  We study liquid-vapor phase separation under shear via the Shan-Chen lattice
Boltzmann model. Besides the rheological characteristics, we analyze the
Kelvin-Helmholtz(K-H) instability resulting from the tangential velocity
difference of the fluids on two sides of the interface. We discuss also the
growth behavior of droplets. The domains being close to the walls are
lamellar-ordered, where the hydrodynamic effects dominate. The patterns in the
bulk of the system are nearly isotropic, where the domain growth results mainly
from the diffusion mechanism. Both the interfacial tension and the K-H
instability make the liquid-bands near the walls tend to rupture. When the
shear rate increases, the inequivalence of evaporation in the upstream and
coagulation in the downstream of the flow as well as the role of surface
tension makes the droplets elongate obliquely. Stronger convection makes easier
the transferring of material particles so that droplets become larger.
