In various contexts such as flows within fractures, lubrication and tribology, watertightness, but also in some biomechanical contexts (cerebrospinal fluid, tissue infusion), the confined flow of one or two liquids between rough surfaces and/or a possibly deformable one are of interest.
The effective transport properties (electric conductance, hydraulic conductance, permeability, dispersion, percolation) of flows confined between rough surfaces are major issues to address. 
We analyzed the transport properties of rough compressed surfaces from realizing that this complicated problem can be decomposed into a succession of similar ones arising nearby the saddle point of the aperture field (Plouraboué et al, 2006). In these saddle points (throats), we have been able to compute the pressure drop resulting from the throats aperture as well as its local curvature (Plouraboué et al, 2004). This approach permits to evaluate the permeability between two compressed rough surface nearby the geometrical percolation threshold in watertightness context (Fluckiger et al, 2006). A similar technique has also been recently adapted to obtain a very fast permeability estimate of core porous samples (Franc et al, 2021).
We generalized this discrete asymptotic pore-network approach to the gas-liquid invasion of throats (Geoffroy et al, 2006) so as to find the invasion percolation criteria for gas invasion within a confined wetting liquid in-between two rough surfaces (Amyot et al., 2007).
We are also interested in confined bi-lubricated flows and their specific behavior within rough surfaces. Air finger in a narrow opening generating periodic bubbles.
Publications
2021
Franc, Jacques; Guibert, Romain; Horgue, Pierre; Debenest, Gérald; Plouraboué, Franck
Image-based effective medium approximation for fast permeability evaluation of porous media core samples Journal Article
In: Computational Geosciences, 25 , pp. 105–117, 2021.
Abstract | Links | BibTeX | Altmetric
@article{oatao26598,
title = {Image-based effective medium approximation for fast permeability evaluation of porous media core samples},
author = {Jacques Franc and Romain Guibert and Pierre Horgue and Gérald Debenest and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/26598/},
doi = {10.1007/s10596-020-09991-0},
year = {2021},
date = {2021-08-01},
journal = {Computational Geosciences},
volume = {25},
pages = {105--117},
publisher = {Springer Verlag (Germany)},
abstract = {An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat?s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image?based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
An image-based effective medium approximation (EMA) is developed so as to permit very fast transport properties evaluations of 3D porous media. From an image-based porous network (IBPN) built upon digital image processing of 3D binary images, we focus on throat?s local geometrical properties at the pore scale, for being the most sensible structural units which build up the local pressure. This approach is a 3D image?based extension of the critical point approach proposed in 2D fractures. We show, from analyzing various core rock samples available in the literature, that the asymptotic assumptions associated with the preeminence of critical points in throats are indeed geometrically relevant. We then describe how the image-based EMA evaluated from the conductances computed from the discrete IBPN can be reliably evaluated. The proposed method is evaluated upon the estimation of core sample permeability from binarized image obtained using X-ray tomography. Since it combines digital image treatments with statistical data post-processing without the need of computational fluid dynamics (CFD) computation, it is extremely cost efficient. The results are compared with a micro-scale Stokes flow computation in various rock samples. The sensitivity to the pore discretization also is discussed and illustrated.
2019
Bigerelle, Maxence; Plouraboué, Franck; Robache, Frederic; Jourani, Abdeljalil; Fabre, Agnes
Mechanical integrity of 3D rough surfaces during contact Journal Article
In: Coatings, 10 (1), pp. 15, 2019, (This article is an open accessarticle distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/).).
Abstract | Links | BibTeX | Altmetric
@article{oatao25673,
title = {Mechanical integrity of 3D rough surfaces during contact},
author = {Maxence Bigerelle and Franck Plouraboué and Frederic Robache and Abdeljalil Jourani and Agnes Fabre},
url = {https://oatao.univ-toulouse.fr/25673/},
doi = {10.3390/coatings10010015},
year = {2019},
date = {2019-12-01},
journal = {Coatings},
volume = {10},
number = {1},
pages = {15},
publisher = {MDPI},
abstract = {Rough surfaces are in contact locally by the peaks of roughness. At this local scale, the pressure of contact can be sharply superior to the macroscopic pressure. If the roughness is assumed to be a random morphology, a well-established observation in many practical cases, mechanical indicators built from the contact zone are then also random variables. Consequently, the probability density function (PDF) of any mechanical random variable obviously depends upon the morphological structure of the surface. The contact pressure PDF, or the probability of damage of this surface can be determined for example when plastic deformation occurs. In this study, the contact pressure PDF is modeled using a particular probability density function, the generalized Lambda distributions (GLD). The GLD are generic and polymorphic. They approach a large number of known distributions (Weibull, Normal, and Lognormal). The later were successfully used to model damage in materials. A semi-analytical model of elastic contact which takes into account the morphology of real surfaces is used to compute the contact pressure. In a first step, surfaces are simulated by Weierstrass functions which have been previously used to model a wide range of surfaces met in tribology. The Lambda distributions adequacy is qualified to model contact pressure. Using these functions, a statistical analysis allows us to extract the probability density of the maximal pressure. It turns out that this density can be described by a GLD. It is then possible to determine the probability that the contact pressure generates plastic deformation.},
note = {This article is an open accessarticle distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/).},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Rough surfaces are in contact locally by the peaks of roughness. At this local scale, the pressure of contact can be sharply superior to the macroscopic pressure. If the roughness is assumed to be a random morphology, a well-established observation in many practical cases, mechanical indicators built from the contact zone are then also random variables. Consequently, the probability density function (PDF) of any mechanical random variable obviously depends upon the morphological structure of the surface. The contact pressure PDF, or the probability of damage of this surface can be determined for example when plastic deformation occurs. In this study, the contact pressure PDF is modeled using a particular probability density function, the generalized Lambda distributions (GLD). The GLD are generic and polymorphic. They approach a large number of known distributions (Weibull, Normal, and Lognormal). The later were successfully used to model damage in materials. A semi-analytical model of elastic contact which takes into account the morphology of real surfaces is used to compute the contact pressure. In a first step, surfaces are simulated by Weierstrass functions which have been previously used to model a wide range of surfaces met in tribology. The Lambda distributions adequacy is qualified to model contact pressure. Using these functions, a statistical analysis allows us to extract the probability density of the maximal pressure. It turns out that this density can be described by a GLD. It is then possible to determine the probability that the contact pressure generates plastic deformation.
