Flux measurement in compartmentalized mono-disperse and bi-disperse granular gases

Abstract

Flux models play a crucial role in understanding clustering behavior of compartmentalized granular gases. In this work we propose a method to measure the flux of monodisperse and bi-disperse granular gases in an equivalent compartmentalized system by molecular dynamics simulation. The simulation results are useful for quantitative comparison with an existing flux model that presents essential features of the oscillatory clustering behavior in a two-compartment system. By some minor improvement to one of the models, we show results of quantitative comparisons between predictions of the model and our simulation results. We also discuss the evolution of the system through oscillatory and degenerate oscillatory states using flux contour maps.

Bifurcation and nonlinear behavior of compartmentalized granular gases

“…In recent few years we have studied these clustering behaviors by experiments, simulations and modeling [10,11,12,13,14,15,16,17,18,19,20,21]. Experimentally we observed the oscillatory clustering of the same size grains; by measuring the oscillation period and amplitude [22,21] we verify that the transition from segregation state to oscillatory state is an infinite-period bifurcation, and from oscillatory state to homogeneous state is a supercritical Hopf bifurcation.…”

“…Under this assumption, the explicit form of temperature can be deduced based on the energy conservation. (12) μ is the effective mass written as…”

“…The dissipation due to particle-boundary collisions, therefore, may not be negligible. Taking into account of the inelastic particle-boundary collisions, we have modified the flux function (see [12] for more details), and applied this modified flux model to numerically solve Eq.10, we are able to reproduce the five states mentioned in the previous section,homogeneous (HOM) state(which is not shown in the figure), segregated (ASC) state, oscillatory (OSC) state, degenerate oscillatory (d-OSC) state and light particles homogeneously distributed (l-HOM) state.…”

DEM simulation of the granular Maxwell’s Demon under zero gravity

“…In order to find a flux function for the segregation condition in microgravity, i.e., to know the number of particles flow instantaneously through the window per unit time, we count the number of particle-wall collisions at a virtual window of a single cell [9] shown in Fig. 3.…”

“…A steady state of the whole system is reached when the dissipation of the system is balanced by the input of the energy. Since both the energy input and dissipation depends crucially on the configurations of the system, many intriguing steady states, such as granular segregation in a twocompartment cell known as Maxwell's Demon phenomenon [9,10] and even oscillatory states can be observed. The segregation phenomenon relies on the existence of a non-monotonic flux, which determines the number of particles per unit time flows between the two compartments [11].…”