  A thermodynamically consistent phase-field model is introduced for simulating
motion and shape transformation of vesicles under flow conditions. In
particular, a general slip boundary condition is used to describe the
interaction between vesicles and the wall of the fluid domain. A second-order
accurate in both space and time C0 finite element method is proposed to solve
the model governing equations. Various numerical tests confirm the convergence,
energy stability, and conservation of mass and surface area of cells of the
proposed scheme. Vesicles with different mechanical properties are also used to
explain the pathological risk for patients with sickle cell disease.
