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 $\Lambda$ measuring the amount of segregation parallel to the thermal gradient. As expected, the sign of the factor $\Lambda$ 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

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 $s$-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.