2010
Guibert, Romain; Plouraboué, Franck; Bergeon, Alain
Steady streaming confined between three-dimensional wavy surfaces Journal Article
In: Journal of Fluid Mechanics, 657 , pp. 430–455, 2010, (Thanks to Cambridge University Press. The definitive version is available at http://journals.cambridge.org. The original PDF of the article can be found at Journal of Fluid Mechanics website : http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7862904).
Abstract | Links | BibTeX | Altmetric
@article{oatao5467,
title = {Steady streaming confined between three-dimensional wavy surfaces},
author = {Romain Guibert and Franck Plouraboué and Alain Bergeon},
url = {https://oatao.univ-toulouse.fr/5467/},
doi = {10.1017/S0022112010001436},
year = {2010},
date = {2010-08-01},
journal = {Journal of Fluid Mechanics},
volume = {657},
pages = {430--455},
publisher = {Cambridge University Press},
abstract = {We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude ensuremathsigma h where ensuremathsigma $sim$ O(1), but long-wavelength variations ensuremathłambda, with h/ensuremathłambda 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel's wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.},
note = {Thanks to Cambridge University Press. The definitive version is available at http://journals.cambridge.org. The original PDF of the article can be found at Journal of Fluid Mechanics website : http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7862904},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude ensuremathsigma h where ensuremathsigma $sim$ O(1), but long-wavelength variations ensuremathłambda, with h/ensuremathłambda 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel’s wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.
Guibert, Romain; Plouraboué, Franck; Bergeon, Alain
Steady streaming confined between three-dimensional wavy surfaces Journal Article
In: Journal of Fluid Mechanics, 657 , pp. 430–455, 2010, (Thanks to Cambridge University Press editor. The definitive version is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7862904).
Abstract | Links | BibTeX | Altmetric
@article{oatao5016,
title = {Steady streaming confined between three-dimensional wavy surfaces},
author = {Romain Guibert and Franck Plouraboué and Alain Bergeon},
url = {https://oatao.univ-toulouse.fr/5016/},
doi = {10.1017/S0022112010001436},
year = {2010},
date = {2010-03-01},
journal = {Journal of Fluid Mechanics},
volume = {657},
pages = {430--455},
publisher = {Cambridge University Press},
abstract = {We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude ensuremathsigma h where ensuremathsigma $sim$ O(1), but long-wavelength variations ensuremathłambda, with h/ensuremathłambda 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel's wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.},
note = {Thanks to Cambridge University Press editor. The definitive version is available at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7862904},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude ensuremathsigma h where ensuremathsigma $sim$ O(1), but long-wavelength variations ensuremathłambda, with h/ensuremathłambda 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel’s wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number.
2008
Flukiger, Frédérique; Plouraboué, Franck; Prat, Marc
Nonuniversal conductivity exponents in continuum percolating Gaussian fractures Journal Article
In: Physical Review E, 77 (4), pp. 047101–1-047101-4, 2008, (Thanks to The American Physical Society. The definitive version is available at http://dx.doi.org/10.1103/PhysRevE.77.047101).
Abstract | Links | BibTeX | Altmetric
@article{oatao5470,
title = {Nonuniversal conductivity exponents in continuum percolating Gaussian fractures},
author = {Frédérique Flukiger and Franck Plouraboué and Marc Prat},
url = {https://oatao.univ-toulouse.fr/5470/},
doi = {10.1103/PhysRevE.77.047101},
year = {2008},
date = {2008-01-01},
journal = {Physical Review E},
volume = {77},
number = {4},
pages = {047101--1-047101-4},
publisher = {The American Physical Society},
abstract = {We study the electrical and hydraulic conductivity percolation exponents in a Gaussian fracture using the method proposed in Plouraboué et al. [Phys. Rev. E 73, 036305, 2006]. Nonuniversal conductivity percolation exponents are found: they differ from the theoretical predictions for in?nite system size for frozen power-law distributions of local conductivities, as with their ?nite size corrections. In the hydraulic case, we also ?nd that the probability density function of the conductivity follows a power-law distribution near the percolation threshold.},
note = {Thanks to The American Physical Society.
The definitive version is available at http://dx.doi.org/10.1103/PhysRevE.77.047101},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the electrical and hydraulic conductivity percolation exponents in a Gaussian fracture using the method proposed in Plouraboué et al. [Phys. Rev. E 73, 036305, 2006]. Nonuniversal conductivity percolation exponents are found: they differ from the theoretical predictions for in?nite system size for frozen power-law distributions of local conductivities, as with their ?nite size corrections. In the hydraulic case, we also ?nd that the probability density function of the conductivity follows a power-law distribution near the percolation threshold.
2007
Amyot, Olivier; Flukiger, Frédérique; Geoffroy, Sandrine; Plouraboué, Franck; Prat, Marc
Critical point network for drainage between rough surfaces Journal Article
In: Transport in Porous Media, 70 (2), pp. 257–277, 2007, (Thanks to Springer. The definitive version is available at http://www.springerlink.com. The original PDF of the article can be found at Transport in Porous Media website : http://www.springerlink.com/content/c088378t11p4880n/?MUD=MP).
Abstract | Links | BibTeX | Altmetric
@article{oatao5472,
title = {Critical point network for drainage between rough surfaces},
author = {Olivier Amyot and Frédérique Flukiger and Sandrine Geoffroy and Franck Plouraboué and Marc Prat},
url = {https://oatao.univ-toulouse.fr/5472/},
doi = {10.1007/s11242-007-9098-3},
year = {2007},
date = {2007-01-01},
urldate = {2007-01-01},
journal = {Transport in Porous Media},
volume = {70},
number = {2},
pages = {257--277},
publisher = {Springer},
abstract = {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.},
note = {Thanks to Springer. The definitive version is available at http://www.springerlink.com. The original PDF of the article can be found at Transport in Porous Media website : http://www.springerlink.com/content/c088378t11p4880n/?MUD=MP},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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.
2006
Geoffroy, Sandrine; Plouraboué, Franck; Prat, Marc; Amyot, Olivier
Quasi-static liquid-air drainage in narrow channels with variations in the gap Journal Article
In: Journal of Colloid and Interface Science, 294 (1), pp. 165–175, 2006, (Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Journal of Colloid and Interface Science website : http://www.sciencedirect.com/science/journal/00219797).
