Conductances between confined rough walls

Abstract

Two-and three-dimensional creeping flows and diffusion transport through constricted and possibly rough surfaces are studied. Asymptotic expansions of conductances are derived as functions of the constriction local geometry. The validity range of the proposed theoretical approximations is explored through a comparison either with available exact results for specific two-dimensional aperture fields or with direct numerical computations for general three-dimensional geometries. The large validity range of the analytical expressions proposed for the hydraulic conductivity ͑and to a lesser extent for the electrical conductivity͒ opens up interesting perspectives for the simulation of flows in highly complicated geometries with a large number of constrictions.

Capillary pinching in a pinched microchannel

“…The momentum equations associated with the fluid flow are the Stokes equations since we are considering the creeping flow limit associated with zero Reynolds number. Following conventional derivations of the lubrication approximation, those equations degenerate into the Reynolds equations relating the local pressure longitudinal variations with the leading-order longitudinal component u of the velocity field u = ͑u , v , w͒, 23,24 …”

Fluid flow across a wavy channel brought in contact

“…Numerical analysis of the fluid flow through contact interfaces was carried out between real [4,47,48,17] or model rough topographies [36,14,34]. In contrast to the complexity and lack of scale separation of nominally flat realistic surface roughness, surface patterning allows to use the concept of scale separation to a certain extent and to limit the analysis to major geometrical features of the surface [40,41,35].…”

Critical point network for drainage between rough surfaces

“…This network is interesting to consider for fluid transport because, most of the viscous pressure drop between two adjacent maxima is located in saddle-points. More precisely, using an asymptotic analysis similar to the one used for the usual lubrication approach, one can find that the pressure drop is controlled by the local aperture and the Hessian matrix eigenvalues at the saddle-point Plouraboué et al (2004). Moreover, when considering two-phase flow, each saddle-point is a constriction where the aperture is minimal along the continuous path linking two maxima.…”