Effect of interface contamination on particle–bubble collision

Abstract

This study focuses on the impact of the interface contamination on the collision efficiency between bubbles and inertial particles. The bubble's surface mobility has been integrated into the collision modelling by using the hydrodynamics stagnant-cap model, in which the clean angle θclean is used to characterise the interface contamination level. Direct numerical simulations have been performed for various bubble's Reynolds numbers (1≤Reb≤100), particle to bubble size ratio (0.001≤rp/rb≤0.02) and particle's Stokes numbers (0.001<Stp<1). The Lagrangian tracking was performed for the solid particles by solving the full particle trajectory equation, in order to find the critical grazing trajectory. The collision efficiency was then calculated, as the ratio of the number of particles located in the body of revolution made by critical trajectory to that of particles located in the cylinder formed by bubble's projection area. The magnitude of hydrodynamic force (buoyancy, drag, shear lift, added mass and history forces) as well as surface forces (electrostatic, Van der Waals and hydrophobic forces) are compared to propose a simplified trajectory equation. The surface contamination was found to play an important effect on the behavior of collision efficiency, especially near θclean. Analysis of collision angle showed that there is a critical angle θcrit, depending on the bubble's Reynolds number. For the bubble with θclean>θcrit, the contact point of the “grazing trajectory” can only be situated on the mobile interface, while for θclean<θcrit, the contact point may be on both mobile and immobile part of the interface and only the positive inertial effect is observed. A simple model has been proposed that makes possible the description of collision efficiency for clean or contaminated bubbles.