Influence of pore roughness on high-frequency permeability

Abstract

The high-frequency behavior of the fluid velocity patterns for smooth and corrugated pore channels is studied. The classical approach of Johnson et al. ͓J. Fluid Mech. 176, 379 ͑1987͔͒ for smooth geometries is obtained in different manners, thus clarifying differences with Sheng and Zhou ͓Phys. Rev. Lett. 61, 1591 ͑1988͔͒ and Avellaneda and Torquato ͓Phys. Fluids A 3, 2529 ͑1991͔͒. For wedge-shaped pore geometries, the classical approach is modified by a nonanalytic extension proposed by Achdou and Avellaneda ͓Phys. Fluids A 4, 2561 ͑1992͔͒. The dependency of the nonanalytic extension on the apex angle of the wedge was derived. Precise numerical computations for various apex angles in two-dimensional channels confirmed this theoretical dependency, which is somewhat different from the original Achdou and Avellaneda predictions. Moreover, it was found that the contribution of the singularities does not alter the parameters of the classical theory by Johnson et al.

Frequency-dependent viscous flow in channels with fractal rough surfaces

“…Remarkably, M is usually found to be almost configuration independent and close to unity, as long as the pore surface is locally smooth 19,21,22 . Experimental observations, however, indicate that pore roughness may exhibit self-similar characteristics over a wide range of length scales.…”

“…will be considered separately elsewhere, as the corrections to the universal scaling associated with this type of singularity 21,22 add-up in a non-trivial way to the effects which are the main object of study here.…”

Computation of the dynamic thermal dissipation properties of porous media by Brownian motion simulation: Application to an open-cell aluminum foam

“…[3][4][5][6][7] Finally, numerical studies based on simulations can be considered. [8][9][10][11][12][13] Each of these ways of considering these questions has advantages and disadvantages. Laboratory measurements are of indisputable values; however, their interpretation may be limited to a specific group of materials.…”

Pore Roughness Effects on Highfrequency Permeability

“…In general, both contributions are of the same order of magnitude. It can also be shown [4] that (16) can be rewritten as…”

“…The second stems from the perturbation field εN [4]. Sheng & Zhou [9] erroneously identified 2/Λ to be the first term on the righthand-side of (16), because they used the incomplete replacement ε −2ṽ → E. Note that in straight pore channels (E = e) the second contribution vanishes while the first reduces to the pore surface-to-volume ratio S p /V p .…”