Yield stress fluids method to determine the pore size distribution of a porous medium

In this paper a new method is presented in order to determine the pore size distribution in a porous medium. This original technique uses the rheological properties of some non-Newtonian yield stress fluids flowing through the porous sample. This technique is based on the capillary bundle model (like the other classical methods) which, despite its apparent simplicity, is capable of properly characterizing the percolating pore size distribution. Then this distribution can be simply obtained from the measurement of the total flow rate as a function of the imposed pressure gradient. The present technique is successfully tested analytically and numerically for usual pore size distributions such as the Gaussian mono and multimodal distributions, using Bingham and Casson fluids. The technique can also be extended to any yield stress fluid and any kind of distribution

Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

In this study, a theoretical framework is developed to predict the equilibrium conditions of a non-neutrally buoyant sphere placed in a vertical conical tube as encountered in liquid rotameters. The analysis presented herein is applicable for a sphere heavier than the surrounding fluid, situated on the axis of a slightly tapered tube. The sphere is subject to the laminar flow conditions with the Reynolds numbers ranging between the Stokes type regimes up to values corresponding to slightly inertial regimes. In this work, we assume that the aperture angle of the tube is small and that the drag force is mainly due to the dissipation located in the gap between the tube and the sphere. Under these conditions, it is possible to consider the tube as locally cylindrical and we can use the results previously obtained for the correction factor of the Stokes force on a sphere subject to a Poiseuille flow in a tube of constant cross-section. We obtain an equation relating the flow rate to the vertical position of the sphere in the tube and the validity of this analysis is demonstrated by applying it to a commercially available rotameter. The present study provides a simple but sound theoretical method to calibrate such flowmeters

A BGK-type model for inelastic Boltzmann equations with internal energy.

final version available on Riv. Mat. Univ. Parma, Volume 1 - Number 2 - 2010.International audienceWe introduce a model of inelastic collisions for droplets in a spray, leading to a speci c Boltzmann kernel. Then, we build caricatures of this kernel of BGK type, in which the behavior of the first moments of the solution of the Boltzmann equation (that is, mass, momentum, directional temperatures, variance of the internal energy) are mimicked. The quality of these caricatures is tested numerically at the end of the paper

A low diffusive Lagrange-remap scheme for the simulation of violent air-water free-surface flows

36p. Submitted to Journal of Computational Physics.In 2002, Després and Lagoutiére proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutiére in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, water-water impact and finally a case of Rayleigh-Taylor instability. One of the advantage of the present interface capturing solver is its natural implementation on parallel processors or computers. In particular, we are confident on its implementation on Graphics Processing Units (GPU) with high speedups

An Eulerian finite volume solver for multi-material fluid flows with cylindrical symmetry.

International audienceIn this paper, we adapt a pre-existing 2D cartesian cell centered finite volume solver to treat the compressible 3D Euler equations with cylindrical symmetry. We then extend it to multi-material flows. Assuming cylindrical symmetry with respect to the z axis (i.e. all the functions do not depend explicitly on the angular variable $\theta$), we obtain a set of five conservation laws with source terms that can be decoupled in two systems solved on a 2D orthogonal mesh in which a cell as a torus geometry. A specific upwinding treatment of the source term is required and implemented for the stationary case. Test cases will be presented for vanishing and non-vanishing azimuthal velocity $u_{\theta}$

Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

In this study, a theoretical framework is developed to predict the equilibrium conditions of a non-neutrally buoyant sphere placed in a vertical conical tube as encountered in liquid rotameters. The analysis presented herein is applicable for a sphere heavier than the surrounding fluid, situated on the axis of a slightly tapered tube. The sphere is subject to the laminar flow conditions with the Reynolds numbers ranging between the Stokes type regimes up to values corresponding to slightly inertial regimes. In this work, we assume that the aperture angle of the tube is small and that the drag force is mainly due to the dissipation located in the gap between the tube and the sphere. Under these conditions, it is possible to consider the tube as locally cylindrical and we can use the results previously obtained for the correction factor of the Stokes force on a sphere subject to a Poiseuille flow in a tube of constant cross-section. We obtain an equation relating the flow rate to the vertical position of the sphere in the tube and the validity of this analysis is demonstrated by applying it to a commercially available rotameter. The present study provides a simple but sound theoretical method to calibrate such flowmeters

Conséquences du confinement dans le transfert de chaleur sur une sphère dans un fluide non newtonien

Le phénomène de transfert de chaleur ou de masse sur une particule sphérique en situation d’interactions hydrodynamiques et thermiques ou massiques est d’un intérêt majeur pour de nombreux problèmes rencontrés dans les procédés industriels faisant intervenir des particules en suspension [1]. Nous avons contribué par ce travail à l’étude de l’influence du confinement sur les phénomènes de transfert en présence d’un fluide de type loi de puissance. La comparaison des résultats numériques avec les calculs asymptotiques effectués par nous-mêmes et ceux obtenus par Acrivos confirment la validité des calculs. Dans le cas des fluides non newtoniens, il apparaît que la rhéofluidification est favorable aux phénomènes de transfert contrairement au cas rhéoépaississant

Nouvelle méthode de détermination de la distribution de la tailles des pores d’un milieu poreux par l’injection d’un fluide à seuil

La caractérisation des milieux poreux (M.P.) en termes de porosité, de surface spécifique, de distribution de tailles des pores etc. est un enjeu important pour de nombreuses filières industrielles : récupération assistée de pétrole, thermique du bâtiment, séquestration de CO2, stockage d'énergie ... Ainsi, les phénomènes de transports liés aux écouelments au sein des M.P. ont occupé et continuent à stimuler une forte activité de recherche aussi bien fondamentale qu'appliquée. Dans cette communication, nous présentons une méthode innovante qui s'appuie sur l'écoulement d'un fluide viscoplastique à seuil au travers d'un poreux permettant de scanner la distribution de taille de pores

Wall effects on the transportation of a cylindrical particle in power-law fluids

The present work deals with the numerical calculation of the Stokes-type drag undergone by a cylindrical particle perpendicularly to its axis in a power-law fluid. In unbounded medium, as all data are not available yet, we provide a numerical solution for the pseudoplastic fluid. Indeed, the Stokes-type solution exists because the Stokes’ paradox does not take place anymore. We show a high sensitivity of the solution to the confinement, and the appearance of the inertia in the proximity of the Newtonian case, where the Stokes’ paradox takes place. For unbounded medium, avoiding these traps, we show that the drag is zero for Newtonian and dilatant fluids. But in the bounded one, the Stokes-type regime is recovered for Newtonian and dilatant fluids. We give also a physical explanation of this effect which is due to the reduction of the hydrodynamic screen length, for pseudoplastic fluids. Once the solution of the unbounded medium has been obtained, we give a solution for the confined medium numerically and asymptotically. We also highlight the consequence of the confinement and the backflow on the settling velocity of a fiber perpendicularly to its axis in a slit. Using the dynamic mesh technique, we give the actual transportation velocity in a power-law “Poiseuille flow”, versus the confinement parameter and the fluidity index, induced by the hydrodynamic interactions