  We study the fully nonlinear, nonlocal dynamics of two-dimensional
multicomponent vesicles in a shear flow with matched viscosity of the inner and
outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we
investigate dynamical patterns induced by inhomogeneous bending for a two phase
system. Numerical results reveal that there exist novel phase-treading and
tumbling mechanisms that cannot be observed for a homogeneous vesicle. In
particular, unlike the well-known steady tank-treading dynamics characterized
by a fixed inclination angle, here the phase-treading mechanism leads to
unsteady periodic dynamics with an oscillatory inclination angle. When the
average phase concentration is around 1/2, we observe tumbling dynamics even
for very low shear rate, and the excess length required for tumbling is
significantly smaller than the value for the single phase case. We summarize
our results in phase diagrams in terms of the excess length, shear rate, and
concentration of the soft phase. These findings go beyond the well known
dynamical regimes of a homogeneous vesicle and highlight the level of
complexity of vesicle dynamics in a fluid due to heterogeneous material
properties.
