Model and experimental visualizations of the interaction of a bubble with an inclined wall

Abstract

In this paper we derive a model based on lubrication theory to describe the interaction of a bubble with an inclined wall. The model is an extension of the model derived by Klaseboer, Chevailier, Mate, Masbernat, Gourdon [2001. Model and experiments of a drop impinging on an immersed wall. Physics of Fluids 13(1), 45–57.] and Moraga, Drew, Larreteguy, Lahey [2005. Modeling wall-induced forces on bubbles for inclined walls. Multiphase Science and Technology 17(4), 483–505.] in the case of a horizontal wall. We consider bubbles of diameter 1–2 mm, which corresponds to high Reynolds numbers Re ∼ O ( 1 0 0 ) , and moderate deformation effects (with a Weber number of O ( 1 ) ). Predictions of the model are compared with experimental visualizations of air bubbles rising in water toward an inclined wall. The dynamical behavior of bubbles is observed to depend on the wall inclination. We find that the model reproduces the bubble trajectories for wall inclinations smaller than 55 ∘ – 60 ∘ . This critical value for the wall inclination corresponds to an experimentally observed transition in the bubble bouncing behavior, which agrees with the observations of Tsao and Koch [1997. Observations of high Reynolds number bubbles interacting with a rigid wall. Physics of Fluids 468, 271.]. We show that the main features of our lubrication-based model for rebound with an inclined wall can be expressed with a simple force model proposed by Moraga et al., suitable for use in direct numerical simulations of multiphase flow.