A tractable molecular theory of flow in strongly inhomogeneous fluids

Abstract

A recently introduced model is used to study several flows in fluids with large density variations over distances comparable to their molecular dimensions (strongly inhomogeneous fluids). According to our model, the local average density model (LADM), local viscosity coefficients can be assigned at each point in a strongly inhomogeneous fluid and the stress tensor retains its Newtonian form provided that the properly defined local viscosities are used. The model has been previously shown to agree with the results of molecular dynamics simulations on diffusion and flow properties in plane Couette flow. Application of this model requires determination of the molecular density profiles in the flow region. Using a successful closure for the pair distribution function, we solve the Yvon–Born–Green (YBG) equation of fluid structure in order to determine the density profiles of a fluid confined between planar micropore walls only a few molecular diameters apart. The fluid confinement produces a strongly inhomogeneous structure. Subsequently we apply LADM to set up the fluid mechanical equations for Couette flow, Poiseuille flow, and squeezing flow between parallel plates. With the use of the YBG theoretical density profiles we solve the flow equations and predict velocity profiles, stress distributions, and effective viscosities. The dependence of these quantities on the fluid inhomogeneity is described. The effective viscosity of strongly inhomogeneous fluids is found to be quite sensitive to the nature of the flow. Our squeezing flow analysis provides a first explanation of recent experimental findings on the effective viscosity of simple fluids confined in very narrow spaces.

Force measurements with the atomic force microscope: Technique, interpretation and applications

“…Though this might be a good assumption for macroscopic systems, it is questionable at molecular dimensions. Measurements with the SFA [994][995][996][997] and computer simulations [998][999][1000] showed that the viscosity of simple liquids can increase many orders of magnitude and liquids can even undergo a liquid-to-solid transition when being confined between solid walls separated only few molecular diameters; water seems to be an exception [1001,1002]. Several experiments also indicated that isolated solid surfaces induce a layering in an adjacent liquid and that the mechanical properties of the first molecular layers are different from the bulk properties [78,724,725,1003].…”

Modeling Mixture Transport at the Nanoscale: Departure from Existing Paradigms

“…Further, while no relation between fluid properties and the partial viscosity has yet been established, we propose that i w i , where is the shear viscosity of the mixture and w i is the weight fraction of species i. This result is obtained by requiring that for a uniform fluid the total shear stress on all of the components is that on the mixture as a whole, i.e., P n i 1 i d v i =dr d v=dr, where v is the mass average mixture velocity.For the nonuniform nanopore fluid, the transport properties i and D ij are nonlocal properties, expressed as functions of locally averaged densities, following the local average density model [7,11,12]. Equation (1) may be PRL 100, 236103 (2008) …”

“…For the nonuniform nanopore fluid, the transport properties i and D ij are nonlocal properties, expressed as functions of locally averaged densities, following the local average density model [7,11,12]. Equation (1) may be PRL 100, 236103 (2008) …”

Mixing of nanofluids: molecular dynamics simulations and modelling

“…It is worth noting that Newton's law of viscosity is not valid for systems where the channel width is very small, i.e. smaller than 6-7 molecular diameters [12,18]. In this case the shear viscocity varies considerably in the system and Newton's law breaks down: The shear viscocity may exhibiting singularities and even become negative [19].…”

“…One might argue that this is a drawback of the truncation. It is very interesting to note, however, that these modulations are also observed in NEMD simulations of Couette and Poiseuille flows for small channel widths [18,12]. It would be necessary to make very long molecular dynamics simulations in order to increase the signal-to-noise ratio and to determine if the modulations are also present at the nanoscale.…”