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Loussaief H.,Laboratoire dIngenierie Mathematique | Pasol L.,Andritz Group | Feuillebois F.,Neumann University
Quarterly Journal of Mechanics and Applied Mathematics | Year: 2015

The motion of a solid spherical particle in the flow of a viscous fluid is calculated in the framework of Stokes equations, when the Navier condition of slippage applies on the wall and the no-slip condition applies on the particle. The problem for the flow around a sphere translating and rotating in a pure shear flow is solved, from the linearity of Stokes equations, as the sum of elementary problems: a sphere held fixed in a shear flow close to a wall, a sphere translating and rotating along a wall in a fluid at rest. The creeping flow is calculated analytically using the bispherical coordinates technique that provides the fluid velocity and pressure as series. The unknown coupled infinite series of coefficients are reduced by combinations from seven to four. This simplifies the formulation compared with earlier works on the translation and rotation problems. The infinite linear system for the coefficients is then solved using an extension of Thomas algorithm that allows to calculate O(105) terms in the series. Such a high number is necessary to obtain a good accuracy at small sphere to wall gaps down to 10-5 sphere radius, in particular for a large slip on the wall. Accurate results for the force and torque on the particle are then obtained for each of the three elementary problems. On this basis, results are provided for the diffusion coefficient of a dilute suspension of freely rotating spheres parallel to a slipping wall and for the translational and rotational velocities of a freely moving sphere in a pure shear flow along such a wall. Simplified formulae are provided for application to various physical problems, like for instance the interpretation of velocity measurements at micro-scales by tracking of particles close to a hydrophobic wall. © 2015 © The Author, 2015. Published by Oxford University Press; all rights reserved. Source

Benkhaldoun F.,University of Paris 13 | Sahmim S.,Laboratoire dIngenierie Mathematique | Seaid M.,Durham University
International Journal for Numerical Methods in Fluids | Year: 2010

We discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics. © 2009 John Wiley & Sons, Ltd. Source

Messaadi A.,El Manar Campus University | Ouerfelli N.,El Manar Campus University | Das D.,Dinhata College | Hamda H.,Laboratoire dIngenierie Mathematique | Hamzaoui A.H.,Center National des Recherche en science des Materiaux
Journal of Solution Chemistry | Year: 2012

The study of physical properties of binary liquid mixtures is of great importance for understanding and characterizing intermolecular interactions. Similarly, some models attempt to correlate viscosity in liquid mixtures in order to illuminate interacting structures and peculiar behaviors. Grunberg-Nissan parameters for viscosity (η) in isobutyric acid + water mixtures over the entire range of mole fractions under atmospheric pressure and from 302.15 to 313.15 K were calculated from experimental dynamic viscosities presented in previous works. Many experimenters investigate physicochemical properties using various models to develop interpretations and conclusions. The present work comes within the framework of correlating different equations. Relationships between the Grunberg-Nissan and Arrhenius and Jouyban-Acree parameters for viscosity are shown in one critical binary mixture. © 2012 Springer Science+Business Media New York. Source

Feuillebois F.,CNRS Computer Science Laboratory for Mechanics and Engineering Sciences | Khabthani S.,Laboratoire dIngenierie Mathematique | Elasmi L.,Laboratoire dIngenierie Mathematique | Sellier A.,Ecole Polytechnique - Palaiseau
AIP Conference Proceedings | Year: 2010

The motion of particles in a viscous fluid close to a porous membrane is modelled for the case when particles are large compared with the size of pores of the membrane. The hydrodynamic interactions of one particle with the membrane are detailed here. The model involves Stokes equations for the fluid motion around the particle together with Darcy equations for the flow in the porous membrane and Stokes equations for the flow on the other side of the membrane. Boundary conditions at the fluid-membrane interface are the continuity of pressure and velocity in the normal direction and the Beavers and Joseph slip condition on the fluid side in the tangential directions. The no-slip condition applies on the particle. This problem is solved here by two different methods. The first one is an extended boundary integral method (EBIM). A Green function is derived for the flow close to a porous membrane. This function is non-symmetric, leading to difficulties hindering the application of the classical boundary integral method (BIM). Thus, an extended method is proposed, in which the unknown distribution of singularities on the particle surface is not the stress, like in the classical boundary integral method. Yet, the hydrodynamic force and torque on the particle are obtained by integrals of this distribution on the particle surface. The second method consists in searching the solution as an asymptotic expansion in term of a small parameter that is the ratio of the typical pore size to the particle size. The various boundary conditions are taken into account at successive orders: order (0) simply represents an impermeable wall without slip and order (1) an impermeable wall with a peculiar slip prescribed by order (0); at least the 3rd order is necessary to enforce all boundary conditions. The methods are applied numerically to a spherical particle and comparisons are made with earlier works in particular cases. © 2010 American Institute of Physics. Source

Feuillebois F.,CNRS Computer Science Laboratory for Mechanics and Engineering Sciences | Ghalya N.,Laboratoire dIngenierie Mathematique | Sellier A.,Ecole Polytechnique - Palaiseau | Elasmi L.,Laboratoire dIngenierie Mathematique
AIP Conference Proceedings | Year: 2011

Consider a suspension of dilute spherical particles transported in the flow of a viscous fluid along a wall. A Navier slip condition applies on the wall, in view of applications to hydrophobic walls in microchannels. The Stokes flow problem for a sphere in a quadratic shear flow is solved here by the method of bispherical coordinates. It is shown how the infinite linear system for four coupled series of coefficients may be solved with a cost that is simply proportional to the number of coefficients. Results are the force and torque on a fixed sphere and the velocities of translation and rotation of a freely moving sphere in a quadratic flow near a slip wall. The stresslet, that is the symmetric moment of surface stresses on the sphere, is also derived in view of applications to suspension rheology. Finally, expansions of the various quantities for a large distance from the wall and for a low slip length are performed on the basis of the analytical solutions, using computer algebra. Padé approximants calculated therefrom provide a good approximation. © 2011 American Institute of Physics. Source

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