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arXiv 0906.4170cond-mat.soft
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剪切作用下粘性囊泡的动力学状态和流体力学升力

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

Sebastian Meßlinger, Benjamin Schmidt, Hiroshi Noguchi, Gerhard Gompper

备注：
13 pages, 13 figures
发表信息：
Phys. Rev. E 80, 011901 (2009).
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摘要：

采用细观尺度模拟技术研究了剪切流中二维粘性囊泡的动力学行为，分别在囊泡内外具有不同的流体粘度$η_{\rm in}$和$η_{\rm out}$。在大剪切速率下，除了常见的踩踏和翻滚运动外，还观察到了振荡摆动运动。这种摆动运动的存在需要在两个维度上激发高阶波动模式（超越椭圆变形）。将Keller-Skalak理论推广到可变形二维囊泡，从而可以预测约化剪切速率和粘度差$η_{\rm in}/η_{\rm out}$的动态相图。模拟结果被发现是在良好的协议与理论预测，当热涨落纳入理论。此外，流体动力学升力，作用于囊泡剪切下靠近壁，确定从模拟各种粘度对比。为了比较，升力的数值计算中没有热波动，使用边界积分法相等的内部和外部的粘度。这两种方法表明，升力的依赖性的距离$y_{\rm {cm}}$的囊泡质心从壁是很好地描述了一个有效的幂律$y_{\rm {cm}}^{-2}$的中间距离$0.8 R_{\rm p} \lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$与囊泡半径$R_{\rm p}$。边界积分计算表明，随着$1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$远离壁面，升力渐近衰减。

英文摘要：

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities $η_{\rm in}$ and $η_{\rm out}$ inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast $η_{\rm in}/η_{\rm out}$. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance $y_{\rm {cm}}$ of the vesicle center of mass from the wall is well described by an effective power law $y_{\rm {cm}}^{-2}$ for intermediate distances $0.8 R_{\rm p} \lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$ with vesicle radius $R_{\rm p}$. The boundary-integral calculation indicates that the lift force decays asymptotically as $1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$ far from the wall.

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