Hydrodynamics in kinetically-constrained lattice-gas models

• Published in: arXiv.org 2016-12
• Main Authors: Teomy, Eial, Shokef, Yair
• Format: Article
• Language: English
• Subjects: Approximation; Computational fluid dynamics; Correlation; Density; Diffusion; Diffusion coefficient; Equilibrium; Fluid flow; Granulation; Hydrodynamics; Mathematical analysis; Mathematical models; Occupancy
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1612.00182

Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We drive such models out of equilibrium by connecting them to two reservoirs of different densities, and measure the response of the system to this perturbation. We find that under the proper coarse-graining, the behavior of these models may be expressed by a nonlinear diffusion equation, with a model- and density-dependent diffusion coefficient. We find a simple approximation for the diffusion coefficient, and show that the relatively mild discrepancy between the approximation and our numerical results arises due to non-negligible correlations that appear as the system is driven out of equilibrium, even when the density gradient is infinitesimally small. Similar correlations appear when such kinetically-constrained models are driven out of equilibrium by applying a uniform external force. We suggest that these correlations are the reason for the same discrepancy between the approximate diffusion coefficient and the numerical results for a broader group of models, non-gradient lattice-gas models, for which kinetically-constrained models are arguably the simplest example thereof.