Analysis of improved Lattice Boltzmann phase field method for soluble surfactants

In this paper we present a novel Lattice Boltzmann model for immiscible fluids with soluble surfactants adsorbing at the interface with improved numerical and extended physical properties. The numerical improvements are based on the use of an analytical representation of a regularized delta-function in the surface free energy functional for the surfactant. Furthermore, the physics of the system have been extended to differential solubility of the surfactant combined with the use of Frumkin sorption behaviour. This enables the scheme to approach more realistic systems like foams and emulsions. This novel scheme is much superior in numerical stability than our previous scheme, based on a squared gradient approximation. Furthermore, we have observed the phenomenon of interface broadening under certain conditions. This phenomenon limits the surface pressure to about 30% of the capillary pressure of a bare droplet. It remains to be investigated whether this interface broadening reflects some physical effect, as has been observed for proteins.