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

Nonlocal hydrodynamic model for gravity-driven transport in nanochannels

It has been established that Newton’s law of viscosity fails for fluids under strong confinement as the strain-rate varies significantly over molecular length-scales. We thereby investigate if a nonlocal shear stress accounting for the strain-rate of an adjoining region by a convolution relation with a nonlocal viscosity kernel can be employed to predict the gravity-driven isothermal flow of a Weeks–Chandler–Andersen fluid in a nanochannel. We estimate, using the local average density model, the fluid’s viscosity kernel from isotropic bulk systems of corresponding state points by the sinusoidal transverse force method. A continuum model is proposed to solve the nonlocal hydrodynamics whose solutions capture the key features and agree qualitatively with the results of non-equilibrium molecular dynamics simulations, with deviations observed mostly near the fluid–channel interface.

Electropumping of nanofluidic water by linear and angular momentum coupling: theoretical foundations and molecular dynamics simulations

In this article we review the relatively new phenomenon of electropumping in nanofluidic systems, in which nonzero net flow results when polar molecules are rotated by external electric fields. The flow is a consequence of coupling of the spin angular momentum of molecules with their linear streaming momentum. By devising confining surfaces that are asymmetric - specifically one surface is more hydrophobic compared to the other - unidirectional flow results and so pumping can be achieved without the use of pressure gradients. We first cover the historical background to this phenomenon and follow that with a detailed theoretical description of the governing hydrodynamics. Following that we summarise work that has applied this phenomenon to pump water confined to planar nanochannels, semi-functionalised single carbon nanotubes and concentric carbon nanotubes. We also report on the energy efficiency of this pumping technique by comparisons with traditional flows of planar Couette and Poiseuille flow, with the surprising conclusion that electropumping at the nanoscale is some 4 orders of magnitude more efficient than pumping by Poiseuille flow.

Microscopic Slip Boundary Conditions in Unsteady Fluid Flows

An algebraic tail in the Green-Kubo integral for the solid-fluid friction coefficient hampers its use in the determination of the slip length. A simple theory for discrete nonlocal hydrodynamics near parallel solid walls with extended friction forces is given. We explain the origin of the algebraic tail and give a solution of the plateau problem in the Green-Kubo expressions. We derive the slip boundary condition with a microscopic expression for the slip length and the hydrodynamic wall position, and assess it through simulations of an unsteady plug flow.

Measuring heat flux beyond Fourier's law

We use nonequilibrium molecular dynamics to explore the effect of shear flow on heat flux. By simulating a simple fluid in a channel bounded by tethered atoms, the heat flux is computed for two systems: a temperature driven one with no flow and a wall driven, Couette flow system. The results for the temperature driven system give Fourier's law thermal conductivity, which is shown to agree well with experiments. Through comparison of the two systems, we quantify the additional components of the heat flux parallel and normal to the walls due to shear flow. To compute the heat flux in the flow direction, the Irving-Kirkwood equations are integrated over a volume, giving the so-called volume average form, and they are also manipulated to get expressions for the surface averaged and method of planes forms. The method of planes and volume average forms are shown to give equivalent results for the heat flux when using small volumes. The heat flux in the flow direction is obtained consistently over a range of simulations, and it is shown to vary linearly with strain rate, as predicted by theory. The additional strain rate dependent component of the heat flux normal to the wall is obtained by fitting the strain rate dependence of the heat flux to the expected form. As a result, the additional terms in the thermal conductivity tensor quantified in this work should be experimentally testable.

Challenges in Nanofluidics—Beyond Navier–Stokes at the Molecular Scale

The fluid dynamics of macroscopic and microscopic systems is well developed and has been extensively validated. Its extraordinary success makes it tempting to apply Navier–Stokes fluid dynamics without modification to systems of ever decreasing dimensions as studies of nanofluidics become more prevalent. However, this can result in serious error. In this paper, we discuss several ways in which nanoconfined fluid flow differs from macroscopic flow. We give particular attention to several topics that have recently received attention in the literature: slip, spin angular momentum coupling, nonlocal stress response and density inhomogeneity. In principle, all of these effects can now be accurately modelled using validated theories. Although the basic principles are now fairly well understood, much work remains to be done in their application.