  When a stationary bubble and a stationary droplet immersed in a liquid pool
are brought in contact with each other, they form a bubble-droplet aggregate.
Its equilibrium morphology and stability largely depend on the combination of
different components' surface tensions, known as spreading factor. In this
study, we look at the interaction between a rising bubble and a stationary
droplet to better understand the dynamics of coalescence and rising as well as
morphological changes for the bubble-droplet aggregate. A systematic study is
conducted on the interaction processes with various bubble sizes and spreading
factors. The current simulation framework consists of the ternary conservative
phase-field Lattice Boltzmann method (LBM) for interface tracking and the
velocity-pressure LBM for hydrodynamics, which is validated for the benchmark
cases such as liquid lens and parasitic currents around a static droplet with
several popular surface tension formulations. We further test our LBM for the
morphology changes of two droplets initially in contact with various spreading
factors and depict the final morphologies in a phase diagram. The separated,
partially engulfed and completely engulfed morphologies can be replicated by
systematically altering the sign of the spreading factors. The rising bubble
and stationary droplet interaction is simulated based on the final morphologies
obtained under stationary conditions by imposing an imaginary buoyancy force on
the rising bubble. The results indicate that the bubble-droplet aggregate with
double emulsion morphology can minimize the distotion of the bubble-droplet
aggregate and achieve a greater terminal velocity than the aggregate with
partially engulfed morphology.
