Development and use of interface-capturing methods for investigation of surfactant-covered drops in electric fields

This thesis investigates the development and use of interface-capturing methods for detailed simulations of surfactant-covered drops in electric fields. A mathematical model is established for the full hydrodynamic behavior of the drops, including both electric forces caused by an applied electric field and forces due to the non-uniform surface tension caused by the presence of surfactants. Equations for the electric field and for the coupled evolution of surfactant on the interface and in the bulk are also considered. Numerical methods suitable for the solution of the mathematical model are investigated. Both the level-set method and the phase-field method are used. For the level-set method, the ghost-fluid method which treats discontinuities across the interface in a sharp manner is considered and compared to the conceptually simpler continuous surface-force method. For the phase-field method, sophisticated numerical approaches including nonlinear multigrid methods on block-structured adaptive grids are used to enable simulations in full 3D. Several physical configurations are examined. It is shown how an electric field can suppress the partial coalescence phenomenon occurring when a drop coalesces with an interface. Is is demonstrated that the presence of a surfactant can considerably slow down a sedimenting drop due to inhibition of internal circulation. Conversely, an electric field speeds up the sedimentation due to stretching which leads to reduced drag. The deformation of a surfactantcovered leaky dielectric drop in an electric field is studied, and rich deformation behavior due to the complex interaction between the electric field and the surfactant is demonstrated. Finally, full 3D simulations of a drop in shear flow are performed, with particular emphasis on the influence of a soluble surfactant. It is shown that the deformation of a drop with soluble surfactant in general lies between that of a clean drop and that of a drop covered with insoluble surfactant. However, for the breakup of a drop, it is shown that for the insoluble case, the drop can break up at a earlier time compared to a clean drop, while for the soluble case, the drop can break up at a later time