Abstract | Links | BibTeX | Altmetric
@article{oatao5479,
title = {Quasi-static liquid-air drainage in narrow channels with variations in the gap},
author = {Sandrine Geoffroy and Franck Plouraboué and Marc Prat and Olivier Amyot},
url = {https://oatao.univ-toulouse.fr/5479/},
doi = {10.1016/j.jcis.2005.07.008},
year = {2006},
date = {2006-02-01},
journal = {Journal of Colloid and Interface Science},
volume = {294},
number = {1},
pages = {165--175},
publisher = {Elsevier},
abstract = {This paper studies the shape of an air bubble quasi-statically flowing in the longitudinal direction of narrow channels. Two bottom topographies are treated, i.e., linear and quadratic variations of the gap along the transverse direction. This work analyses the main characteristics of the gas?liquid interface with respect to the wedge aspect ratio. From the convergence of asymptotic, numerical and experimental analyses, we found simple dependences for the finger width and total curvature as a function of channel aspect ratio. These results provide simple and general expressions for the pressure drop needed to overcome capillary forces and push the air finger inside the channel.},
note = {Thanks to Elsevier editor. The definitive version is available at http://www.sciencedirect.com The original PDF of the article can be found at Journal of Colloid and Interface Science website : http://www.sciencedirect.com/science/journal/00219797},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
This paper studies the shape of an air bubble quasi-statically flowing in the longitudinal direction of narrow channels. Two bottom topographies are treated, i.e., linear and quadratic variations of the gap along the transverse direction. This work analyses the main characteristics of the gas?liquid interface with respect to the wedge aspect ratio. From the convergence of asymptotic, numerical and experimental analyses, we found simple dependences for the finger width and total curvature as a function of channel aspect ratio. These results provide simple and general expressions for the pressure drop needed to overcome capillary forces and push the air finger inside the channel.
Plouraboué, Franck; Flukiger, Frédérique; Prat, Marc; Crispel, Pierre
Geodesic network method for flows between two rough surfaces in contact Journal Article
In: Physical Review E (PRE), 73 (3), pp. 036305–1, 2006.
Abstract | Links | BibTeX | Altmetric
@article{oatao5473,
title = {Geodesic network method for flows between two rough surfaces in contact},
author = {Franck Plouraboué and Frédérique Flukiger and Marc Prat and Pierre Crispel},
url = {https://oatao.univ-toulouse.fr/5473/
http://pre.aps.org/abstract/PRE/v73/i3/e036305},
doi = {10.1103/PhysRevE.73.036305},
year = {2006},
date = {2006-01-01},
urldate = {2006-01-01},
journal = {Physical Review E (PRE)},
volume = {73},
number = {3},
pages = {036305--1},
publisher = {American Physical Society},
abstract = {A discrete network method based on previous asymptotic analysis for computing fluid flows between confined rough surfaces is proposed. This random heterogeneous geodesic network method could be either applied to surfaces described by a continuous random field or finely discretized on a regular grid. This method tackles the difficult problem of fluid transport between rough surfaces in close contact. We describe the principle of the method as well as detail its numerical implementation and performances. Macroscopic conductances are computed and analyzed far from the geometrical percolation threshold. Numerical results are successfully compared with the effective medium approximation, the application of which is also studied analytically.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A discrete network method based on previous asymptotic analysis for computing fluid flows between confined rough surfaces is proposed. This random heterogeneous geodesic network method could be either applied to surfaces described by a continuous random field or finely discretized on a regular grid. This method tackles the difficult problem of fluid transport between rough surfaces in close contact. We describe the principle of the method as well as detail its numerical implementation and performances. Macroscopic conductances are computed and analyzed far from the geometrical percolation threshold. Numerical results are successfully compared with the effective medium approximation, the application of which is also studied analytically.
2005
Jacono, David Lo; Plouraboué, Franck; Bergeon, Alain
Weak-inertial flow between two rough surfaces Journal Article
In: Physics of Fluids, 17 (6), pp. 063602–1-033101-10, 2005.
Abstract | Links | BibTeX | Altmetric
@article{oatao5480,
title = {Weak-inertial flow between two rough surfaces},
author = {David Lo Jacono and Franck Plouraboué and Alain Bergeon},
url = {https://aip.scitation.org/doi/full/10.1063/1.1923347
https://oatao.univ-toulouse.fr/5480/},
doi = {10.1063/1.1923347},
year = {2005},
date = {2005-05-01},
urldate = {2005-05-01},
journal = {Physics of Fluids},
volume = {17},
number = {6},
pages = {063602--1-033101-10},
publisher = {American Institute of Physics},
abstract = {Oseen-Poiseuille equations are developed from an asymptotic formulation of the three-dimensional Navier-Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier?Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Oseen-Poiseuille equations are developed from an asymptotic formulation of the three-dimensional Navier-Stokes equations in order to study the influence of weak inertia on flows between rough surfaces. The impact of the first correction on macroscopic flow due to inertia has been determined by solving these equations numerically. From the numerical convergence of the asymptotic expansion to the three-dimensional Navier?Stokes flows, it is shown that, at the macroscopic scale, the quadratic correction to the Reynolds equation in the weak-inertial regime vanishes generalizing a similar result in porous media.
Hinch, E. John; Plouraboué, Franck
Kelvin-Helmholtz instability in a Hele-Shaw cell: Large effect from the small region near the meniscus Journal Article
In: Physics of Fluids, 17 (5), pp. 052107(1)–052107(13), 2005.
Abstract | Links | BibTeX | Altmetric
@article{oatao5489,
title = {Kelvin-Helmholtz instability in a Hele-Shaw cell: Large effect from the small region near the meniscus},
author = {E. John Hinch and Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/5489/},
doi = {10.1063/1.1914729},
year = {2005},
date = {2005-01-01},
urldate = {2005-01-01},
journal = {Physics of Fluids},
volume = {17},
number = {5},
pages = {052107(1)--052107(13)},
publisher = {American Institute of Physics},
abstract = {In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region.
2004
Plouraboué, Franck; Geoffroy, Sandrine; Prat, Marc
Conductances between confined rough walls Journal Article
In: Physics of Fluids, 16 (3), pp. 615–624, 2004.
