Effects of nanoscale density inhomogeneities on shearing fluids

Abstract

It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system unsuitable for a comprehensive study of the effect on density inhomogeneity on nanofluidic flow. In this paper, we employ an external force compatible with periodic boundary conditions to induce the density variation, which greatly simplifies the problem when compared to flow in nonperiodic nanoconfined systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components. This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether local thermal expansion due to nonuniform viscous heating is sufficient to account for shear-induced density inhomogeneities. We also consider the local Newtonian constitutive relation relating the shear stress to the velocity gradient and show that the local model breaks down for sufficiently large density inhomogeneities over atomic length scales.

Nonlocal response functions for predicting shear flow of strongly inhomogeneous fluids. I. Sinusoidally driven shear and sinusoidally driven inhomogeneity

“…We know that thermal expansion and normal pressure differences due to shear may induce density inhomogeneities [7,12]. The shear-induced density inhomogeneity is due to the even-order contributions of F x (y).…”

“…In Ref. [7] we saw that for large values of the STF strengths, higher-order nonlinear terms are induced in the velocity profile of shearing fluids. This effect is independent of the SLF strength.…”

“…The LADM introduces a viscosity that depends nonlocally on the density but is independent of the strain rate, which is then used to define a constitutive equation for the shear pressure that depends locally on the strain rate. The LADM represents a considerable improvement over the fully local model, but it still fails to describe some features of the velocity profiles that have been observed in molecular-dynamics simulations of confined fluid flow [6,7]. Hoang and Galliero [8,9] have recently investigated the effect of density inhomogeneity on shear flow by combining simple planar shear with a sinusoidally varying potential (SVP) to create density inhomogeneities.…”

“…In a recent paper, we extended this method by combining the SLF with a sinusoidal transverse force (STF) to generate shear flow in an inhomogeneous fluid [7]. The STF method is well known as a method for studying the wave-vector-dependent viscosity, which is the Fourier transform of the spatial viscosity kernel [3,10,11].…”

A localized momentum constraint for non-equilibrium molecular dynamics simulations

“…For mass control, there are a number of particle insertion techniques such as USHER 10 and FADE 11 as well as mass control by the pycnostat. 12 Control of intermolecular separation is possible using iterative schemes which enforce constraints with algorithms such as SHAKE and its derivatives. 13 Synthetic equations of motion have been proposed to impose flow profiles which act on the entire simulation domain (i.e., the whole periodic cell 8 ).…”