沿弹性管中心线运动的球体的水动力导纳
Hydrodynamic mobility of a sphere moving on the centerline of an elastic tube
摘要：
弹性通道是许多软物质系统的重要组成部分，其中流体动力学与限制膜的相互作用决定了颗粒在流动中的行为。在这项工作中，我们推导出解析表达式的格林函数相关的一个点力（Stokeslet）平行或垂直于轴的弹性圆柱形通道表现出抗剪切和弯曲。然后，我们计算的主导秩序的自我和对流动性函数的粒子在圆柱轴上，发现流动性主要是由膜剪切和弯曲不起重要作用。在准稳态极限的消失频率，粒子的自和对附近的无滑移硬柱迁移率恢复，只有当膜具有非零剪切刚度。我们进一步计算膜变形，发现变形通常在轴向（径向）方向上更明显，分别为沿（垂直）圆柱中心线的运动。我们的分析计算的弹性圆柱体中的格林函数可以作为一个基本的积木为未来的研究，并通过完全解决边界积分模拟得到了很好的协议进行验证。
英文摘要：
Elastic channels are an important component of many soft matter systems, in which hydrodynamic interactions with confining membranes determine the behavior of particles in flow. In this work, we derive analytical expressions for the Green's functions associated to a point-force (Stokeslet) directed parallel or perpendicular to the axis of an elastic cylindrical channel exhibiting resistance against shear and bending. We then compute the leading order self- and pair mobility functions of particles on the cylinder axis, finding that the mobilities are primarily determined by membrane shear and that bending does not play a significant role. In the quasi-steady limit of vanishing frequency, the particle self- and pair mobilities near a no-slip hard cylinder are recovered only if the membrane possesses a non-vanishing shear rigidity. We further compute the membrane deformation, finding that deformation is generally more pronounced in the axial (radial) directions, for the motion along (perpendicular) to the cylinder centerline, respectively. Our analytical calculations for the Green's functions in an elastic cylinder can serve as a fundamental building block for future studies and are verified by fully resolved boundary integral simulations where a very good agreement is obtained.
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