平面弹性膜附近的流体动力耦合和转动迁移率
Hydrodynamic coupling and rotational mobilities near planar elastic membranes
摘要：
我们从理论上和数值上研究了球形颗粒之间的耦合和旋转流体动力学相互作用的平面弹性膜，表现出对剪切和弯曲阻力。使用的多极展开和Faxen的定理的组合，我们表示的频率依赖的流体动力学迁移率函数作为一个幂级数的粒子半径的比率从膜的自迁移率的距离，并作为一个幂级数的半径的比率粒子间的距离对迁移率。在准稳定的极限为零的频率，我们发现，剪切和弯曲相关的贡献的颗粒迁移率可能有添加剂或抑制效果取决于膜的性质，除了相互作用的粒子相对于限制膜的几何配置。为了阐明在粒子自身和对迁移率中观察到的符号变化的影响和作用，我们考虑一个例子，该例子涉及一个无扭矩的对弹性膜附近的反向旋转粒子。我们发现，诱导的旋转率的偶极子围绕其质心的大小和方向取决于膜的剪切和弯曲性能。在仅对剪切变形具有能量阻力的膜附近，例如在某种类型的弹性胶囊的膜附近，双合线经历与在无滑动壁附近观察到的相同方向的旋转。在一个仅能抵抗弯曲的膜附近，例如一个流体囊泡的膜附近，我们发现了一个反向的旋转方向。我们的分析预测的补充和完全解决边界积分模拟得到一个非常好的协议，在整个范围内的应用频率。
英文摘要：
We study theoretically and numerically the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance towards shear and bending. Using a combination of the multipole expansion and Faxen's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities, and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied frequencies.
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