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.