title: Derivation and thermodynamics of a lattice Boltzmann model with soluble amphiphilic surfactant.
abstract: We derive a lattice Boltzmann model of a ternary fluid mixture, one component of which consists of amphiphilic molecules with a rotational degree of freedom. The model was first introduced elsewhere where it was constructed on the basis of the earlier Shan-Chen type lattice Boltzmann model for binary fluids. We provide a rigorous derivation of the model from an underlying continuum kinetic theory. In particular, we show how the model can be interpreted as a discretization of a Vlasov-Boltzmann type kinetic theory for a fluid composed of two species of oppositely charged monopoles and a composite, dipolar molecule. We also derive a free-energy functional for the model, including the contribution from the amphiphiles, and confirm that the free energy is lowered during phase separation and during the formation of a stable emulsion.
authors.affiliation: Institute for Energy Technology, 2027 Kjeller, Norway. kalli.furtado@ife.no
authors.forename: Kalli
authors.initials: K
authors.lastname: Furtado
authors.forename: Roar
authors.initials: R
authors.lastname: Skartlien