Interaction between two spherical bubbles rising in a viscous liquid

Abstract

The three-dimensional flow around two spherical bubbles moving in a viscous fluid is studied numerically by solving the full Navier–Stokes equations. The study considers the interaction between two bubbles for moderate Reynolds numbers (50 ≤ Re ≤ 500, Re being based on the bubble diameter) and for positions described by the separation S (2.5 ≤ S ≤ 10, S being the distance between the bubble centres normalised by the bubble radius) and the angle θ (0° ≤ θ ≤ 90°) formed between the centreline and the direction perpendicular to the direction of the motion. We provide a general description of the interaction extending the results obtained for two bubbles moving side by side (θ = 0°) by Legendre, Magnaudet & Mougin (J. Fluid Mech., vol. 497, 2003, p. 133) and for two bubbles moving in line (θ = 90°) by Yuan & Prosperetti J. Fluid Mech., vol. 278, 1994, p. 325). Simple models based on physical arguments are given for the drag and lift forces experienced by each bubble. The interaction is the combination of three effects: a potential effect, a viscous correction (Moore's correction) and a significant wake effect observed on both the drag and the transverse forces of the second bubble when located in the wake of the first one.

Hydrodynamic interaction between a pair of bubbles ascending in shear-thinning inelastic fluids

“…Experimentally, an unstable equilibrium distance can indeed be found for clean bubbles which preserve its spherical shape as increasing the Re number (i.e., rising in silicone oils) [24]. Such equilibrium distance, which has been numerically found to be dependent on the Re number [23,25], is unstable in the sense that bubbles often escape from the vertical line.…”

“…Several experimental and numerical studies of the interaction of two bubbles at intermediate Re numbers have been devoted to the construction of the bridge that joins the creeping and potential flows [13,[25][26][27]8,9]. These studies have revealed that two bubbles rising in-line follow the viscous dominated flow behavior at least up to a Reynolds number of O(1 0 0), i.e., the trailing bubble approximating the leading one.…”

Conditions for the sliding-bouncing transition for the interaction of a bubble with an inclined wall

“…In short, it could slide at constant speed or repeatedly bounce with a constant mean velocity. We characterize this final state considering also the Reynolds and Weber numbers but using the wall velocity V w such that Re w = Re term V w /V term and We w = We term (V w /V term ) 2 . The ratio V w /V term is determined experimentally.…”

“…Significant advances have been reached in recent years due to the mature understanding of the hydrodynamic forces that affect the motion of single bubbles ascending in Newtonian liquids [1]. There is a clear understanding of the effects of viscous and inertial forces around interacting bubbles [2]. Conversely, despite their omnipresence, the understanding of wall effects is still modest.…”

A microfluidic study of oil-water separation kinetics

“…During the collision, the leading droplet will induce a wake which will effect the drag force acting on the trailing droplet [24]. Depending on the magnitude of the absolute velocities of the droplets and the collision angle, the wake effect can cause a net attraction or repulsion of the droplets [25]. The magnitude of the effect increases with decreasing h. Further, as the droplets are subjected to shear flow, droplet deformation during the collision can be expected to be asymmetrical.…”