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

Abstract

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