A computational study of drops, capsules, cells andtheir emulsions is presented here motivated by theirdiverse applications in industries and biologicalscience. Particle deformation is the focus of thisstudy. Front-tracking method is developed toinvestigate deformation and interactions.Inertia-induced drop behavior gives rise to unusualrheological responses such as shear thickening and asign change of normal stresses in shear, and anegative elastic modulus in an oscillatingextensional flow.Simulation is also applied to explore the mechanicsof capsules and biological cells with constitutivemodels for membrane elasticity and molecular adhesionincorporated into the numerical framework. Celldeformation induces a hydrodynamic lift affectingcell adhesion to a substrate. Deformable cells detachfrom the substrate at the same bond parameters whererigid ones do not, indicating importance ofdeformation on the leukocyte adhesion cascade.
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