Dynamics of a particle attachment to an immersed bubble

We propose an extended smooth profile method which can deal with particle-dynamics dispersed in a binary fluid. The smooth profile method, originally developed for the simulation of particle transport in a homogeneous fluid, has been successfully combined with a binary fluid model based on Ginzburg-Landau free energy functional. In this approach, the three types of interfaces among particles and two fluids are treated as diffuse interfaces. By using the method, we simulated the attachment and detachment dynamics of a colloidal particle to the surface of a position fixed bubble in a Newtonian fluid under various capillary numbers. It is found that the method can reproduce the three micro-processes associated with the particle attachment ((i) particle approach, (ii) collision, (iii) sliding down on the bubble surface) (Gregory et al, 2016). The present method will make it possible to simulate a froth flotation process, where the capture of hydrophobic particles by rising bubbles is of primary importance.