Department of Mathematics, UCI

The presence of surfactants, ubiquitous at most gas/liquid interfaces, has a pronounced effect on the surface tension, hence on the stress balance at the phase boundary: local variations of the capillary forces induce transport of momentum along the interface - so-called Marangoni effects. Surfactants are often soluble in one of the adjacent bulk phases, in which case there is also exchange of surfactant between the relevant bulk phase and the interface by adsorption and desorption. Along the interface surfactant is transported by convection and diffusion. Further, changes of the interfacial area due to compression or stretching cause corresponding changes in surfactant concentration.

We discuss the mathematical model governing the dynamics of such systems. This leads to the two-phase balances of mass and momentum, complemented by a species equation for both the interface and the relevant bulk phases. Within the model, the motions of the surfactant and of the adjacent bulk fluids are coupled by means of an interfacial momentum source term that represents Marangoni forces. Employing Lp-maximal regularity we obtain local (in time) strong well-posedness of this model for certain initial configurations. The proof is based on recent Lp-theory for two-phase flows without surfactant. Joint work with Gieri Simonett (Vanderbilt University, Nashville TN) and Jan Pruss (Universitat Halle-Wittenberg, Germany)