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Dynamics of Fluid Vesicles in Oscillatory Shear Flow

The dynamics of fluid vesicles in oscillatory shear flow was studied using differential equations of two variables: the Taylor deformation parameter and inclination angle $θ$. In a steady shear flow with a low viscosity $η_{\rm {in}}$ of internal fluid, the vesicles exhibit steady tank-treading motion with a constant inclination angle $θ_0$. In the oscillatory flow with a low shear frequency, $θ$ oscillates between $\pm θ_0$ or around $θ_0$ for zero or finite mean shear rate $\dotγ_{\rm m}$, respectively. As shear frequency $f_γ$ increases, the vesicle oscillation becomes delayed with respect to the shear oscillation, and the oscillation amplitude decreases. At high $f_γ$ with $\dotγ_{\rm m}=0$, another limit-cycle oscillation between $θ_0-π$ and $-θ_0$ is found to appear. In the steady flow, $θ$ periodically rotates (tumbling) at high $η_{\rm {in}}$, and $θ$ and the vesicle shape oscillate (swinging) at middle $η_{\rm {in}}$ and high shear rate. In the oscillatory flow, the coexistence of two or more limit-cycle oscillations can occur for low $f_γ$ in these phases. For the vesicle with a fixed shape, the angle $θ$ rotates back to the original position after an oscillation period. However, it is found that a preferred angle can be induced by small thermal fluctuations.