  We numerically investigate the hydrodynamics and membrane dynamics of
multicomponent vesicles in two strongly confined geometries. This serves as a
simplified model for red blood cells undergoing large deformations while
traversing narrow constrictions. We propose a new parameterization for the
bending modulus that remains positive for all lipid phase parameter values. For
a multicomponent vesicle passing through a stenosis, we establish connections
between various properties: lipid phase coarsening, size and flow profile of
the lubrication layers, excess pressure, and the tank-treading velocity of the
membrane. For a multicomponent vesicle passing through a contracting channel,
we find that the lipid always phase separates so that the vesicle is stiffer in
the front as it passes through the constriction. For both cases of confinement,
we find that lipid coarsening is arrested under strong confinement and proceeds
at a high rate upon relief from extreme confinement. The results may be useful
for efficient sorting lipid domains using microfluidic flows by controlled
release of vesicles passing through strong confinement
