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.

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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...