Temperature probes in binary granular gases

Abstract

We investigate the validity of Fluctuation-Dissipation (FD) relations for a mixture of two granular gases with different physical properties (restitution coefficients or masses) subject to stochastic driving. It is well known that the partial granular temperatures T1 and T2 of the two components are different, i.e. energy equipartition is broken. We observe, with numerical simulations of inelastic hard disks in homogeneous and non-homogeneous situations, that the classical equilibrium GreenKubo relations are satisfied separately for each component of the gas, the role of the equilibrium temperature being played by the granular temperature of each component. Of particular interest is the limit in which one of the two components consists of only one particle, representing a nonperturbing thermometer. In this case it turns out that such a thermometer is measuring its own temperature and not that of the surrounding granular media, which in general will be different.

Mass transport of an impurity in a strongly sheared granular gas

“…A similar conclusion has been found when the gas is under HCS [32,33,34]. There are basically two independent reasons for this violation: the occurrence of different kinetic temperatures between the impurity and gas particles and the inherent non-Newtonian properties of the reference state.…”

Violation of the Einstein relation in granular fluids: the role of correlations

“…Recently numerical studies have been performed showing that, in homogeneous situations, the Fluctuation-Response relation (FR) is valid in its near-equilibrium formulation, replacing the bath temperature with the internal granular temperature [18,19]. This has interesting consequences in the case of mixtures, where different components have different temperatures [20]: for instance, a linear response experiment on a massive tracer, performed to obtain a temperature measurement (a granular thermometer), yields the temperature of the tracer and not that of the surrounding gas. The verification of FR has been explained by means of a hydrodynamic approach by Garzo [21], who connected it to the very small departures from the Maxwell-Boltzmann statistics.…”

Kinetic Theory for Binary Granular Mixtures at Low Density

“…Given that the deviations of the gas distribution f (0) 2 from its Maxwellian form are small [15], the discrepancies of ǫ from unity could be difficult to detect in computer simulations. This conclusion agrees with recent MD simulations [52] of granular mixtures subjected to the stochastic driving of the form (30), where no deviations from the (modified) Einstein relation ǫ = 1 have been observed for a wide range of values of the coefficients of restitution and parameters of the system.…”

“…In the undriven case, the analysis shows that this violation is due to three independent reasons [23]: the absence of the Gibbs state, the cooling of the reference state, and the occurrence of different temperatures for the particle and surrounding fluid. However, when the mixture is subjected to stochastic driving, a modified Einstein relation suggested by recent MD simulations [52] has also been analyzed. In this case, the results show that the deviations of the (modified) Einstein ratio from unity are in general very small (less than 1%), in agreement with MD simulations [52].…”