弹性球腔内固体颗粒的蠕动运动
Creeping motion of a solid particle inside a spherical elastic cavity
摘要：
本文从线性流体力学方程组出发，给出了一个固体颗粒在一个较大的球形弹性空腔中的低雷诺数运动的解析理论。在颗粒与腔体同心的特殊情况下，我们利用流函数技术求出了弹性腔体两侧流体运动方程的精确解析解。在这种特殊的情况下，我们发现，流体动力学方程的解决方案是完全由膜剪切性能和弯曲不起作用。对于球形空腔内固体颗粒的任意位置，我们采用镜像解技术来计算由点力（Stokeslet）诱导的轴对称流场。然后，我们得到的首阶迁移率函数的解析表达式描述流体介导的流体动力学之间的相互作用的颗粒和封闭的弹性腔。在准定常的消失频率极限，我们发现粒子的自迁移率函数高于刚性无滑移腔中的预测值。考虑空穴运动，我们发现对迁移率函数仅由膜剪切性质决定。我们的分析预测的补充和验证完全解决的边界积分模拟，在整个范围内获得了很好的协议施加强迫频率。
英文摘要：
On the basis of the linear hydrodynamic equations, we present an analytical theory for the low-Reynolds-number motion of a solid particle moving inside a larger spherical elastic cavity which can be seen as a model system for a fluid vesicle. In the particular situation where the particle is concentric with the cavity, we use the stream function technique to find exact analytical solutions of the fluid motion equations on both sides of the elastic cavity. In this particular situation, we find that the solution of the hydrodynamic equations is solely determined by membrane shear properties and that bending does not play a role. For an arbitrary position of the solid particle within the spherical cavity, we employ the image solution technique to compute the axisymmetric flow field induced by a point force (Stokeslet). We then obtain analytical expressions of the leading order mobility function describing the fluid-mediated hydrodynamic interactions between the particle and confining elastic cavity. In the quasi-steady limit of vanishing frequency, we find that the particle self-mobility function is higher than that predicted inside a rigid no-slip cavity. Considering the cavity motion, we find that the pair-mobility function is determined only by membrane shear properties. Our analytical predictions are supplemented and validated by fully-resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied forcing frequencies.
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