Abstract | Links | BibTeX | Altmetric
@article{oatao5484,
title = {Conductances between confined rough walls},
author = {Franck Plouraboué and Sandrine Geoffroy and Marc Prat},
url = {https://aip.scitation.org/doi/abs/10.1063/1.1644152
https://oatao.univ-toulouse.fr/5484/},
doi = {10.1063/1.1644152},
year = {2004},
date = {2004-03-01},
urldate = {2004-03-01},
journal = {Physics of Fluids},
volume = {16},
number = {3},
pages = {615--624},
publisher = {American Institute of Physics},
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 conductivity) opens up interesting perspectives for the simulation of flows in highly complicated geometries with a large number of constrictions.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
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 conductivity) opens up interesting perspectives for the simulation of flows in highly complicated geometries with a large number of constrictions.
2002
Letalleur, Nicolas; Plouraboué, Franck; Prat, Marc
Average Flow Model of Rough Surface Lubrication: Flow Factors for Sinusoidal Surfaces Journal Article
In: Journal of Tribology, 124 (3), pp. 539–546, 2002.
Abstract | Links | BibTeX | Altmetric
@article{oatao5487,
title = {Average Flow Model of Rough Surface Lubrication: Flow Factors for Sinusoidal Surfaces},
author = {Nicolas Letalleur and Franck Plouraboué and Marc Prat},
url = {http://dx.doi.org/10.1115/1.1467084
https://oatao.univ-toulouse.fr/5487/},
doi = {10.1115/1.1467084},
year = {2002},
date = {2002-07-01},
urldate = {2002-07-01},
journal = {Journal of Tribology},
volume = {124},
number = {3},
pages = {539--546},
publisher = {American Society of Mechanical Engineers (ASME)},
abstract = {The effects of lubricant film flow, pressurized and sheared between two parallel sinusoidal wavy surfaces in sliding motion is studied analytically. Results are presented using a flow factor model which provides an average description of the surfaces roughness impact. Two distinct cases are studied in order to compare stationary or time dependent local aperture configurations. Flow factors are computed respectively for each case through spatial or spatio-temporal average, revealing striking differences. The results shed light on the relevance of the composite roughness concept. Special attention is paid to the flow factor analytical behavior when surfaces are near contact.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The effects of lubricant film flow, pressurized and sheared between two parallel sinusoidal wavy surfaces in sliding motion is studied analytically. Results are presented using a flow factor model which provides an average description of the surfaces roughness impact. Two distinct cases are studied in order to compare stationary or time dependent local aperture configurations. Flow factors are computed respectively for each case through spatial or spatio-temporal average, revealing striking differences. The results shed light on the relevance of the composite roughness concept. Special attention is paid to the flow factor analytical behavior when surfaces are near contact.
Plouraboué, Franck; Hinch, E. John
Kelvin-Helmholtz instability in a Hele-Shaw cell Journal Article
In: Physics of Fluids, 14 (3), pp. 922–929, 2002.
Abstract | Links | BibTeX | Altmetric
@article{oatao5481,
title = {Kelvin-Helmholtz instability in a Hele-Shaw cell},
author = {Franck Plouraboué and E. John Hinch},
url = {https://oatao.univ-toulouse.fr/5481/},
doi = {10.1063/1.1446884},
year = {2002},
date = {2002-03-01},
urldate = {2002-03-01},
journal = {Physics of Fluids},
volume = {14},
number = {3},
pages = {922--929},
publisher = {American Institute of Physics},
abstract = {A linear stability analysis is presented for the Kelvin-Helmholtz instability in a Hele-Shaw cell, an analysis based on the Navier-Stokes equation to improve on the previous Euler-Darcy study that Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] made of their own experiments.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A linear stability analysis is presented for the Kelvin-Helmholtz instability in a Hele-Shaw cell, an analysis based on the Navier-Stokes equation to improve on the previous Euler-Darcy study that Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] made of their own experiments.
Prat, Marc; Plouraboué, Franck; Letalleur, Nicolas
Averaged Reynolds Equation for Flows between Rough Surfaces in Sliding Motion Journal Article
In: Transport in Porous Media, 48 (3), pp. 291–313, 2002, (Thanks to Springer. The original publication is available at www.springerlink.com).
Abstract | Links | BibTeX | Altmetric
@article{oatao5486,
title = {Averaged Reynolds Equation for Flows between Rough Surfaces in Sliding Motion},
author = {Marc Prat and Franck Plouraboué and Nicolas Letalleur},
url = {https://oatao.univ-toulouse.fr/5486/},
doi = {10.1023/A:1015772525610},
year = {2002},
date = {2002-01-01},
journal = {Transport in Porous Media},
volume = {48},
number = {3},
pages = {291--313},
publisher = {Springer},
abstract = {The ?ow between rough surfaces in sliding motion with contacts between these surfaces,
is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation
at the roughness scale, an average ?ow model is obtained combining spatial and time average. Time
average, which is often omitted in previous works, is specially discussed. It is shown that the effective
transport coef?cients, traditionally termed ??ow factors? in the lubrication literature, that appear in
the average equations can be obtained from the solution to two closure problems. This allows for the
numerical determination of ?ow factors on ?rmer bases and sheds light on some arguments to the
literature. Moreover, ?uid ?ows through fractures form an important subset of problems embodied
in the present analysis, for which macroscopisation is given.},
note = {Thanks to Springer. The original publication is available at www.springerlink.com},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The ?ow between rough surfaces in sliding motion with contacts between these surfaces,
is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation
at the roughness scale, an average ?ow model is obtained combining spatial and time average. Time
average, which is often omitted in previous works, is specially discussed. It is shown that the effective
transport coef?cients, traditionally termed ??ow factors? in the lubrication literature, that appear in
the average equations can be obtained from the solution to two closure problems. This allows for the
numerical determination of ?ow factors on ?rmer bases and sheds light on some arguments to the
literature. Moreover, ?uid ?ows through fractures form an important subset of problems embodied
in the present analysis, for which macroscopisation is given.
is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation
at the roughness scale, an average ?ow model is obtained combining spatial and time average. Time
average, which is often omitted in previous works, is specially discussed. It is shown that the effective
transport coef?cients, traditionally termed ??ow factors? in the lubrication literature, that appear in
the average equations can be obtained from the solution to two closure problems. This allows for the
numerical determination of ?ow factors on ?rmer bases and sheds light on some arguments to the
literature. Moreover, ?uid ?ows through fractures form an important subset of problems embodied
in the present analysis, for which macroscopisation is given.
