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arXiv physics/0608039physics.bio-phphysics.flu-dyn
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线性流中粘性囊泡的动力学

Dynamics of a viscous vesicle in linear flows

Petia M. Vlahovska, Ruben Serral Gracia

摘要:

建立了一种描述封闭的脂双层膜(囊泡)在一般线性流中自由悬浮的动力学的解析理论。考虑到近球形的形状,蠕动流方程的解作为一个规则的摄动展开在多余的区域。该分析考虑了膜的流动性、不可压缩性和抗弯曲性。固定的总面积的约束导致非线性形状演化方程在领先的顺序。因此,两个政权的囊泡行为,坦克踩踏和翻滚,预测取决于内部和外部流体之间的粘度对比。低于临界粘度对比度,这取决于过剩面积,囊泡变形成一个坦克踩踏椭圆体,其相对于流动方向的取向角是独立的膜的弯曲刚度。在翻滚制度,囊泡表现出周期性的形状变形的频率,增加与粘度对比度。非牛顿流变学,如正常的应力预测为一个稀悬浮液的囊泡。该理论与已发表的简单剪切流中囊泡行为的实验数据吻合得很好。

英文摘要:

An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) freely suspended in a general linear flow. Considering a nearly spherical shape, the solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, incompressibility and resistance to bending. The constraint for a fixed total area leads to a non-linear shape evolution equation at leading order. As a result two regimes of vesicle behavior, tank-treading and tumbling, are predicted depending on the viscosity contrast between interior and exterior fluid. Below a critical viscosity contrast, which depends on the excess area, the vesicle deforms into a tank--treading ellipsoid, whose orientation angle with respect to the flow direction is independent of the membrane bending rigidity. In the tumbling regime, the vesicle exhibits periodic shape deformations with a frequency that increases with the viscosity contrast. Non-Newtonian rheology such as normal stresses is predicted for a dilute suspension of vesicles. The theory is in good agreement with published experimental data for vesicle behavior in simple shear flow.

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