Interaction of a deformable bubble with a rigid wall at moderate Reynolds numbers

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Abstract
The unsteady viscous flow induced by a deformable gas bubble approaching or receding away from a rigid boundary is investigated for moderate Reynolds numbers. The full Navier–Stokes equations were solved by means of a finite-element method. The bubble is driven by the buoyancy force. The performance of the numerical scheme is displayed for two different configurations of the flow: the bubble moves (i) in the half-space bounded by a rigid plate; (ii) in a spherical container filled with viscous fluid. Results are obtained for the evolution of the flow pattern and bubble shape for a number of values of Reynolds and Eötvös numbers: 2.2 × 10−3 < [Rscr ] < 60, 1 < [Escr ] < 360. The influence of specific values of [Rscr ][Escr ] and wall curvature on the shape of the deformable interface is thoroughly investigated. Several physical effects are included in our theory: dimpling and film formation; appearance of a concavity at the rear of the bubble for intermediate Reynolds numbers; and elongation of the bubble receding from the wall. Where possible comparisons are carried out with other experimental or numerical investigations. The good agreement achieved confirms the reliability of the numerical technique developed, of the results presented and the conclusions.