2001
Plouraboué, Franck; Prat, Marc; Letalleur, Nicolas
Sliding lubricated anisotropic rough surfaces Journal Article
In: Physical Review E, 64 (1), pp. 011202(1)–011202(10), 2001.
Abstract | Links | BibTeX | Altmetric
@article{oatao5492,
title = {Sliding lubricated anisotropic rough surfaces},
author = {Franck Plouraboué and Marc Prat and Nicolas Letalleur},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.64.011202
https://oatao.univ-toulouse.fr/5492/},
doi = {10.1103/PhysRevE.64.011202},
year = {2001},
date = {2001-01-01},
urldate = {2001-01-01},
journal = {Physical Review E},
volume = {64},
number = {1},
pages = {011202(1)--011202(10)},
publisher = {American Physical Society},
abstract = {The object of this paper is to study the effects of lubricant film flow, pressurized and sheared between two parallel rough surfaces in sliding motion. The influence of microscopic surface roughness on lubricant film flow macroscopic behavior is described through five nondimensional parameters called flow factors. These macroscopic transport parameters are related to the local geometry of apertures and surfaces. Short- and long-range-correlated surface roughnesses display very different macroscopic behaviors when surfaces are close to contact. These behaviors are related to underlying surface roughness parameters such as the correlation length and the self-affine Hurst exponent. The problem is numerically studied, and results are compared to some analytical asymptotic results.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The object of this paper is to study the effects of lubricant film flow, pressurized and sheared between two parallel rough surfaces in sliding motion. The influence of microscopic surface roughness on lubricant film flow macroscopic behavior is described through five nondimensional parameters called flow factors. These macroscopic transport parameters are related to the local geometry of apertures and surfaces. Short- and long-range-correlated surface roughnesses display very different macroscopic behaviors when surfaces are close to contact. These behaviors are related to underlying surface roughness parameters such as the correlation length and the self-affine Hurst exponent. The problem is numerically studied, and results are compared to some analytical asymptotic results.
Vandembroucq, Damien; Tarrats, Annie; Greffet, Jean-Jacques; Roux, Stéphane; Plouraboué, Franck
Light scattering from cold rolled aluminum surfaces Journal Article
In: Optics Communications, 187 (4-6), pp. 289–294, 2001.
Abstract | Links | BibTeX | Altmetric
@article{oatao5495,
title = {Light scattering from cold rolled aluminum surfaces},
author = {Damien Vandembroucq and Annie Tarrats and Jean-Jacques Greffet and Stéphane Roux and Franck Plouraboué},
url = {http://www.sciencedirect.com/science/journal/00304018
https://oatao.univ-toulouse.fr/5495/},
doi = {10.1016/S0030-4018(00)01136-6},
year = {2001},
date = {2001-01-01},
urldate = {2001-01-01},
journal = {Optics Communications},
volume = {187},
number = {4-6},
pages = {289--294},
publisher = {Elsevier},
abstract = {We present experimental light scattering measurements from aluminum surfaces obtained by cold rolling. We show that our results are consistent with a scale invariant description of the roughness of these surfaces. The roughness parameters that we obtain from the light scattering experiment are consistent with those obtained from atomic force microscopy measurements.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present experimental light scattering measurements from aluminum surfaces obtained by cold rolling. We show that our results are consistent with a scale invariant description of the roughness of these surfaces. The roughness parameters that we obtain from the light scattering experiment are consistent with those obtained from atomic force microscopy measurements.
Plouraboué, Franck; Bergeon, Alain; Azaïez, Mejdi
Generalized Lagrangian Coordinates for Transport and Two-Phase Flows in Heterogeneous Anisotropic Porous Media Journal Article
In: Transport in Porous Media, 44 (2), pp. 281–304, 2001.
Abstract | Links | BibTeX | Altmetric
@article{oatao5491,
title = {Generalized Lagrangian Coordinates for Transport and Two-Phase Flows in Heterogeneous Anisotropic Porous Media},
author = {Franck Plouraboué and Alain Bergeon and Mejdi Azaïez},
url = {https://oatao.univ-toulouse.fr/5491/},
doi = {10.1023/A:1010786423656},
year = {2001},
date = {2001-01-01},
urldate = {2001-01-01},
journal = {Transport in Porous Media},
volume = {44},
number = {2},
pages = {281--304},
publisher = {Springer},
abstract = {We show how Lagrangian coordinates provide an effective representation of how difficult non-linear, hyperbolic transport problems in porous media can be dealt with. Recalling Lagrangian description first, we then derive some basic but remarkable properties useful for the numerical computation of projected transport operators. We furthermore introduce new generalized Lagrangian coordinates with their application to the Darcy-Muskat two-phase flow models. We show how these generalized Lagrangian coordinates can be constructed from the global mass conservation, and that they are related to the existence of a global pressure previously de?ned in the literature about the subject. The whole representation is developed in two or three dimensions for numerical purposes, for isotropic or anisotropic heterogeneous porous media.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We show how Lagrangian coordinates provide an effective representation of how difficult non-linear, hyperbolic transport problems in porous media can be dealt with. Recalling Lagrangian description first, we then derive some basic but remarkable properties useful for the numerical computation of projected transport operators. We furthermore introduce new generalized Lagrangian coordinates with their application to the Darcy-Muskat two-phase flow models. We show how these generalized Lagrangian coordinates can be constructed from the global mass conservation, and that they are related to the existence of a global pressure previously de?ned in the literature about the subject. The whole representation is developed in two or three dimensions for numerical purposes, for isotropic or anisotropic heterogeneous porous media.
2000
Plouraboué, Franck; Kurowski, Pascal; Boffa, Jean-Marc; Hulin, Jean-Pierre; Roux, Stéphane
Experimental study of the transport properties of rough self-affine fractures Journal Article
In: Journal of Contaminant Hydrology, 46 (3-4), pp. 295–318, 2000.
