Direct Numerical Simulation of Bubble-Particle Interactions under Microgravity Conditions

"The interaction between a deformable bubble and a rigid particle in viscous liquids under microgravity conditions is studied by direct numerical simulation via an Arbitrary-Lagrangian-Eulerian (ALE) method. Due to the microgravity, the bubble will stay as a sphere in the fluid without external forces and its deformation is caused by the moving particle. In this study we assume the flow field is axisymmetric and the motion of the gas inside the bubble is neglected. The particle equations and the Navier-Stokes equations for the fluid are solved in a unified finite element framework. The particle obtains an impact velocity by an external force and the impact velocity is varied over a wide range. A ‘critical time scale’ T0 was identified for the interaction process. For successful contacts between particle and bubble, the time scale of their relative motion must be less than T0.INTRODUCTIONThe particle-bubble interaction is an important process in many applied industrial domains such as water treatment, froth flotation and liquid steel purification. It is a complex three phase process in that it embraces many research areas: fluid hydrodynamics, interfacial forces, particle and bubble behaviour and solution chemistry.Derjaguin and Dukhin(1961) clarified the particle-bubble interaction by introducing three-zone model for small and medium size particles. When the particle is far away from the bubble surface, the hydrodynamic forces are dominant. The particle is driven toward the bubble surface by the particle inertial and gravity. This region is regarded as Zone 1 and the interaction in this zone is a collision subprocess. As the particle gets close to the bubble, it exits a zone where the liquid flow around the bubble surface creates a tangential stream from the upper surface of the bubble toward the rear of the bubble. This is Zone 2 which is called the diffusiophoretic zone. In Zone 3, the particle is very closed to the bubble, surface forces like van der Waals, electrostatic and structural forces are considered. Contrast to Zone 1, Zone3 can be regarded as an attachment subprocess."