Propagating hydrodynamic modes in confined fluids.

Abstract

In molecular dynamics simulations in the microcanonical ensemble (MEMD) we calculate the intermediate scattering function F(k(||),t) for a "simple" fluid confined to nanoscopic slit pores with chemically homogeneous, planar substrate surfaces. Since system properties are translationally invariant in the x-y plane, we focus on the propagation of density modes parallel with the confining substrates by choosing a two-dimensional wave vector |k(||)|=k(||)=(k(x),k(y)) for our analysis. Within the framework of classical hydrodynamics, we develop conservation laws for z-averaged fluxes of heat and momentum. Using in-plane versions of the macroscopic stress tensor and internal-energy current as constitutive equations we derive an expression for F(k(||),t) in the hydrodynamic limit depending on the thermal diffusivity D(T), the sound attenuation coefficient Gamma, the in-plane adiabatic velocity of sound v(||), and the ratio of heat capacities at constant transverse stress and volume gamma. Through a fit of F(k(||),t) in the hydrodynamic limit and its associated memory function M(k(||),t) to MEMD data, reliable values for the set [D(T),Gamma,v(||),gamma] of material coefficients can be obtained. Variations in [D(T),Gamma,v(||),gamma] with s(z) may be correlated with variations in the solvation pressure -tau(zz)-P(b) with s(z) (tau(zz) is the stress exerted by the fluid along the surface normal and P(b) is the bulk pressure) and therefore linked to stratification of the confined fluid.