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 propertie s of the ternary oil-water-surfactant system are modeled by a Ginzburg-Land au-type free energy. The lattice Boltzmann method is used to solve the dyna mic equations. The dynamics is found to be governed by a complicated interp lay of convection and diffusion as the two relevant transport mechanisms. A s long as the interface is almost flat, we find the interfacial area to gro w first exponentially and then linearly in time. Later finger-like structur es form which grow with a constant velocity. The tip velocity is found to i ncrease roughly linearly with the mobility of the amphiphile, and to decrea se as nu(-1/2) with the solvent viscosity nu.