| In this thesis a model and numerical method to simulate insoluble and soluble surfactants in two phase flows is presented. In many practical multiphase flow problems, surfactants, or surface reacting agents, are present. Surfactants are absorbed from the bulk fluid as a monomolecular layer to the interfaces between fluids, which modifies the surface tension at these interfaces. The effect of surfactants is important in many real world applications, i.e. treatment of gas emboli, microfluidic applications, and electrical components.The surfactant concentration on an interface separating the fluids can be modeled with a time dependent differential equation defined on the moving and deforming interface. When the surfactants are soluble and therefore present in the bulk fluid, this equation is coupled with a partial differential equation modeling the soluble surfactant concentration in the bulk fluid on one side of the interface. The equations for the location of the interface and the surfactant concentration on the interface and in the bulk are coupled with the Navier-Stokes equations. These equations include the singular surface tension forces from the interface on the fluid, which depend on the interfacial surfactant concentration.We develop a second order numerical method based on an explicit yet Eulerian discretization of the interface and the interfacial surfactant concentration. For soluble surfactants, the bulk concentration is discretized on a uniform grid. The boundary of the bulk surfactant concentration domain is defined by the interface location, and an embedded boundary method is used to enforce the boundary condition here. A finite difference method is used to solve the Navier-Stokes equations on a regular grid with the forces from the interface spread to this grid using a regularized delta function.Drop deformation in shear flows in two dimensions is studied. The deformation of clean drops and drops in the presence of insoluble and soluble surfactants are presented. We study the effects of surfactant concentration on the deformation of the drop. In the soluble case, we look at the effect of varying parameters dealing with the adsorption and desorption of surfactant to the interface. |
