We consider the response of a Newtonian fluid, saturating the pore space of a rigid isotropic porous medium, subjected to an infinitesimal oscillatory pressure gradient across the sample. We derive the analytic properties of the linear response function as well as the high- and low-frequency limits. In so doing we present a new and well-defined parameter Λ, which enters the high-frequency limit, characteristic of dynamically connected pore sizes. Using these results we construct a simple model for the response in terms of the exact high- and low-frequency parameters; the model is very successful when compared with direct numerical simulations on large lattices with randomly varying tube radii. We demonstrate the relevance of these results to the acoustic properties of non-rigid porous media, and we show how the dynamic permeability/tortuosity can be measured using superfluid 4He as the pore fluid. We derive the expected response in the case that the internal walls of the pore space are fractal in character.

No abstract

No abstract

No abstract

We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities, and both simple and chainmolecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.PACS numbers: 51.10.+y, 34.10.+x, 92.20.Bk The principal theme of this paper is a study of the nature of the boundary conditions (BC) of fluid flow past a solid surface, a crucial ingredient in any continuum fluid mechanical calculation. The BC cannot be deduced from the continuum differential equations themselves, and it is often not easy to determine them experimentally. While the normal component of the fluid velocity must vanish at an impermeable wall for kinematic reasons, the parallel component, when extrapolated toward the wall, may match that of the wall only at some distance ζ away from it. This phenomenon is known as slip and ζ is the slip length [1]. Since the pioneering work of Maxwell [2], it has been recognized that the scale of ζ for a simple dilute gas is set by the mean free path λ of the fluid molecules, with an O(1) proportionality constant for a thermalizing wall. However, for a specularly reflecting wall, the proportionality constant could become large and lead to large slip. In the limit of low fluid density, ρ, λ becomes large suggesting that ζ would be large as well. Furthermore, in this limit the continuum approximation need not hold, and it is hard to glean the nature of the BC without a detailed knowledge of the influence of the fluid-solid interaction [3]. This is indeed the situation for micro-electro-mechanical systems [4] which operate in the Knudsen regime, in which λ can be larger than the system size. Earlier molecular dynamics (MD) studies have indicated substantial velocity slip for repulsive walls and deviations in hydrodynamic velocity profiles near the wall on lowering ρ [5-8].In our MD simulations, we find that the flow profile in the middle of a channel does indeed correspond to that predicted by continuum theory, but we observe a range of behaviors near the walls. Our work provides a molecular basis for the large variability in the amount of slip observed experimentally [9]. We find that ζ is an excellent descriptor of the boundary conditions, independent of the channel width and the nature of the flow. Even at high densities, significant slip is induced on weakening the wall-fluid attraction. In the low ρ subcontinuum regime, a large ζ is found in virtually all cases, except for a chain molecule liquid and a strongly attractive wall. These two distinct classes of behavior lead to predictions amenable to experimental test. First, in a pressure driven flow, the speed with which fluid is transported shows a maximum as ρ is varied for all the large slip situations and none when the slip length remains small. Second, this maximum speed should scale linearly with the channel width for th...

A useful physical model for superfluid turbulence considers the flow to consist of a dense tangle of vortex lines which evolve and interact. It has been suggested that these vortex lines can dynamically reconnect upon close approach. Here, we consider the nonlinear Schrodinger equation model of superfluid quantum mechanics, and use numerical simulation to study this topology changing core-scale process. Our results support the idea that vortex reconnection will occur whenever filaments come within a few core lengths of one another.

We report on molecular-dynamics simulations of the low-Reynolds-number flow of Lennard-Jones fluids through a channel. Application of a pressure gradient to a single fluid produces Poiseuille flow with a no-slip boundary condition and Taylor-Aris hydrodynamic dispersion. For an immiscible twofluid system we find a (predictable) static contact angle and, when accelerated, velocity-dependent advancing-and receding-contact angles. The approximate local velocity field is obtained, in which the no-slip condition appears to break down near the contact line.PACS numbers: 47. 15.6f, 51.10.+y, 61.20.Ja Although the low-Reynolds-number flow of continuum Newtonian Auids has been successfully described by the Stokes equations for over a century, there remain a number of unsettled questions concerning the appropriate boundary conditions at solid surface. " and fluid interfaces. For example, overwhelming phenomenological evidence supports the "no-slip" condition of zero fluid velocity at a solid boundary, ' yet there is no compelling theoretical argument for why this should be the case. A problem of principle arises when a meniscus separating two immiscible fluids moves along a solid surface. When the Stokes equations are combined with the usual boundary conditions, the viscous dissipation diverges logarithmically at the contact line. This singularity indicates that the problem is not properly formulated, but at present the cure is not known. Various proposals have been advanced to yield a finite result, e.g. , a finite "slip length, " an appeal to surface roughness, nontrivial interfacial shapes near the solid, and precursor films, but no consensus exists.In these and related problems, the macroscopic flow description must be augmented with knowledge of the microscopic physics of the boundary region between the fluids. To this end, we have carried out molecular dynamics (MD) simulations ' of viscous fluid Aows past solid boundaries. We have studied systems consisting of 1536 molecules (per fluid) confined to a region of size 40-100 A, over times up to 10 sec, the computations requiring hours of central processing unit time on a Cray XMP-12. Our results indicate that even such a small system behaves in almost all respects like a continuum fluid in motion. The starting point is a standard molecular-dynamics code in which each pair of molecules interacts through a Lennard-Jones potential r r VLs(r) =4e 0 0 +rBV cut off at r =2. 5a, where BV is chosen so that the force vanishes at the cutoff. For numerical illustration, we will refer to parameters appropriate for liquid argon, where the distance and energy scales are o 3.4 A. and e/ka 120 K, the natural time unit is z=o(m/e)' 2. 16 X10 ' sec, and the molecular mass is m 40 a.u.Newton's law is numerically integrated with a fifth-order predictor-corrector scheme, with a time step of 0.005z. The molecules are initialized on an fcc lattice whose spacing is chosen to obtain the desired density, with initial velocities randomly assigned subject to a fixed temperature. The substance ...

Molecular dynamics techniques are used to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids it is found that the no-slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow-independent slip-length boundary condition. The trajectories of individual molecules in Poiseuille flow are examined, and it is also found that their average behavior is given by Taylor–Aris hydrodynamic dispersion. An immiscible two-fluid system is simulated by a species-dependent intermolecular interaction. A static meniscus is observed whose contact angle agrees with simple estimates and, when motion occurs, velocity-dependent advancing and receding angles are observed. The local velocity field near a moving contact line shows a breakdown of the no-slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan [AIChE J. 23, 131 (1977)].