Lévitation d’une particule sphérique dans un tube légèrement conique : application aux rotamètres aux faibles débits

摘要

We propose a theoretical basis on the phenomenon of levitation of a sphere in a slightly conical tube. Usingthe results of our previous calculations on the effects of the hydrodynamic interactions on the Stokes forceundergone by a sphere in Poiseuille flow of a Newtonian fluid, we obtain the stable equilibrium conditions ofthis particle according to its position in this tube. In this non inertial regime, this approach was madepossible by the use of the superposition method. It is justified because the gap between the sphere and thetube is very small. Then only the surface in the vicinity of the equator of the ball contributes to thehydrodynamic force. These results allow us to give a relation between the measured flow rate according tothe float vertical position in a tube constituting an industrial low flow rate rotameter.