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 Interactions hydrodynamiques entre une particule solide et une paroi plane avec condition de glissement de Navier

Abstract :  This thesis is concerned with the flow field of a viscous fluid around a solid particle embedded in a parabolic shear flow, near a solid plane wall on which a slip boundary condition applies. For a spherical particle, this flow field is first resolved by the bispherical coordinates technique. We obtain in this way the force and torque on the particle when fixed in this flow field, as well as the stresslet, that is the symmetric moment of stress. By linearity of Stokes equations, the problem of a freely moving sphere in a parabolic flow with slip on the wall is treated as a combination of the following elementary problems: a fixed sphere in a parabolic flow, a translating and a rotating sphere. We calculate in this way the stresslet for a freely moving sphere in this flow field with slip on the wall. In a second part of this work, we apply the boundary element method with the appropriate Green's tensor to solve the problem of a solid particle of any shape in the parabolic flow of a viscous fluid near a wall with slip. We recover our results for the case of a spherical particle. This method is then applied to the case of a fixed ellipsoidal particle with the same volume as that of the sphere, its axis being normal to the wall. The influence of the particle shape is deduced by comparison of the results for both particles. In the last chapter, we present novel results concerning the forces, torques, velocities and stresslets for the case of an ellipsoid with inclined axis relative to the wall ,
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Submitted on : Thursday, December 20, 2012 - 11:16:50 AM
Last modification on : Wednesday, March 27, 2019 - 4:39:25 PM
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  • HAL Id : pastel-00767656, version 1



Nejiba Ghalya.  Interactions hydrodynamiques entre une particule solide et une paroi plane avec condition de glissement de Navier. Mécanique des fluides [physics.class-ph]. Ecole Polytechnique X, 2012. Français. ⟨pastel-00767656⟩



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