Terminal shape and velocity of a rising bubble by phase-field-based incompressible Lattice Boltzmann model

•Bubble rise is simulated using the incompressible Lattice Boltzmann model.•Effect of the Cahn–Hilliard mobility is evaluated in detail.•Effect of dynamic viscosity ratio is investigated. This article describes the simulation of three-dimensional buoyancy-driven bubble rise using a phase-field-based incompressible Lattice Boltzmann model. The effect of the Cahn–Hilliard mobility parameter, which is the rate of diffusion relaxation from non-equilibrium toward equilibrium state of chemical potential, is evaluated in detail. In contrast with previous work that pursues a high density ratio of binary fluids in the hydrodynamic equation, we apply a large dynamic viscosity ratio, together with a matched density pair and a separate compensating gas phase buoyant force, and the numerical results fit previous experimental results well. Through analysis, it is noted that for cases with moderate Reynolds number, a large value of mobility keeps a relatively sharp interface, while smaller values of mobility would result in diffusive interfacial regions. Moreover, for cases with large Reynolds number, small bubbles at the tail tend to separate more easily when the value of mobility is larger. This article offers some potentially useful details for performing phase-field-based simulations.