Dynamics of Fluid Vesicles in Oscillatory Shear Flow

Abstract

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 ${\eta }_{\mathrm{in}}$ 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 ${\dot{\gamma }}_{\mathrm{m}}=0$, another limit-cycle oscillation between ${\theta }_0-\pi$ and $-{\theta }_0$ is found to appear. In the steady flow, $\theta$ periodically rotates (tumbling) at high ${\eta }_{\mathrm{in}}$, and $\theta$ and the vesicle shape oscillate (swinging) at middle ${\eta }_{\mathrm{in}}$ 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.

11 pages, 13 figures

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• Dynamics of Vesicles in shear and rotational flows: Modal Dynamics and Phase Diagram
• Dynamic Modes of Red Blood Cells in Oscillatory Shear Flow
• Dynamic Modes of Microcapsules in Steady Shear Flow: Effects of Bending and Shear Elasticities
• Swinging and tumbling of multicomponent vesicles in flow
• Growth and shrinkage of tissue sheets on substrates: buds, buckles, and pores
• Dynamical behavior of compound vesicles in wall-bounded shear flow