Wall collision of deformable bubbles in the creeping flow regime

A systematic study of the hydrodynamic mechanisms governing the collision of a rising bubble with a solid wall in the creeping flow regime (Re<1) is presented, using direct numerical simulation. The presented results reveal self-similar aspects of the bubble-wall collision with respect to the capillary number, in particular of the film between the bubble and the wall as well as of the deformation and shape of the bubble. This similarity holds despite the extreme deformation of the bubble in some of the considered cases and is shown to be independent of the approach velocity and the fluid properties, indicating that the collision of a bubble with a solid wall in the creeping flow regime is governed by the balance of viscous stresses and surface tension, while the inertia of the bubble has a negligible influence. The timescale associated with the drainage of the film separating the bubble surface and the wall is also related to the viscocapillary balance, and is found to be independent of the size of the bubble. An empirical correlation is proposed based on the presented results to a priori estimate the drainage time of this film. Because the behaviour of a bubble during film drainage is quasi-stationary, the findings associated with film drainage also apply to bubble-wall collisions outside the remit of the creeping flow regime (Re≫1).