Reversal of the transverse force on a spherical bubble rising close to a vertical wall at moderate-to-high Reynolds numbers

The flow past a clean spherical bubble translating steadily parallel to a no-slip wall in a stagnant fluid is studied numerically over a wide range of moderate to high Reynolds numbers. We focus on situations where the distance separating the bubble from the wall is smaller than the size of the bubble in order to explore the competition between viscous and inertial effects in the gap. More precisely, the range of the wall distance considered is $1.1\leq \LR \leq 2$ ($\LR$ being the distance from the bubble center to the wall normalized by the bubble radius), and that of the Reynolds number is $50\leq \Rey \leq 1000$ ($\Rey$ being based on the bubble diameter and the slip velocity). In contrast to predictions based on potential flow theory, the numerical results reveal that, when the gap is smaller than a critical value that depends on the Reynolds number, the transverse force starts to decrease with decreasing separation and may finally reverse, changing from attractive to repulsive. This effect is found to be due to the strong shear generated in the gap, which, combined with the local transverse gradient of the streamwise velocity, results in a system of two counter-rotating streamwise vortices and, consequently, a shear-induced lift pointing away from the wall. Computational results together with available high-Reynolds-number theory provide empirical expressions for the drag and transverse forces in the steady-state limit. Then the competition between the various transverse forces on a bubble bouncing close to the wall is examined, based on previously measured data for bubble trajectory. The central role of the history effects due to the misalignment between the wake and the instantaneous angle of the bubble path is confirmed. Computational results also reveal that, depending on the initial separation, a freely moving bubble may either reach a stable equilibrium position close to the wall or depart from the wall up to infinity.