Scaling behavior for the pressure and energy of shearing fluids

Abstract

Recent simulation work has established that the widely accepted mode-coupling theory for the strain rate dependence of the pressure and energy of simple fluids under shear (i.e., energy and pressure are functions of strain rate to the power 3 / 2) is observed in the vicinity of the triple point. Away from the triple point, the scaling exponent of the strain rate was seen to be closer to 2 than 3 / 2, suggesting a possible analytic behavior. In this paper, we accurately determine the scaling exponent behavior for a Lennard-Jones fluid in the dense fliud region and find that it varies continuously between approximately 1.2 and approximately 2 as a function of density and temperature, thus confirming its nonanalyticity. We furthermore find that the behavior is characterized by a simple linear function of density and temperature.

Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

“…Data published by Ge et al [19] are consistent with our results. They showed that for a dense LJ liquid under shear flow, the potential energy and the pressure can be fitted by a power-law dependence on strain rate, U = U 0 + aγ α (31)…”

“…They found [19] that the linear expression α = A + BT − Cρ represents well their simulations with A = 3.67, B = 0.69, and C = 3.35. To make a connection between these results and isomorph theory, recall that the collapse seen in Fig.…”

Thermodynamic relationships for shearing linear viscoelastic fluids

“…An alternative analysis of the density dependence of the pressure versus shear rate data has been presented by Ge et al [15]. They fitted a power law to the pressure versus shear rate data for an atomic fluid over a fixed range of shear rates, allowing the exponent to vary with density.…”

Nonlinear shear and elongational rheology of model polymer melts at low strain rates

“…Apart from a few detailed computational investigations for atomic fluids [27,28], this equation of state has received little attention, but it is possible to obtain one from the retarded motion expansion. Most derivations of the retarded motion expansion introduce the incompressibility assumption at an early stage [11,12,29], but it is possible to carry out the derivation without making this assumption.…”