Hydrodynamic coupling between a viscoelastic gas/liquid interface and a swirling vortex flow

In this thesis, we study the hydrodynamic coupling between a viscoelastic gas/liquid interface and a swirling vortex flow. In particular, we model and numerically simulate a swirling free surface flow in the presence of insoluble and soluble surfactants. All previous numerical work treated surface viscosities as constant or zero functions. Here we are the first to derive new interfacial stress boundary conditions accounting for spatial variation in both elastic and viscous properties of the surfactants, and employ the unsteady axisymmetric Navier-Stokes equations in vorticity-streamfunction form to solve for the bulk flow coupled with nonlinear boundary conditions. A tensor formulation is adopted in the derivation of the boundary conditions for the nondeforming surface. A model for the equation of state based on experimental measurement, a surfactant transport equation and its numerical stability analysis, and a numerical method for the coupling between the interface and the bulk flow dynamics are given. We carry out parameter studies to characterize the viscoelastic effects of surfactants. We compare our results with those using a clean free surface and a no-slip stationary top. In addition, we discuss the influence of surface deformation by including first-order curvature effects in the boundary conditions and the surfactant transport equation. We provide a general coordinate system transformation and a numerical method. The numerical results using uniform grid spacing and assuming small surface deformation are given and compared with the results using a nondeforming surface. The roles of the governing parameters are examined. For soluble surfactants, we give a numerical example modeling adsorption-desorption ratio as a function of surfactant concentration. All numerical computations in this thesis have been carried out on SGI Power Challenge, a shared memory multiprocessor system.