The Well-Posedness Of Diffuse Interface Modeling Of Surfactants In Two-Phase Fluid Flow

Authors: Do-Quang, M., Engblom, S, Tornberg, A.-K., Amberg, G.A.
Document Type: Conference
Pubstate: Published
Journal: Int. Workshop on Wetting and evaporation: droplets of pure and complex fluids, Marseilles - June 2013
Year: 2013


In this paper, we analyze the well-posedness of the phase-field model of two immiscible fluids with a single soluble surfactant and provide strong evidence that it is mathematically ill-posed for a large set of physically relevant parameters. As a consequence, critical modifications to the model are suggested that substantially increase the domain of validity. Carefully designed numerical simulations offer informative demonstrations as to the sharpness of our theoretical results and qualities of the physical model. A fully coupled hydrodynamic case demonstrates the potential to capture also non-trivial effects on the overall flow.