Long-ranged stress correlations in viscoelastic liquids

Abstract

This work presents computer simulations of a binary mixture of hard particles in two and three dimensions. The packing fraction is chosen to be close to the glass transition, but still in the liquid phase. In this case the time dependent shear modulus shows a distinct plateau over several decades in time, indicating the onset of mechanical elasticity. Solid like spatial stress correlations proportional to r-D and r-D-2 in D dimensions are observed in Newtonian dynamics. These results are successfully compared to theory predictions based on the Zwanzig-Mori projection operator formalism. The transition to a diffusive propagation is observed in Brownian dynamics simulations. Correlated stresses over one decade in particle diameters are observed but the signal is not strong enough for a quantitative analysis. The emergence of the r-D power law reflects the Eshelby pattern, derived from linear elasticity theory, as the liquid solidifies. The stress correlation function is described by a fourth order tensor. This object simplifies significantly when the isotropy of the system is explicitly used by a decomposition of the stress correlation function into spherical tensors.