Numerical Modeling of Bubble-Particle Attachment in a Volume-of-Fluid Framework

A numerical method is presented to simulate bubble–particle interaction phenomena in particle-laden flows. The bubble surface is represented in an Eulerian framework by a volume-of-fluid (VOF) method, while particle motions are predicted in a Lagrangian framework. Different frameworks for describing bubble surfaces and particles make it difficult to predict the exact locations of collisions between bubbles and particles. An effective bubble, defined as having a larger diameter than the actual bubble represented by the VOF method, is introduced to predict the collision locations. Once the collision locations are determined, the attachment of particles to the bubble surface is determined using a novel numerical algorithm based on collision/induction times. The proposed numerical method is validated through simulations of a rising bubble moving through a layer of particles. The validity of the collision detection algorithm is examined by comparing the collision probability predicted by the present numerical method with that predicted from a theoretical relationship based on bubble/particle diameters. The attachment probability predicted by the present algorithm is found to agree well with that of an experiment.