Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid body rotating flow

A single bubble is placed in a solid body rotating flow of silicon oil. From the measurement of its equilibrium position, lift and drag forces are determined. Five different silicon oils have been used, providing five different viscosities and Morton numbers. Experiments have been performed over a wide range of bubble Reynolds numbers (0.7 ≤ Re ≤ 380), Rossby numbers (0.58 ≤ Ro ≤ 26) and bubble aspect ratios (1 ≤ χ ≤ 3). For spherical bubbles, the drag coefficient at the first order is the same as that of clean spherical bubbles in a uniform flow. It noticeably increases with the local shear S = Ro−1, following a Ro−5/2 power law. The lift coefficient tends to 0.5 for large Re numbers and rapidly decreases as Re tends to zero, in agreement with existing simulations (Magnaudet and Legendre 1998). It becomes hardly measurable for Re approaching unity. When bubbles start to shrink with Re numbers decreasing slowly, drag and lift coefficients instantaneously follow their stationary curves versus Re. In the standard Eötvös Reynolds diagram, the transitions from spherical to deformed shapes slightly differ from the uniform flow case, with asymmetric shapes appearing. The aspect ratio χ for deformed bubbles increases with the Weber number following a law which lies in between the two expressions derived from the potential flow theory by Moore (1959, 1965) at low and moderate We, and the bubble orients with an angle between its minor axis and the direction of the flow that increases for low Ro. The drag coefficient increases with χ, to an extent which is well predicted by the Moore (1965) drag law at high Re and Ro numbers. The lift coefficient is a function both of χ and Re. It increases linearly with (χ− 1) at high Re in line with the inviscid theory, while in the intermediate range of Reynolds numbers, a decrease of lift with aspect ratio is observed. But the deformation is not sufficient for a reversal of lift to occur.