  In this work, the nonlinear dynamics of a fully three-dimensional
multicomponent vesicle in shear flow are explored. Using a volume- and
area-conserving projection method coupled to a gradient-augmented level set and
surface phase method, the dynamics are systematically studied as a function of
the membrane bending rigidity difference between the components, the speed of
diffusion compared to the underlying shear flow, and the strength of the phase
domain energy compared to the bending energy. Using a pre-segregated vesicle,
three dynamics are observed: stationary phase, phase-treading, and a new
dynamic called vertical banding. These regimes are very sensitive to the
strength of the domain line energy, as the vertical banding regime is not
observed when line energy is larger than the bending energy. These findings
demonstrate that a complete understanding of multicomponent vesicle dynamics
require that the full three-dimensional system be modeled, and show the
complexity obtained when considering heterogeneous material properties.
