  The steady motion and deformation of a lipid-bilayer vesicle translating
through a circular tube in low Reynolds number pressure-driven flow are
investigated numerically using an axisymmetric boundary element method. This
fluid-structure interaction problem is determined by three dimensionless
parameters: reduced volume (a measure of the vesicle asphericity), geometric
confinement (the ratio of the vesicle effective radius to the tube radius), and
capillary number (the ratio of viscous to bending forces). The physical
constraints of a vesicle -- fixed surface area and enclosed volume when it is
confined in a tube -- determine critical confinement beyond which it cannot
pass through without rupturing its membrane. The simulated results are
presented in a wide range of reduced volumes [0.6, 0.98] for different degrees
of confinement; the reduced volume of 0.6 mimics red blood cells. We draw a
phase diagram of vesicle shapes and propose a shape transition line separating
the parachute-like shape region from the bullet-like one in the reduced volume
versus confinement phase space. We show that the shape transition marks a
change in the behavior of vesicle mobility, especially for highly deflated
vesicles. Most importantly, high-resolution simulations make it possible for us
to examine the hydrodynamic interaction between the wall boundary and the
vesicle surface at conditions of very high confinement, thus providing the
limiting behavior of several quantities of interest, such as the thickness of
lubrication film, vesicle mobility and its length, and the extra pressure drop
due to the presence of the vesicle. This extra pressure drop holds implications
for the rheology of dilute vesicle suspensions. Furthermore, we present various
correlations and discuss a number of practical applications.