Abstract | Links | BibTeX | Altmetric
@article{oatao5496,
title = {Experimental study of the transport properties of rough self-affine fractures},
author = {Franck Plouraboué and Pascal Kurowski and Jean-Marc Boffa and Jean-Pierre Hulin and Stéphane Roux},
url = {https://doi.org/10.1016/S0169-7722(00)00134-0
https://oatao.univ-toulouse.fr/5496/},
doi = {10.1016/S0169-7722(00)00134-0},
year = {2000},
date = {2000-01-01},
urldate = {2000-01-01},
journal = {Journal of Contaminant Hydrology},
volume = {46},
number = {3-4},
pages = {295--318},
publisher = {Elsevier},
abstract = {An experimental study of the transport properties of fluid-saturated joints composed of two complementary rough fracture surfaces, translated with respect to each other and brought in contact, is reported. Quantitative roughness measurements on different fractured granite samples show that the surfaces have a self-affine geometry from which the dependence of the mean aperture on the relative displacement of fracture surfaces kept in contact can be predicted. Variations of the hydraulic and electrical conductances of the joint are measured as functions of its mean aperture. A simple parallel plane model accounts for the global trend of the measurements, but significant deviations are observed when a relative lateral displacement of the surfaces is introduced. A theoretical analysis of their origin shows that they are due both to the randomness of the aperture field and to a nonzero local slope of the surface near the injection hole; the corresponding conductivity fluctuation amplitudes have power law and linear variations with the lateral displacement, and are enhanced by the radial injection geometry.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
An experimental study of the transport properties of fluid-saturated joints composed of two complementary rough fracture surfaces, translated with respect to each other and brought in contact, is reported. Quantitative roughness measurements on different fractured granite samples show that the surfaces have a self-affine geometry from which the dependence of the mean aperture on the relative displacement of fracture surfaces kept in contact can be predicted. Variations of the hydraulic and electrical conductances of the joint are measured as functions of its mean aperture. A simple parallel plane model accounts for the global trend of the measurements, but significant deviations are observed when a relative lateral displacement of the surfaces is introduced. A theoretical analysis of their origin shows that they are due both to the randomness of the aperture field and to a nonzero local slope of the surface near the injection hole; the corresponding conductivity fluctuation amplitudes have power law and linear variations with the lateral displacement, and are enhanced by the radial injection geometry.
1999
Boffa, Jean-Marc; Allain, C.; Chertcoff, R.; Hulin, Jean-Pierre; Plouraboué, Franck; Roux, Stéphane
Roughness of sandstone fracture surfaces: Profilometry and shadow length investigations Journal Article
In: The European Physical Journal B, 7 (2), pp. 179–182, 1999.
Abstract | Links | BibTeX | Altmetric
@article{oatao5497,
title = {Roughness of sandstone fracture surfaces: Profilometry and shadow length investigations},
author = {Jean-Marc Boffa and C. Allain and R. Chertcoff and Jean-Pierre Hulin and Franck Plouraboué and Stéphane Roux},
url = {https://oatao.univ-toulouse.fr/5497/},
doi = {10.1007/s100510050602},
year = {1999},
date = {1999-01-01},
urldate = {1999-01-01},
journal = {The European Physical Journal B},
volume = {7},
number = {2},
pages = {179--182},
publisher = {Springer},
abstract = {The geometrical properties of fractured sandstone surfaces were studied by measuring the length distribution of the shadows appearing under grazing illumination. Three distinct domains of variation were found: at short length scales a cut-off of self-affinity is observed due to the inter-granular rupture of sandstones, at long length scales, the number of shadows falls off very rapidly because of the non-zero illumination angle and of the finite roughness amplitude. Finally, in the intermediate domain, the shadow length distribution displays a power law decrease with an exponent related to the roughness exponent measured by mechanical profilometry. Moreover, this method is found to be more sensitive to deviations from self-affinity than usual methods.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The geometrical properties of fractured sandstone surfaces were studied by measuring the length distribution of the shadows appearing under grazing illumination. Three distinct domains of variation were found: at short length scales a cut-off of self-affinity is observed due to the inter-granular rupture of sandstones, at long length scales, the number of shadows falls off very rapidly because of the non-zero illumination angle and of the finite roughness amplitude. Finally, in the intermediate domain, the shadow length distribution displays a power law decrease with an exponent related to the roughness exponent measured by mechanical profilometry. Moreover, this method is found to be more sensitive to deviations from self-affinity than usual methods.
Plouraboué, Franck; Boehm, Matthieu
Multi-scale roughness transfer in cold metal rolling Journal Article
In: Tribology International, 32 (1), pp. 45–57, 1999.
Abstract | Links | BibTeX | Altmetric
@article{oatao5498,
title = {Multi-scale roughness transfer in cold metal rolling},
author = {Franck Plouraboué and Matthieu Boehm},
url = {http://dx.doi.org/10.1016/S0301-679X(99)00013-4
https://oatao.univ-toulouse.fr/5498/},
doi = {10.1016/S0301-679X(99)00013-4},
year = {1999},
date = {1999-01-01},
urldate = {1999-01-01},
journal = {Tribology International},
volume = {32},
number = {1},
pages = {45--57},
publisher = {Elsevier},
abstract = {We report on a comparative Atomic Force Microscope (AFM) multi-scale roughness analysis of cold rolled Al alloy and steel roll, in order to characterize the roughness transfer from the steel roll to the workpiece in cold strip rolling processes. More than three orders of length-scale magnitudes were investigated from 100 μ to 50 nm on both types of surfaces. The analysis reveals that both types of surfaces are anisotropic self-affine surfaces. Transverse and longitudinal height profiles exhibit a different roughness exponent (Hurst exponent) ζ⊥=0.93±0.03 and ζ⊥=0.5±$0.05 Different length-scale cut-offs are obtained in each direction lsup=50mm, lsup>100mm. Height and slope distributions are also computed to complement this study. The above mentionned self-affine characteresitics are found to be very similar for the roll and the strip surfaces, which suggest that roughness transfer takes place from the macroscopic (100 μm) to the very small scale (50 nm).},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We report on a comparative Atomic Force Microscope (AFM) multi-scale roughness analysis of cold rolled Al alloy and steel roll, in order to characterize the roughness transfer from the steel roll to the workpiece in cold strip rolling processes. More than three orders of length-scale magnitudes were investigated from 100 μ to 50 nm on both types of surfaces. The analysis reveals that both types of surfaces are anisotropic self-affine surfaces. Transverse and longitudinal height profiles exhibit a different roughness exponent (Hurst exponent) ζ⊥=0.93±0.03 and ζ⊥=0.5±$0.05 Different length-scale cut-offs are obtained in each direction lsup=50mm, lsup>100mm. Height and slope distributions are also computed to complement this study. The above mentionned self-affine characteresitics are found to be very similar for the roll and the strip surfaces, which suggest that roughness transfer takes place from the macroscopic (100 μm) to the very small scale (50 nm).
