Computational study of fluid particles: Dynamics of drops, rheology of emulsions and mechanics of biological cells

This computational study of fluid particles such as drops, capsules and biological cells is motivated by their diverse applications in industrial and biological systems. Effects of particle deformation are the focus of investigation. The underlying two-fluid flow problem with a moving interface is solved using a front-tracking finite-difference direct numerical simulation method.; We first investigate the deformation and breakup of a single drop in two time-periodic extensional flows---vortex and oscillating extensional flow. Effects of flow inertia and time-periodicity are explored. An ordinary-differential-equation model based on the physics of drop deformation is used for explaining the simulation results. It is found that a natural frequency exists for a drop in time-periodic flows at finite inertia, similar to a harmonic oscillator. When the natural frequency matches with frequency of the imposed flow, the drop experiences enhanced deformation due to resonance. Large deformation at resonance may induce breakup possibly occurring in turbulent flow of emulsions with a range of length scales and frequencies. A dynamic pressure also arises due to the periodic flow at finite inertia. It leads to a negative phase of deformation. The complex phase dynamics has a significant impact on the rheology of emulsions in such flows.; We next investigate the material response of an emulsion of such drops. A numerical methodology for calculating the rheological stresses based on drop shapes is developed. We use it to study the rheology of a dilute emulsion in steady shear as well as oscillating extensional flow at finite inertia. Inertia-induced morphological change of drops gives rise to abnormal rheological responses such as shear thickening and sign change of normal stresses in shear flow, and a negative elastic modulus in oscillating extensional flow.; The front-tracking simulation is also applied to explore the mechanics of capsules and biological cells. Models for membrane elasticity and molecular adhesion are implemented into the front-tracking framework, with the purpose to study the role of deformation in leukocyte (white blood cell) adhesion cascades. The membrane model is first validated by careful comparison with high order boundary element simulations in predicting a membrane-enclosed capsule (model cell) in simple shear. A deformation-induced lateral migration of the cell due to the presence of a wall is investigated. Significant upstream-downstream asymmetry due to large deformation induces a lift force on the cell. The effects of such lift on a cell adhered to a rigid substrate is further studied. It is found that the lift gives rise to smaller contact area, fast bond dissociation and less number of bonds. Therefore, deformable cells detach from the substrate at the same bond parameters where rigid ones do not. The investigation elucidates an important effect of cell hydrodynamics on leukocyte adhesion cascades, not considered in previous investigations of cell adhesion.