Orientation and internal flow of a vesicle in tank-treading motion in shear flow.

: Deformation, orientation and internal flow of lipid bilayer vesicles in linear shear flows are investigated using phase contrast microscopy. We construct a rotating-cylinder apparatus, which can generate a linear shear flow with constant shear rates. Vesicles are prepared from 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) by the gentle hydration method. When visualizing internal flows, polystyrene tracer particles are mixed with the hydration water solution. In our observation, vesicles deform to steady ellipsoidal shapes and show constant orientations given by θ(i), which is the angle between the major axis and the flow direction. The tracer particles inside a vesicle rotate around the center of the vesicle along ellipsoidal orbits, which are homothetic to the shape of the vesicle. It is shown that the relationship between θ(i) and the swelling ratio (volume/surface ratio) S(w) agrees quantitatively with the experimental result of Abkarian et al. [Biophys. J.89, 1055 (2005)], which was obtained with vesicles in wall-bounded shear flows. It also agrees with a theoretical analysis of Keller and Skalak [J. Fluid Mech.120, 27 (1982)] and other numerical simulations. It is also shown that angular velocities of the particles near the membrane change periodically and agree quantitatively with the experimental result for the motion of a particle adhering to the membrane of a tank-treading vesicle [Kantsler and Steinberg, Phys. Rev. Lett.95, 258101 (2005)]. A statistical analysis indicates that the velocity of the internal fluid close to the membrane is not constant along the circumference, which implies the possibility of a three-dimensional flow field of the lipid molecules or an apparent stretching motion of the membrane by the effect of hidden surface area due to thermal fluctuation.