Long ranged stress correlations in the hard sphere liquid

TL;DR

This study reveals that stress correlations in hard sphere liquids develop long-range power-law patterns similar to elastic solids, with dynamics influenced by sound speeds and diffusion processes.

Contribution

It demonstrates the emergence of unscreened Eshelby stress patterns in liquids and analyzes their tensorial and dynamic properties through simulations.

Findings

Stress correlations exhibit power-law decay $r^{-D}$ and $r^{-D-2}$.

Shear stresses relax diffusively within growing regions.

Regions grow with sound speeds, indicating elastic-like behavior.

Abstract

The smooth emergence of shear elasticity is an hallmark of the liquid to glass transition. In a liquid, viscous stresses arise from local structural rearrangements. In the solid, Eshelby has shown that stresses around an inclusion decay as a power law $r^{-D}$, where $D$ is the dimension of the system. We study glass-forming hard sphere fluids by simulation and observe the emergence of the unscreened power-law Eshelby pattern in the stress correlations of the isotropic liquid state. By a detailed tensorial analysis, we show that the fluctuating force field, viz.~the divergence of the stress field, relaxes to zero with time in all states, while the shear stress correlations develop spatial power-law structures inside regions that grow with longitudinal and transverse sound speeds; we observe the predicted exponents $r^{-D}$ and $r^{-D-2}$. In Brownian systems, shear stresses relax diffusively within these regions, with the diffusion coefficient determined by the shear modulus and the friction coefficient.