Numerical study of surfactant effects on the rise of a single bubble and two coaxial bubbles

A hybrid lattice Boltzmann and finite difference method is presented for two-phase flows with unequal densities and insoluble surfactants. This method simulates two-phase flows through an improved lattice Boltzmann color-gradient model, which is developed from the previous density ratio model but considers surfactant effect by incorporating dynamic surface tension and Marangoni stress, and solves surfactant transport by a finite difference method. We first use it to simulate a single bubble rise and explore the surfactant roles on bubble motion and deformation for varying Bond (Bo) and Galilei (Ga) numbers. Results show that the addition of surfactants always retards bubble motion and deformation but the retarding effect decreases with increasing Bo. As Ga increases, the retarding effect of surfactants increases due to the increased Marangoni stress and a wake vortex would arise behind the surfactant-laden bubble, which opposes the surfactant accumulation at bubble bottom. We then simulate the rise of two coaxial bubbles and study the surfactant roles on bubble coalescence for varying Ga and radius ratios of leading to trailing bubbles. It is found that the presence of surfactants delays bubble coalescence when Ga or radius ratio is relatively low, but promotes coalescence when Ga or radius ratio is high.