Étude du mouvement libre d'une particule dans un fluide en rotation solide à faibles nombres de Reynolds : mise en évidence des forces d'histoire et d'inertie

Abstract : The motion of a spherical inclusion released in a vertical solid-body rotation flow is investigated theoretically and experimentally. Solid spheres, bubbles and drop are considered. The particle Reynolds number and the Taylor number nimber are smaller than unity. The motion equations of the inclusion are obtained by revisiting the hydrodynamic equations. The axial (vertical) motion and the horizontal motion are uncoupled, even though they are sensitive to the rotation rate of the flow. Analytical solutions of the particle motin equation are compared to experimental results obtained by releasing a particle in a rotating tank filled-up with silicone oil. For solid spheres and bubbles, both the terminal velocity and the particle ejection rate (or trapping rate) predicted by the theory agree with experiments, without any empirical adjustment. ln particular, the experimental device enables to check the validity of various theories involving solid or fluid inclusions with or without inertia or history effects. ln agreement with Miyazaki's theory (1995), the mobility tensor of Herron, Davis and Bretherton (1975), obtained by writing the fluid motion equations in the rotating frame, accurately predicts the horizontal particle trajectory, like the Boussinesq-Basset equation obtained by writing the fluid motion equations in the non-rotating frame and neglecting the horizontal contribution of inertia effects.
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Fabien Candelier. Étude du mouvement libre d'une particule dans un fluide en rotation solide à faibles nombres de Reynolds : mise en évidence des forces d'histoire et d'inertie. Autre [cond-mat.other]. Institut National Polytechnique de Lorraine, 2005. Français. ⟨NNT : 2005INPL055N⟩. ⟨tel-01749743⟩

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