Modeling viscoelastic free surface and interfacial flows, with applications to the deformation of droplets and blood cells

This thesis models viscoelastic free surface and interfacial flows. Capillarity and viscoelasticity are important in many interesting problems, e.g. the deformation of droplets and blood cells, coating flows of polymer solutions, and blood flow in arteries and capillaries. The study of the combined effects of capillarity and viscoelasticity is still in its infancy due to complex physics combined with the numerical difficulties in three-dimension. This thesis extends to three-dimensional flows from the previous studies focused on two-dimensional problem.; Modeling viscoelastic free surface flows presents several challenges which include modeling the liquid viscoelasticity, locating free surface boundaries, and implementing large-scale computations. Conformation tensor models are used to model the fluid viscoelasticity because they balance generality, realistic physics, and computational cost. A new, convenient open-flow boundary condition is developed for the transport equation of the conformation tensor. The domain deformation method is used to locate both two- and three-dimensional free surfaces and interfaces by treating the mesh as an elastic pseudo-solid. In addition, an isochoric domain deformation method is developed to conserve domain volumes for certain free surface flows where the volume of a liquid domain is prescribed, such as a cell deforming in shear flow.; The equations for solving viscoelastic free surface flows are discretized by the finite element method. The non-linear discretized equations are solved by Newton's method and the resulting large set of linear algebraic equations is solved by parallel GMRES preconditioned by a new sparse approximate inverse preconditioner (SPAI). The parallel solver together with SPAI is scalable in a wide range of capillary and Weissenberg numbers; tests on benchmark viscoelastic free surface flows show that problems with millions of unknowns can be tackled on Linux clusters.; The development of viscoelastic free surface flow modeling and isochoric domain deformation method is applied to model cell (viscoelastic drop) deformation.