1998
Plouraboué, Franck
Un nouveau système de coordonnées pour les équations de Darcy-Muskat diphasiques en milieux poreux hétérogènes isotropes à deux dimensions Journal Article
In: Comptes Rendus de l’Académie des Sciences – Series IIB – Mechanics-Physics-Astronomy, 326 (12), pp. 827–832, 1998, (Thanks to Elsevier publ. The original PDF is available at http://www.sciencedirect.com/science/journal/12874620).
Abstract | Links | BibTeX | Altmetric
@article{oatao5499,
title = {Un nouveau système de coordonnées pour les équations de Darcy-Muskat diphasiques en milieux poreux hétérogènes isotropes à deux dimensions},
author = {Franck Plouraboué},
url = {https://oatao.univ-toulouse.fr/5499/},
doi = {10.1016/S1251-8069(99)80035-0},
year = {1998},
date = {1998-01-01},
journal = {Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy},
volume = {326},
number = {12},
pages = {827--832},
publisher = {Elsevier},
abstract = {Nous formulons les équations Darcy-Muskat pour les écoulements diphasiques en milieu poreux hétérogène `a l'aide d'équations non linéaires couplées entre la saturation et la fonction de courant globale (ou la pression globale). A deux dimensions, le système de coordonnées associé `a la fonction de courant globale et la pression globale monophasique équivalente dans la limite des nombres capillaires infinis permet de dire l'évolution de la saturation des phases comme unidimensionnelle. Nous montrons comment ce système de coordonnées permet à grand nombre capillaires, la mise en œuvre d'une méthode de calcul numérique performante, pour le problème diphasique complet.},
note = {Thanks to Elsevier publ. The original PDF is available at http://www.sciencedirect.com/science/journal/12874620},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Nous formulons les équations Darcy-Muskat pour les écoulements diphasiques en milieu poreux hétérogène `a l’aide d’équations non linéaires couplées entre la saturation et la fonction de courant globale (ou la pression globale). A deux dimensions, le système de coordonnées associé `a la fonction de courant globale et la pression globale monophasique équivalente dans la limite des nombres capillaires infinis permet de dire l’évolution de la saturation des phases comme unidimensionnelle. Nous montrons comment ce système de coordonnées permet à grand nombre capillaires, la mise en œuvre d’une méthode de calcul numérique performante, pour le problème diphasique complet.
Plouraboué, Franck; Hulin, Jean-Pierre; Roux, Stéphane; Koplik, Joel
Numerical study of geometrical dispersion in self-affine rough fractures Journal Article
In: Physical Review E, 58 (3), pp. 3334–3346, 1998, (Thanks to APS editor. The original PDF is available at http://pre.aps.org/).
Abstract | Links | BibTeX | Altmetric
@article{oatao5500,
title = {Numerical study of geometrical dispersion in self-affine rough fractures},
author = {Franck Plouraboué and Jean-Pierre Hulin and Stéphane Roux and Joel Koplik},
url = {https://oatao.univ-toulouse.fr/5500/},
doi = {10.1103/PhysRevE.58.3334},
year = {1998},
date = {1998-01-01},
journal = {Physical Review E},
volume = {58},
number = {3},
pages = {3334--3346},
publisher = {American Physical Society},
abstract = {We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-af?ne curve whose exponent is equal to that of the fracture surface.},
note = {Thanks to APS editor. The original PDF is available at http://pre.aps.org/},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-af?ne curve whose exponent is equal to that of the fracture surface.
Roux, Stéphane; Plouraboué, Franck; Hulin, Jean-Pierre
Tracer Dispersion in Rough Open Cracks Journal Article
In: Transport in Porous Media, 32 (1), pp. 97–116, 1998.
Abstract | Links | BibTeX | Altmetric
@article{oatao5501,
title = {Tracer Dispersion in Rough Open Cracks},
author = {Stéphane Roux and Franck Plouraboué and Jean-Pierre Hulin},
url = {https://oatao.univ-toulouse.fr/5501/},
doi = {10.1023/A:1006553902753},
year = {1998},
date = {1998-01-01},
urldate = {1998-01-01},
journal = {Transport in Porous Media},
volume = {32},
number = {1},
pages = {97--116},
publisher = {Springer},
abstract = {Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface. This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface. This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained.
1996
Plouraboué, Franck; Roux, Stéphane
Experimental study of the roughness of crumpled surfaces Journal Article
In: Physica A Statistical Mechanics and its Applications, 227 (3-4), pp. 173–182, 1996.
Abstract | Links | BibTeX | Altmetric
@article{oatao5503,
title = {Experimental study of the roughness of crumpled surfaces},
author = {Franck Plouraboué and Stéphane Roux},
url = {http://dx.doi.org/10.1016/0378-4371(95)00380-0
https://oatao.univ-toulouse.fr/5503/},
doi = {10.1016/0378-4371(95)00380-0},
year = {1996},
date = {1996-06-01},
urldate = {1996-06-01},
journal = {Physica A Statistical Mechanics and its Applications},
volume = {227},
number = {3-4},
pages = {173--182},
publisher = {Elsevier},
abstract = {We report on the experimental study of the roughness of randomly crumpled surfaces which are unfolded. This system provides a natural example of random surfaces which exhibit long-range correlations. It is shown that such rough surfaces are self-affine with a Hurst exponent H textttchar126 0.9. A simple one-dimensional model illustrates the way long-range correlations may naturally occur in the crumpling process.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We report on the experimental study of the roughness of randomly crumpled surfaces which are unfolded. This system provides a natural example of random surfaces which exhibit long-range correlations. It is shown that such rough surfaces are self-affine with a Hurst exponent H textttchar126 0.9. A simple one-dimensional model illustrates the way long-range correlations may naturally occur in the crumpling process.
