Droplet size distributions in turbulent emulsions: breakup criteria and surfactant effects from direct numerical...

Lattice Boltzmann simulations of water-in-oil (W/O) type emulsions of moderate viscosity ratio (≃1/3) and with oil soluble amphiphilic surfactant were used to study the droplet size distribution in forced, steady, homogeneous turbulence, at a water volume fraction of 20%. The viscous stresses internal to the droplets were comparable to the interfacial stress (interfacial tension), and the droplet size distribution (DSD) equilibrated near the Kolmogorov scale with droplet populations in both the viscous and inertial subranges. These results were consistent with known breakup criteria for W/O and oil-in-water emulsions, showing that the maximum stable droplet diameter is proportional to the Kolmogorov scale when viscous stresses are important (in contrast to the inviscid Hinze-limit where energy loss by viscous deformation in the droplet is negligible). The droplet size distribution in the inertial subrange scaled with the known power law ~d(-10/3), as a consequence of breakup by turbulent stress fluctuations external to the droplets. When the turbulent kinetic energy was sufficiently large (with interfacial Péclet numbers above unity), we found that turbulence driven redistribution of surfactant on the interface inhibited the Marangoni effect that is otherwise induced by film draining during coalescence in more quiescent flow. The coalescence rates were therefore not sensitive to varying surfactant activity in the range we considered, and for the given turbulent kinetic energies. Furthermore, internal viscous stresses strongly influenced the breakup rates. These two effects resulted in a DSD that was insensitive to varying surfactant activity.