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

Centre for Molecular Simulation, Swinburne University of Technology, 

Applied Physics, School of Applied Sciences, RMIT University, 

Centre for Molecular Simulation, Swinburne University of Technology, 

G.P.O. Box 2476, Melbourne, Victoria 3001, Australia 

R. M. Puscasu ∗ and B. D. Todd † 

PO Box 218, Hawthorn, Victoria 3122, Australia 

PO Box 218, Hawthorn, Victoria 3122, Australia 

(Dated: November 2, 2018) 

P. J. Daivis ‡ 

J. S. Hansen § 

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. 

Fluid dynamics at atomic and molecular scales still present a challenge for theoreticians as well as for experi- mentalists. Molecular dynamics (MD) is a computational tool that has contributed significantly to the fundamen- tal understanding of these systems by providing informa- tion about processes not directly approachable by exper- imental studies. A central problem in the study of fluids at such small length and time scales is the computation of meaningful transport properties. Many equilibrium molecular dynamics (EMD) as well as nonequilibrium molecular dynamics (NEMD) simulations of nanofluids have been performed since the early 1980s [1–5]. In most of these simulations the stress was treated as being de- pendent of the local strain rate rather than the entire strain rate distribution in the system. Todd et al. have recently shown that in all but the simplest flows (e.g. pla- nar Couette and Poiseuille flows) and for velocity fields with high gradients in the strain rate over the width of the real space viscosity kernel, non-locality can play a significant role [6, 7]. In the case of a homogeneous fluid, 

## I. INTRODUCTION 

a local viscosity defined by Newton’s viscosity law as 

<img src='content_image/403575.jpg'>

even exhibits singularities at points where the strain rate is zero [8–11]. In Eq. (1) P$_{xy}$ ( r , t ) represents the ( x, y ) off-diagonal component of the pressure tensor, ˙ γ ( r , t ) is the shear strain rate at position r and time t , and η$_{0}$ is the local shear viscosity. In general, a nonlocal constitutive equation that allows for spatial and temporal non-locality can be expressed as [12, 13] 

<img src='content_image/403576.jpg'>

for a homogeneous fluid. In the situation where the strain rate is constant in time and only varies with respect to the spatial coordinate y , Eq. (2) can be written as 

In reciprocal space Eq. (3), can be expressed as 

<img src='content_image/403577.jpg'>

<img src='content_image/403578.jpg'>