Plouraboué, Franck; Winkler, Kenneth; Petitjean, Luc; Hulin, Jean-Pierre; Roux, Stéphane
Experimental study of fracture surface roughness on rocks with crack velocity Journal Article
In: Physical Review E, 53 (1), pp. 277–283, 1996.
Abstract | Links | BibTeX | Altmetric
@article{oatao5504,
title = {Experimental study of fracture surface roughness on rocks with crack velocity},
author = {Franck Plouraboué and Kenneth Winkler and Luc Petitjean and Jean-Pierre Hulin and Stéphane Roux},
url = {https://oatao.univ-toulouse.fr/5504/
http://pre.aps.org/abstract/PRE/v53/i1/p277_1},
doi = {PhysRevE.53.277},
year = {1996},
date = {1996-01-01},
urldate = {1996-01-01},
journal = {Physical Review E},
volume = {53},
number = {1},
pages = {277--283},
publisher = {American Physical Society},
abstract = {In this paper we address the question of the influence of crack velocity on the fractured surface roughness. We studied samples made of Berea sandstone, chosen for their good macroscopic homogeneity and their granular microstructure. The samples were fractured in a double cantilever geometry, which allowed for a controlled crack speed that was maintained constant for each sample using an imposed displacement quadratic in time. The range of speed covered in the experiments was 5.10-4 m/s to 2.10-1 m/s. Systematic profilometry measurements of the fractured surfaces revealed a self-affine geometry characterized by a roughness exponent, which was found to be independent of the crack speed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In this paper we address the question of the influence of crack velocity on the fractured surface roughness. We studied samples made of Berea sandstone, chosen for their good macroscopic homogeneity and their granular microstructure. The samples were fractured in a double cantilever geometry, which allowed for a controlled crack speed that was maintained constant for each sample using an imposed displacement quadratic in time. The range of speed covered in the experiments was 5.10-4 m/s to 2.10-1 m/s. Systematic profilometry measurements of the fractured surfaces revealed a self-affine geometry characterized by a roughness exponent, which was found to be independent of the crack speed.
1995
Plouraboué, Franck; Kurowski, Pascal; Hulin, Jean-Pierre; Roux, Stéphane; Schmittbuhl, Jean
Aperture of rough cracks Journal Article
In: Physical Review E, 51 (3), pp. 1675–1685, 1995.
Abstract | Links | BibTeX | Altmetric
@article{oatao5505,
title = {Aperture of rough cracks},
author = {Franck Plouraboué and Pascal Kurowski and Jean-Pierre Hulin and Stéphane Roux and Jean Schmittbuhl},
url = {http://dx.doi.org/10.1103/PhysRevE.51.1675
https://oatao.univ-toulouse.fr/5505/},
doi = {10.1103/PhysRevE.51.1675},
year = {1995},
date = {1995-03-01},
urldate = {1995-03-01},
journal = {Physical Review E},
volume = {51},
number = {3},
pages = {1675--1685},
publisher = {The American Physical Society},
abstract = {We analyse the problem of the geometrical aperture between the two faces of a crack described as a self-affine surface. We consider the contact of the two surfaces after a relative rigid-body displacement (translation and/or rotation) of one side of the crack with respect to the opposite one. A number of properties are obtained analytically and illustrated by numerical simulations on generated self-affine surfaces. The results concern the scaling of the average aperture which is shown to include a very slowly varying correction term (logarithmic with respect to the displacement) : this affects severely the dependence of the measured aperture on the displacement. These results are used to analyse experimental data obtained on a granite sample and to estimate the roughness exponent from a global measurement. This estimate is shown to agree with an analysis of the roughness based on profilometry measurements.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We analyse the problem of the geometrical aperture between the two faces of a crack described as a self-affine surface. We consider the contact of the two surfaces after a relative rigid-body displacement (translation and/or rotation) of one side of the crack with respect to the opposite one. A number of properties are obtained analytically and illustrated by numerical simulations on generated self-affine surfaces. The results concern the scaling of the average aperture which is shown to include a very slowly varying correction term (logarithmic with respect to the displacement) : this affects severely the dependence of the measured aperture on the displacement. These results are used to analyse experimental data obtained on a granite sample and to estimate the roughness exponent from a global measurement. This estimate is shown to agree with an analysis of the roughness based on profilometry measurements.
Plouraboué, Franck; Roux, Stéphane; Schmittbuhl, Jean; Vilotte, Jean-Pierre
Geometry of contact between self-affine surfaces Journal Article
In: Fractals, 3 (1), pp. 113–122, 1995.
Abstract | Links | BibTeX | Altmetric
@article{oatao11898,
title = {Geometry of contact between self-affine surfaces},
author = {Franck Plouraboué and Stéphane Roux and Jean Schmittbuhl and Jean-Pierre Vilotte},
url = {https://oatao.univ-toulouse.fr/11898/},
doi = {10.1142/S0218348X95000114},
year = {1995},
date = {1995-01-01},
urldate = {1995-01-01},
journal = {Fractals},
volume = {3},
number = {1},
pages = {113--122},
publisher = {Word scientific publishing},
abstract = {We study the geometry of the contact between two rigid self-affine surfaces. We investigate the mean shape of the surface in the vicinity of the contact point as well as the probability distribution of apertures a as a function of the distance to the contact point. The latter reveals two distinct scaling regimes which are characterized. We show that as the two surfaces are shifted with respect to each other, the contact point on one surface undergoes a "Levy walk". If u is the relative shift of the surfaces, the distance d between the two contact points (before and after the shift), scales as d ? u alpha where the exponent ensuremathalpha is shown to be equal to the roughness exponent of the surfaces.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the geometry of the contact between two rigid self-affine surfaces. We investigate the mean shape of the surface in the vicinity of the contact point as well as the probability distribution of apertures a as a function of the distance to the contact point. The latter reveals two distinct scaling regimes which are characterized. We show that as the two surfaces are shifted with respect to each other, the contact point on one surface undergoes a "Levy walk". If u is the relative shift of the surfaces, the distance d between the two contact points (before and after the shift), scales as d ? u alpha where the exponent ensuremathalpha is shown to be equal to the roughness exponent of the surfaces.