Laser-induced fluorescence measurements of buoyancy driven mixing in tilted tubes

The front of a light fluid rising into a miscible heavier fluid inside a long tilted tube has been analyzed by laser-induced fluorescence. Both the local concentration field and the front velocity $Vf$ have been studied in the inertial flow regime as a function of the tilt angle $θ$ for a constant density contrast $(At=4×10−3)$⁠. We demonstrate experimentally that the velocity $Vf$ is directly related to the local density contrast $Cf$ by the relation $Vf∝(Cf)0.5$⁠. This relation reflects a local instantaneous equilibrium between inertia and buoyancy; it is valid in the transient relaxation phase as well as in the quasistationary regime reached thereafter.