130 K). Density functional calculations confirm the dihydrogen/hydride structure as the ground state for the molecule and give estimates for the energy of two hydrogen exchange processes in good agreement with experiment. The presence of the C ansa bridge is shown to decrease the ability of the metallocene fragment to donate to the hydrogens, thus stabilizing the (eta(2)-H(2)) unit and modulating the barrier to H(2) rotation.
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