Flow-Induced Density Gradients In Microscale Flows

We report the results of non-equilibrium molecular dynamics simulations of pressure-driven flows of liquid argon in planar conduits.  At equilibrium our molecular dynamics results are in excellent agreement with those found in the literature.  In the simulations, the conduits were ~ 60 atomic diameters across with ~25,000 atoms.  Simple shear flows were generated by moving the walls of the channel and the pressure driven flows were generated by applying a body force to each of the atoms ranging from 0.01 to 0.1 pN.  When the flow rates are very small, the liquid is on the average incompressible and a parabolic profile as predicted by incompressible creeping flow equations is observed.  However, as the flow rates increases in isothermal simulations, we find that in the pressure-driven flows the molecules migrate to the low-shear-rate region in the center of the conduits and establish large radial density gradients under conditions that were previously assumed to be incompressible. The magnitude of the density gradients in the inhomogeneous shear flows increase monotonically with flow rate in the conduit under conditions such that there is no significant slip at the walls.  The migration of the atoms to the center of the flow channels results in a blunted velocity profile that deviates from the solutions to the compressible Navier-Stokes equations that predict a parabolic velocity profile and a density that is only a function of the axial position in the channel. When these same systems are subjected to linear simple shear flow at the same shear rates, aside from localized wall-induced order, there is no variation of the average density across the channel.  Hence this phenomenon is associated with the inhomogeneous or nonlinear shear in the pressure driven flows and not the magnitude of the shear rate. These results are distinctly different than simulations in which the walls were isothermal and viscous heating leads to density decrease in the center of the channel.