Some Aspects of the Lift Force on a Spherical Bubble

Several situations in which a spherical bubble experiences a lift force are examined, especially through the use of computational results obtained by solving the full Navier–Stokes equations. The lift force is computed over a wide range of Reynolds number for the case of pure shear flow, pure strain and solid body rotation. Using these results, the validity of asymptotic solutions derived in the limit of low Reynolds number or inviscid flow is discussed. A general expression of the lift force valid for low to moderate shears is proposed. It is shown that for such shears, the lift force in a complex flow can be predicted by superposing the results obtained in pure strain flow and solid body rotation flow. Finally, the interaction force experienced by two bubbles rising side-by-side is studied. The computational results reveal that, at variance with the predictions of potential theory, the sign of this force changes when the Reynolds number or the separation distance between the bubbles decreases below a critical value. All these results are discussed in terms of vorticity. The respective role played by the vorticity generated at the bubble surface and by the one that is eventually present in the unperturbed flow is emphasized.