Vaso-occlusion, the stoppage of blood flow in sickle-cell disease, is a complex dynamical process
spanning multiple time and length scales. Motivated by recent ex vivo microfluidic measurements of
hemostasis using blood from sickle-cell patients, we develop a multiphase model that couples the kinetics
and hydrodynamics of a flowing suspension of normal and sickled cells in a fluid. We use the model to
derive expressions for the cell velocities and concentrations that quantify the hydrodynamics of hemostasis, and provide simple criteria as well as a phase diagram for occlusion, consistent with our simulations
and earlier observations.