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A computational study of drops, capsules, cells and
their emulsions is presented here motivated by their
diverse applications in industries and biological
science. Particle deformation is the focus of this
study. Front-tracking method is developed to
investigate deformation and interactions.
Inertia-induced drop behavior gives rise to unusual
rheological responses such as shear thickening and a
sign change of normal stresses in shear, and a
negative elastic modulus in an oscillating
extensional flow.
Simulation is also applied to explore the mechanics
of capsules and biological cells with constitutive
models for membrane elasticity and molecular adhesion
incorporated into the numerical framework. Cell
deformation induces a hydrodynamic lift affecting
cell adhesion to a substrate. Deformable cells detach
from the substrate at the same bond parameters where
rigid ones do not, indicating importance of
deformation on the leukocyte adhesion cascade.

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