Showing papers by "Billy D. Todd published in 1997"

Departure from navier-stokes hydrodynamics in confined liquids

Abstract: In this work we use nonequilibrium molecular dynamics (NEMD) to simulate an atomic liquid undergoing gravity-fed flow down a narrow channel. We compare the simulation results against the predictions of classical Navier-Stokes theory for two different channel widths. For a channel width of 5.1 molecular diameters, we find that the velocity profile deviates significantly from the hydrodynamic prediction. The shape of this velocity profile is found to be independent of the applied field (pressure gradient). We find that the heat flux profile does not agree with the cubic profile predicted by Navier-Stokes hydrodynamics, but shows significant oscillations located about one molecular diameter from the walls. This result differs from the earlier work of Todd and Evans [B. D. Todd and D. J. Evans, J. Chem. Phys. 103, 9804 (1995)], in which an assumption of a purely quadratic velocity profile resulted in very weak oscillations in the heat flux. We find that in narrow channels the viscosity cannot be described by a linear, local constitutive relation. However, classical Navier-Stokes behavior is approached for a channel width of g\ensuremath{\sim}10 molecular diameters.

Temperature profile for Poiseuille flow

Abstract: For planar Poiseuille flow of an atomic fluid in the weak-flow regime, we find that the classical Navier-Stokes prediction of a quartic temperature profile is incorrect. Our results, which confirm a prediction made by Baranyai, Evans, and Daivis (BED) [Phys. Rev. A 46, 7593 (1992)], indicate that near the center of the channel the temperature profile is quadratic. When the temperature profile is fitted to the theoretical predictions of BED we obtain estimates of the thermal conductivity that are in excellent agreement with accurate independent estimates of this transport coefficient. If the presence of the quadratic component of the temperature profile is ignored, the derived value of the thermal conductivity is in error by some 50%.

Poiseuille flow of molecular fluids

Abstract: We examine a generalised Navier-Stokes theory applicable to fluids composed of non-spherical molecules. We compare the theoretical predictions for flow velocity and viscosity with results obtained from nonequilibrium molecular dynamics (NEMD) simulations of a fluid undergoing gravity fed flow down a rectangular channel. We study two different fluids: one composed of spherical particles and the other composed of uniaxial molecules at two different channel widths, W = 5.1 and 10.2 molecular diameters. Our results show that aside from boundary effects due to the roughness of the atomistic walls, the generalised Navier-Stokes theory gives a reasonable qualitative account of a fluid composed of molecules that possess spin, even in a channel that is only 10.2 molecular diameters wide. In the simple fluid case, we find that classical behaviour is behaviour is approached at this same channel width ( W = 10.2) but in the W = 5.1 channel, Navier-Stokes theory begins to break down. For both channel widths we find that the assumption of a constant shear viscosity is incorrect and, further, that the viscosity in the narrow channel of 5.1 molecular diameters is probably non-local.

A study of viscosity inhomogeneity in porous media

Abstract: The theory of transport in highly inhomogeneous systems, developed recently by Pozhar and Gubbins, and the nonequilibrium molecular dynamics (NEMD) technique are employed to study the viscosity of WCA fluids confined in narrow slit pores of width 5.1 and 20σ at reduced densities ρσ3 of 0.422–0.713. Calculated quantities include the equilibrium and nonequilibrium density profiles, equilibrium pair correlation functions, flow velocity profiles, and the viscosity profiles. NEMD simulation results are compared with the theoretical predictions. The agreement is good except for the region within one molecular diameter from the walls. The viscosity was found to vary with position across the pore.

Application of transient-time correlation functions to nonequilibrium molecular-dynamics simulations of elongational flow

Abstract: The transient-time correlation function (TTCF) technique of Morriss and Evans [Mol. Phys. 54, 629 (1985); Phys. Rev. A 35, 792 (1987); Mol. Phys. 61, 1151 (1987); Phys. Rev. A 38, 4142 (1988); Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)] is applied to the case of an atomic fluid undergoing steady isothermal elongational flow. It is found that nonequilibrium molecular-dynamics TTCF calculations of the diagonal elements of the pressure tensor are extremely efficient for small applied strain rates, where the signal-to-noise ratio for the equivalent direct time-averaged pressures is far too low. At higher strain rates, TTCF is seen to faithfully reproduce the long-time steady-state values of the pressures, but is unable to account for observed transient oscillations. The technique thus provides an unambiguous means of calculating the long-time steady-state response of a fluid under steady elongational flow and opens the possibility of studying more complex molecular fluids under relatively weak flow, allowing for greater simulation time compared to the relaxation time of the fluid.

Elongational viscosities from nonequilibrium molecular dynamics simulations of oscillatory elongational flow

Abstract: We present a simple new technique to simulate the elongational flow of a simple atomic fluid by nonequilibrium molecular dynamics (NEMD). This technique involves simulating elongational flow by applying a frequency-dependent strain rate that ensures that the system attains a temporally periodic steady state. For a given magnitude of the strain rate, quantities of interest, such as the diagonal elements of the pressure tensor, and hence elongational viscosities, are then calculated by extrapolating their frequency-dependent values down to zero frequency. The zero frequency results are in excellent agreement with independent conventional NEMD calculations of these quantities. The main advantage of this technique is that it provides a convenient and consistent means of extrapolating to the zero-frequency (steady elongation) elongational viscosity, unlike the standard method, in which it may be difficult to distinguish between the transient response and the steady-state response.

Elongational viscosities from nonequilibrium molecular dynamics simulations of oscillatory elongational flow

Abstract: We present a simple new technique to simulate the elongational flow of a simple atomic fluid by nonequilibrium molecular dynamics ~NEMD!. This technique involves simulating elongational flow by applying a frequency-dependent strain rate that ensures that the system attains a temporally periodic steady state. For a given magnitude of the strain rate, quantities of interest, such as the diagonal elements of the pressure tensor, and hence elongational viscosities, are then calculated by extrapolating their frequency-dependent values down to zero frequency. The zero frequency results are in excellent agreement with independent conventional NEMD calculations of these quantities. The main advantage of this technique is that it provides a convenient and consistent means of extrapolating to the zero-frequency ~steady elongation! elongational viscosity, unlike the standard method, in which it may be difficult to distinguish between the transient response and the steady-state response. © 1997 American Institute of Physics.@S0021-9606~97!50829-4#