Development of accurate and efficient numerical methods for bubble-particle interaction

Abstract

Accurate and efficient numerical methods have been developed to simulate flow including bubble-particle interaction. First, to achieve high scalability for large computation, the Navier-Stokes equations are solved by an alternating-directional- implicit (ADI) method parallelized by a parallel diagonal dominant (PDD) algorithm. Second, the phase interface is tracked by a conservative volume-of-fluid (VOF) method. The developed numerical methods have been further improved by modeling bubble-particle interaction. New algorithms are proposed to predict that particles are attached or slide away on the bubble surface in a VOF framework. Fluid motions are predicted in an Eulerian frame, while particle motions are predicted in a Lagrangian framework. To consider bubble-particle interaction, numerical models connecting phase interfaces and solid particles are required. In this study, algorithms that are used to detect collision and determine the sliding or attachment of the particle are developed. An effective bubble is also introduced to model the bubble-particle interaction in a VOF framework. The proposed numerical method is validated through experimental cases that entail the rising of a single bubble with particles. Collision and attachment probabilities obtained from the simulation are compared to theoretical and experimental results based on bubble diameters, particle diameters, and contact angles. The particle trajectories near the bubble are presented to show differences with and without the proposed bubble-particle interaction model. The sliding and attachment of the colliding particle are observed using this model.