Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment

Abstract

Edwards has proposed1,2,3 a thermodynamic description of dense, slowly flowing granular matter, in which the grains (the ‘atoms’ of the system) interact with inelastic forces and enduring contacts. In Edwards' ensemble—one of the very few generalizations of standard statistical mechanics—thermodynamic quantities are computed as flat averages over configurations in which the grains are static or jammed, leading to a natural definition of configurational temperature. But the approach is not justified from first principles and hence, in the absence of explicit tests of its validity, has not been widely accepted. Here we report a numerical experiment involving a realistic model of slowly sheared granular matter; our results strongly support the thermodynamic description. Considering particles of different sizes in a slowly sheared dense granular system, we extract an effective temperature from a relation connecting their diffusivity and mobility. We then perform an explicit computation to show that the effective temperature measured from this relation coincides with the Edwards configurational temperature. Our approach, which is specifically conceived to be reproducible in the laboratory, may thus render the Edwards temperature accessible to experiments.

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Figure 1: Diffusion (a) and response function (b) for the large and small particles in a sheared granular material measured perpendicular to the shear plane as a function of time in MD steps.
Figure 2: Parametric plot of diffusion versus response function for small and large grains interacting with tangential forces and without tangential forces (Coulomb frictionless).
Figure 3: Annealing procedure to calculate TEdw at different elastic compressional energies.

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Acknowledgements

This work was partially supported by The Petroleum Research Fund.

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Correspondence to Hernán A. Makse.

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Makse, H., Kurchan, J. Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment. Nature 415, 614–617 (2002). https://doi.org/10.1038/415614a

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