Bubble rising and interaction in ternary fluid flow: a phase field study

Bubble-droplet interaction is essential in the gas-flotation technique employed in wastewater treatment. However, due to the limitations of experimental methods, the details of the fluid flow involved have not been fully understood. Therefore, a phase field model for a three-phase flow was developed to study the rise of a single bubble and bubble-droplet interactions. The fluid-fluid interfaces are tracked by the Cahn-Hilliard equation, which is coupled with the Navier-Stokes equations with an equivalent volumetric force substituted for interfacial tensions. The model was discretized using an explicit finite difference method on a half staggered grid, and the pressure velocity coupling was tackled using the projection method. The in-house code was written in Fortran and run with the help of OpenMP, a shared memory parallelism. The model was validated against experiments with gratifying agreement achieved. Bubble-droplet interaction was simulated in two distinct situations: the first features a gas bubble crossing the interface between two other phases, and the second features a gas bubble chasing from behind an oil droplet in a surrounding fluid of the third phase.