Geodesic network method for flows between two rough surfaces in contact

Plouraboué, Franck; Flukiger, Frédérique; Prat, Marc; Crispel, Pierre

doi:10.1103/physreve.73.036305

Cited by 8 publications

(11 citation statements)

References 20 publications

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“…This relationship is the cornerstone of a discrete network method to compute the pressure distribution inside very complex networks since the continuous mechanical equations have been integrated analytically within an asymptotic formulation to obtain this discrete version as in Plouraboué et al (2006). It is important to realize that this relationship also ignores Stokes pressure drop contributions coming from the complex flow in the vicinity of each bifurcation.…”

Section: Lubrication Approximationmentioning

confidence: 98%

A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow

2009

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The modeling of blood flows confined in micro-channels or micro-capillary beds depends on the interactions between the cell-phase, plasma and the complex geometry of the network. In the case of capillaries or channels having a high aspect ratio (their longitudinal size is much larger than their transverse one), this modeling is much simplified from the use of a continuous description of fluid viscosity as previously proposed in the literature. Phase separation or plasma skimming effect is a supplementary mechanism responsible for the relative distribution of the red blood cell's volume density in each branch of a given bifurcation. Different models have already been proposed to connect this effect to the various hydrodynamics and geometrical parameters at each bifurcation. We discuss the advantages and drawbacks of these models and compare them to an alternative approach for modeling phase distribution in complex channels networks. The main novelty of this new formulation is to show that albeit all the previous approaches seek for a local origin of the phase segregation phenomenon, it can arise from a global non-local and nonlinear structuration of the flow inside the network. This new approach describes how elementary conservation laws are sufficient principles (rather than the complex parametric models previously proposed) to provide non local phase separation. Spatial variations of the hematocrit field thus result from the topological complexity of the network as well as nonlinearities arising from solving a new free boundary problem associated with the flux and mass conservation. This network model approach could apply to model blood flow distribution either on artificial micro-models, micro-fluidic networks, or realistic reconstruction of biological micro-vascular networks.

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Section: Lubrication Approximationmentioning

confidence: 98%

A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow

2009

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“…Furthermore, this study presents the first direct comparison between local IP rules obtained on saddle-points, and experimental observations in a similar numerically generated random fracture. Finally, as indicated previously, the present paper can be considered as a follow-up of the paper by Plouraboué et al (2006), which was devoted to the computation of single-phase flow in similar systems as those considered here for the study of drainage. As we shall see, the capillary pressure threshold depends on the fluid/fluid in-plane curvature and is studied here through an asymptotic analysis.…”

Section: Introductionmentioning

confidence: 92%

“…Those simple criteria permit to identify the maxima and saddle-points. From these one can construct the network by determining the paths from maximum to maximum through the saddle-points as detailed by Plouraboué et al (2006). 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.…”

Section: Bond Network Of Critical Pointsmentioning

confidence: 99%

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Critical point network for drainage between rough surfaces

et al. 2007

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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.

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“…The method used for generating a two-dimensional short-range correlated Gaussian random field h(x, y) is the same as the one described in Plouraboué et al (2006). We focus on the impact of permeability disorder.…”

Section: Heterogeneities Generationmentioning

confidence: 99%

Stagnation Points as Loci of Solute Concentration Extrema at the Evaporative Surface of a Random Porous Medium

et al. 2018

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Evaporation of a saline solution from a porous medium often leads to the precipitation of salt at the surface of the porous medium. It is commonly observed that the crystallized salt does not form everywhere at the porous medium surface but at some specific locations. This is interpreted at the signature of spatial variations in the salt concentration at the surface of the porous medium prior to the onset of crystallization. We explore numerically the link between the ion concentration spatial variations at the surface and porous medium heterogeneities considering strongly anisotropic short-range correlated permeabil-ity Gaussian fields corresponding to a vertical layering perpendicular to the top evaporative surface for the case of the evaporation-wicking situation. It is shown that the ion concentration extrema at the surfaces correspond to stagnation points with minima corresponding to divergent stagnation points and maxima to convergent stagnation points. Counter-intuitively, the ion concentration maxima are shown to correspond to permeability minima. However, the ion concentration absolute maximum does not necessarily always correspond to the per-meability absolute minimum. More generally, the study emphasizes the key role played by the impact of heterogeneities on the velocity field induced in the medium by the evaporation process. It is also shown that the number of ion mass fraction maxima at the porous medium surface is generally much lower than the naive prediction based on the number of correlation lengths spanning the medium.

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Geodesic network method for flows between two rough surfaces in contact

Cited by 8 publications

References 20 publications

A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow

A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow

Critical point network for drainage between rough surfaces

Stagnation Points as Loci of Solute Concentration Extrema at the Evaporative Surface of a Random Porous Medium

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