An extended analysis of the viscosity kernel for monatomic and diatomic fluids

Abstract

We present an extended analysis of the wave-vector dependent shear viscosity of monatomic and diatomic (liquid chlorine) fluids over a wide range of wave-vectors and for a variety of state points. The analysis is based on equilibrium molecular dynamics simulations, which involves the evaluation of transverse momentum density and shear stress autocorrelation functions. For liquid chlorine we present the results in both atomic and molecular formalisms. We find that the viscosity kernel of chlorine is statistically indistinguishable with respect to atomic and molecular formalisms. The results further suggest that the real space viscosity kernels of monatomic and diatomic fluids depends sensitively on the density, the potential energy function and the choice of fitting function in reciprocal space. It is also shown that the reciprocal space shear viscosity data can be fitted to two different simple functional forms over the entire density, temperature and wave-vector range: a function composed of n-Gaussian terms and a Lorentzian type function. Overall, the real space viscosity kernel has a width of 3 to 6 atomic diameters which means that the generalized hydrodynamic constitutive relation is required for fluids with strain rates that vary nonlinearly over distances of the order of atomic dimensions.

Pressure dependence of confined liquid behavior subjected to boundary-driven shear

“…The strong variation of physical properties on a molecular scale in a molecularly thin channel has motivated the proposal of a non-local viscosity kernel. 28,29 Bair et al 30 observed shear localization in high pressure flow experiments of liquid lubricants under shear. The shear bands were inclined typically at ∼20 • to the walls and occurred just before the traction ("friction") coefficient became strongly nonlinear with shear rate.…”

A localized momentum constraint for non-equilibrium molecular dynamics simulations

“…As a result, the Dirac delta is often replaced by a Gaussian or other smoothed functionals. [35][36][37] As these functionals have an arbitrary analytic form, the exact equivalence between the Irving and Kirkwood 33 equations and the continuum equations is lost in this procedure. This loss of equivalence is unimportant when a point in the continuum corresponds to a large finite region in the molecular system.…”

Nonlocal viscosity kernel of mixtures

“…In order to decrease the statistical error in the further analysis we fit the data to a Lorentzian functional form where α and β are fitting parameters that depend on the fraction of A, x A , and η 0 (x A ) is the zero-frequency viscosity for k = 0. Equation (2) has been shown to fit viscosity kernel data well for a range of different noncharged single-component fluids [4][5][6] and is here extended to include the composition dependence. The result of the fitting is depicted in Fig.…”

“…The wave-vector-dependent viscosity kernel has been predicted by mode-coupling theory [7]; however, the theoretical predictions do not agree with the data from simulations [3,4]. Nevertheless, at present, the effect of the multiscale response is understood fairly well for a range of simple single-component fluids [3][4][5][6] and glasses [8,9].…”

“…The wave-vector-dependent viscosity, i.e., the viscosity kernel, accounts for the momentum flux due to a nonzero strain rate. It has been evaluated for onecomponent fluids through molecular dynamics simulations and it was found that it follows a simple functional form reasonably well for atomic, diatomic, and polymer fluids [3][4][5][6]. The wave-vector-dependent viscosity kernel has been predicted by mode-coupling theory [7]; however, the theoretical predictions do not agree with the data from simulations [3,4].…”