caa a22 4500 463162706 CHVBK 20180406164752.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s11242-007-9098-3 doi (NATIONALLICENCE)springer-10.1007/s11242-007-9098-3 Critical point network for drainage between rough surfaces [Elektronische Daten] [O. Amyot, F. Flukiger, S. Geoffroy, F. Plouraboué, M. Prat] In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations. Springer Science+Business Media, Inc., 2007 Invasion percolation nationallicence Fracture nationallicence Two-phase flow nationallicence Drainage nationallicence Micro-models nationallicence Small capillary number nationallicence Lubrication nationallicence Rough surfaces nationallicence g : Gravity acceleration nationallicence h ( x , y ) : Local aperture field between surfaces nationallicence h 0 : Local aperture of critical points nationallicence h ∞ : Local aperture associated with the interface whose position along coordinate y is y∞ nationallicence H = ∂2 ij h : Is the local Hessian matrix of the aperture field nationallicence H xx & H yy : Are the Hessian principal eigenvalues nationallicence ℓ : Local width of the saddle-point throats nationallicence ℓcap : Capillary length nationallicence ℓ c : Spacial correlation length of aperture field nationallicence L : Total width of the micro-channel nationallicence Δ P : Difference of pressure between gas and liquid nationallicence Q : Volumetric flow rate per unit width nationallicence R i , i = 1,2 : Are the principal radii of curvature of the interface nationallicence R 0 : Is the in-plane radius of curvature of the interface at the origin O nationallicence y( x ) : Is the in-plane (i.e., (x,y) plane) position of the interface in direction y at coordinate x nationallicence y∞ : Is the in-plane (i.e., (x,y) plane) asymptotic position of the interface in direction y nationallicence β,β′ : Local angle associated with the slope of the upper and lower surfaces nationallicence ε : Small parameter associated with the aspect ratio of the critical points: local aperture divided by width nationallicence ε′ : Small parameter associated with the surface slopes nationallicence κ : Mean curvature of the interface nationallicence μ : Dynamic viscosity of the fluid nationallicence ρ : Fluid density nationallicence σ i : Is the root mean square roughness of surface i = 1,2 nationallicence $$\sigma=\sqrt{\sigma_1^2+\sigma_2^2}$$ : Is the composite roughness nationallicence θ,θ′ : Wettability angles nationallicence Amyot O. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut Flukiger F. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut Geoffroy S. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut Plouraboué F. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut Prat M. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut Transport in Porous Media Springer Netherlands 70/2(2007-11-01), 257-277 0169-3913 70:2<257 2007 70 11242 https://doi.org/10.1007/s11242-007-9098-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-007-9098-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Amyot O. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut NATIONALLICENCE 700 1- Flukiger F. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut NATIONALLICENCE 700 1- Geoffroy S. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut NATIONALLICENCE 700 1- Plouraboué F. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut NATIONALLICENCE 700 1- Prat M. Institut de Mécanique des Fluides, UMR CNRS-INPT-UPS n° 5502, Allée du Pr C. Soula, 31400, Toulouse, France aut NATIONALLICENCE 773 0- Transport in Porous Media Springer Netherlands 70/2(2007-11-01), 257-277 0169-3913 70:2<257 2007 70 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer