The emptying of an ideal bottle of water in a rotating frame
Résumé
Who hasn't experienced this once in his/her life? Everyone knows that to empty a bottle of water faster, all it has to do is rotate it... But is this always true? If the evolution of the glug-glug of bottles in the ideal case of a closed cylindrical tank without rotation has been widely studied in the literature since Whalley [1], the case with rotation is, to our knowledge, very little referenced. It would however be very interesting for industrial applications to know the optimal emptying regime of a cylindrical tank. We have carried out an experimental study of the emptying of a tank sealed at the top in a rotating reference frame. We found that there is an optimal rotation velocity Ω for the draining efficiency and that it is not always more efficient to rotate the water bottle (Figure 1a). Three different emptying regimes are identified, namely a bubble regime (Regime 1), a vortical air jet regime (Regime 2) and a vortex emptying regime (Regime 3). The three regimes, characterised by the shape of the air-water interface (see Figure 1b), have different draining velocity trends and thus three different draining efficiencies. The lifetime of each regime, as well as the transitions between regimes and stability depend on both the water level and Ω. From the observations made on these different experiments, a second protocol was tested to improve the emptying time.