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 $\theta$. In a steady shear flow with a low viscosity ${\eta }_{\mathrm{i}\mathrm{n}}$ of internal fluid, the vesicles exhibit steady tank-treading motion with a constant inclination angle ${\theta }_0$. In the oscillatory flow with a low shear frequency, $\theta$ oscillates between $\pm {\theta }_0$ or around ${\theta }_0$ for zero or finite mean shear rate ${\dot{\gamma }}_{\mathrm{m}}$, respectively. As shear frequency $f_{\gamma }$ increases, the vesicle oscillation becomes delayed with respect to the shear oscillation, and the oscillation amplitude decreases. At high $f_{\gamma }$ with $\dot\gamma_{\rm m}=0$,anotherlimit-cycleoscillationbetween$\theta_0-\pi$and$-\theta_0$isfoundtoappear\mathrm{.}Inthesteadyflow,$\theta$ periodically rotates (tumbling) at high ${\eta }_{\mathrm{i}\mathrm{n}}$, and $\theta$ and the vesicle shape oscillate (swinging) at middle ${\eta }_{\mathrm{i}\mathrm{n}}$ and high shear rate. In the oscillatory flow, the coexistence of two or more limit-cycle oscillations can occur for low $f_{\gamma }$ in these phases. For the vesicle with a fixed shape, the angle $\theta$ 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.