Lattice-Boltzmann study of spontaneous emulsification

We study the dynamics of spontaneous emulsification of an initially planar oil-water interface when surfactants are added. The thermodynamic properties of the ternary oil-water-surfactant system are modeled by a Ginzburg-Landau-type free energy. The lattice Boltzmann method is used to solve the dynamic equations. The dynamics is found to be governed by a complicated interplay of convection and diffusion as the two relevant transport mechanisms. As long as the interface is almost flat, we find the interfacial area to grow first exponentially and then linearly in time. Later finger-like structures form which grow with a constant velocity. The tip velocity is found to increase roughly linearly with the mobility of the amphiphile, and to decrease as $\nu^{-1/2}$ with the solvent viscosity ν