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.