The motion of a train of vesicles in channel flow

The inertialess motion of a train of lipid-bilayer vesicles flowing through a channel is simulated using a 3D boundary integral equation method. Steady-state results are reported for vesicles positioned concentrically inside cylindrical channels of circular, square, and rectangular cross sections. The vesicle translational velocity U and excess channel pressure drop $\Delta $p$^{\mathrm{+}}$ depend strongly on the ratio of the vesicle radius to the hydraulic radius $\lambda $ and the vesicle reduced volume $\upsilon $. ``Deflated vesicles'' of lower reduced volume $\upsilon $ are more streamlined and translate with greater velocity U relative to the mean flow velocity V. Increasing the vesicle size ($\lambda )$ increases the wall friction force and extra pressure drop $\Delta $p$^{\mathrm{+}}$, which in turn reduces the vesicle velocity U. Hydrodynamic interactions between vesicles in a periodic train are largely screened by the channel walls, in accordance with previous results for spheres and drops. The hydraulic resistance is compared across different cross sections, and a simple correction factor is proposed to unify the results. Nonlinear effects are observed when $\beta $ -- the ratio of membrane bending elasticity to viscous traction -- is changed. The simulation results show excellent agreement with available experimental measurements as well as a previously reported ``small-gap theory'' valid for large values of $\lambda $.