  We employ a multi-phase smoothed particle hydrodynamics (SPH) method to study
droplet dynamics in shear flow. With an extensive range of Reynolds number,
capillary number, wall confinement, and density/viscosity ratio between the
droplet and the matrix fluid, we are able to investigate systematically the
droplet dynamics such as deformation and breakup. We conduct the majority of
the simulations in two dimensions due to economical computations, while perform
a few representative simulations in three dimensions to corroborate the former.
Comparison between current results and those in literature indicates that the
SPH method adopted has an excellent accuracy and is capable of simulating
scenarios with large density or/and viscosity ratios. We generate slices of
phase diagram in five dimensions, scopes of which are unprecedented. Based on
the phase diagram, critical capillary numbers can be identified on the boundary
of different states. As a realistic application, we perform simulations with
actual parameters of water droplet in air flow to predict the critical
conditions of breakup, which is crucial in the context of atomization.
