  A numerical method using discontinuous polynomial approximations is
formulated for solving a phase-field model of two immiscible fluids with a
soluble surfactant. The scheme recovers the Langmuir adsorption isotherms at
equilibrium. Simulations of spinodal decomposition, flow through a cylinder and
flow through a sequence of pore throats show the dynamics of the flow with and
without surfactant. Finally the numerical method is used to simulate fluid
flows in the pore space of Berea sandstone obtained by micro-CT imaging.
