Broken Symmetry

Macroscopic liquid-state molecular hydrodynamics

“…As described in ‘Hydrodynamic Modes’ below, for example, we observe viscously damped acoustic modes propagating throughout the grain pile. While not detailed in the paper, our analyses also indicate existence of a weak diffusive entropy mode, as well as (two) uncoupled (diffusive) vorticity modes; the first is consistent with experimental observations in dense fluids 1 3 6 , and the second with well-known theoretical predictions 3 6 22 . Exact molecular- and grain-scale, i.e., discrete-particle versions of mass, momentum, and energy conservation, can be restated - via a little-used coarse-graining procedure appropriate to dense, interacting systems 6 7 - in continuum form; see Supplement 2 .…”

“…While not detailed in the paper, our analyses also indicate existence of a weak diffusive entropy mode, as well as (two) uncoupled (diffusive) vorticity modes; the first is consistent with experimental observations in dense fluids 1 3 6 , and the second with well-known theoretical predictions 3 6 22 . Exact molecular- and grain-scale, i.e., discrete-particle versions of mass, momentum, and energy conservation, can be restated - via a little-used coarse-graining procedure appropriate to dense, interacting systems 6 7 - in continuum form; see Supplement 2 . Introduction of empirical constitutive relations, tying local (ensemble averaged) mass, momentum, and energy fluxes to local gradients in equilibrium thermodynamic variables, as well as gradients in local (bulk) dynamical variables, e.g., the local bulk velocity, then leads to the Navier-Stokes equations (which govern continuum-scale transport).…”

“…This paper adapts this theoretical framework to derive self-consistent continuum mass, momentum, and energy transport equations appropriate to vibrated grain systems; see Supplements 1 and 2 . We describe two rough consistency checks on the proposed theoretical framework: (i) A macroscale Green-Kubo relation 3 6 20 for the effective grain-fluid dynamic viscosity is used to obtain rough estimates of the effective kinematic viscosities of the nine grains used in our experiments; see Supplement 2 . (ii) A simplified model of vibration-driven flow of a Newtonian fluid within a hemisphere, subjected to the same multimodal vibration used in our experiments, is used to predict the continuum flow of grains within our experimental system; see ‘Time-Averaged Grain Flow’ below and Supplement 2 .…”

“…Molecular hydrodynamics typically uses two approaches to study molecular-scale dynamics in liquids and gases, the first measuring light 1 , neutrons 2 , or high-frequency sound scattered from an interrogation volume 3 , the second computationally simulating the dynamics of spatially-limited, N-body systems subject to various forcing mechanisms, and interacting through specified interparticle potentials 3 4 5 6 7 .…”

“…Kinetic models require modeling of intergranular collisions; in dense, interacting systems this remains an unresolved challenge, manifesting itself most apparently in unreliable transport property predictions 13 17 . By contrast, combined application of the Gibbs equilibrium model 14 15 and any of several models of linear, nonequilibrium fluctuation 3 6 18 19 20 circumvents collision modeling. Two important points are noted.…”