35 research outputs found
“Opening-Up” the WTO: What Does It Mean for China?
Text of speech delivered at China University of Political Science and Law (CUPL), Beijing, October 9; Tsinghua Law School, Beijing, October 10; Wuhan University, WTO Center, October 12; Fudan University, Shanghai, October 13, 200
Stokes' Cradle: Newton's Cradle with Liquid Coating
Flows involving liquid-coated grains are ubiquitous in nature (pollen
capture, avalanches) and industry (air filtration, smoke-particle
agglomeration, pharmaceutical mixing). In this work, three-body collisions
between liquid-coated spheres are investigated experimentally using a "Stokes'
cradle", which resembles the popular desktop toy known as the Newton's cradle.
Surprisingly, previous work indicates that every possible outcome was observed
in the wetted system except the traditional Newton's cradle (NC) outcome. Here,
we are able to experimentally achieve NC via guidance from a first-principles
model, which revealed that controlling the volume of the liquid bridge
connecting the two target particles is the key parameter in attaining the NC
outcome. By independently decreasing the volume of the liquid bridge, we not
only achieved NC but also uncovered several new findings. For example, in
contrast to previous work on two-body collisions, three-body experiments
provide direct evidence that the fluid resistance upon rebound cannot be
completely neglected due to presumed cavitation; this resistance also plays a
role in two-body systems yet cannot be isolated experimentally in such systems.
The herein micro-level description provides an essential foundation for
macro-level descriptions of wetted granular flows.Comment: 4 pages, 5 figures, accepted into Physical Review Letter
Thermal diffusion segregation in granular binary mixtures described by the Enskog equation
Diffusion induced by a thermal gradient in a granular binary mixture is
analyzed in the context of the (inelastic) Enskog equation. Although the Enskog
equation neglects velocity correlations among particles which are about to
collide, it retains spatial correlations arising from volume exclusion effects
and thus it is expected to apply to moderate densities. In the steady state
with gradients only along a given direction, a segregation criterion is
obtained from the thermal diffusion factor measuring the amount of
segregation parallel to the thermal gradient. As expected, the sign of the
factor provides a criterion for the transition between the Brazil-nut
effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters
of the mixture (masses, sizes, concentration, solid volume fraction, and
coefficients of restitution). The form of the phase diagrams for the BNE/RBNE
transition is illustrated in detail for several systems, with special emphasis
on the significant role played by the inelasticity of collisions. In
particular, an effect already found in dilute gases (segregation in a binary
mixture of identical masses and sizes {\em but} different coefficients of
restitution) is extended to dense systems. A comparison with recent computer
simulation results shows a good qualitative agreement at the level of the
thermal diffusion factor. The present analysis generalizes to arbitrary
concentration previous theoretical results derived in the tracer limit case.Comment: 7 figures, 1 table. To appear in New J. Phys., special issue on
"Granular Segregation
Clustering Instabilities in Gas-Solid Systems: Role of Dissipative Collisions vs. Viscous Losses
https://digitalrepository.unm.edu/abq_mj_news/4755/thumbnail.jp
Enskog kinetic theory for monodisperse gas–solid flows
The Enskog kinetic theory is used as a starting point to model a suspension of solid particles in a viscous gas. Unlike previous efforts for similar suspensions, the gas-phase contribution to the instantaneous particle acceleration appearing in the Enskog equation is modelled using a Langevin equation, which can be applied to a wide parameter space (e.g. high Reynolds number). Attention here is limited to low Reynolds number flow, however, in order to assess the influence of the gas phase on the constitutive relations, which was assumed to be negligible in a previous analytical treatment. The Chapman–Enskog method is used to derive the constitutive relations needed for the conservation of mass, momentum and granular energy. The results indicate that the Langevin model for instantaneous gas–solid force matches the form of the previous analytical treatment, indicating the promise of this method for regions of the parameter space outside of those attainable by analytical methods (e.g. higher Reynolds number). The results also indicate that the effect of the gas phase on the constitutive relations for the solid-phase shear viscosity and Dufour coefficient is non-negligible, particularly in relatively dilute systems. Moreover, unlike their granular (no gas phase) counterparts, the shear viscosity in gas–solid systems is found to be zero in the dilute limit and the Dufour coefficient is found to be non-zero in the elastic limit
On the role of the Knudsen layer in rapid granular flows
A combination of molecular-dynamics simulations, theoretical predictions, and
previous experiments are used in a two-part study to determine the role of the
Knudsen layer in rapid granular flows. First, a robust criterion for the
identification of the thickness of the Knudsen layer is established: a rapid
deterioration in Navier-Stokes-order prediction of the heat flux is found to
occur in the Knudsen layer. For (experimental) systems in which heat flux
measurements are not easily obtained, a rule-of-thumb for estimating the
Knudsen layer thickness follows, namely that such effects are evident within
2.5 (local) mean free paths of a given boundary. Second, comparisons of
simulation and experimental data with Navier-Stokes order theory are used to
provide a measure as to when Knudsen layer effects become non-negligible.
Specifically, predictions that do not account for the presence of a Knudsen
layer appear reliable for Knudsen layers collectively composing up to 20% of
the domain, whereas deterioration of such predictions becomes apparent when the
domain is fully comprised of the Knudsen layer.Comment: 9 figures, accepted to Journal of Fluid Mechanic
Enskog Theory for Polydisperse Granular Mixtures. I. Navier-Stokes order Transport
A hydrodynamic description for an -component mixture of inelastic, smooth
hard disks (two dimensions) or spheres (three dimensions) is derived based on
the revised Enskog theory for the single-particle velocity distribution
functions. In this first portion of the two-part series, the macroscopic
balance equations for mass, momentum, and energy are derived. Constitutive
equations are calculated from exact expressions for the fluxes by a
Chapman-Enskog expansion carried out to first order in spatial gradients,
thereby resulting in a Navier-Stokes order theory. Within this context of small
gradients, the theory is applicable to a wide range of restitution coefficients
and densities. The resulting integral-differential equations for the zeroth-
and first-order approximations of the distribution functions are given in exact
form. An approximate solution to these equations is required for practical
purposes in order to cast the constitutive quantities as algebraic functions of
the macroscopic variables; this task is described in the companion paper.Comment: 36 pages, to be published in Phys. Rev.