标题： 楔形几何中具有直线边的弹性位移和粘性流动：垂直力的Green函数 显示英文标题

标题： Elastic displacements and viscous flows in wedge-shaped geometries with a straight edge: Green's functions for perpendicular forces

摘要： 当弹性固体沿导轨滑动或流体被限制在容器内时，边缘现象非常丰富。我们在此关注弹性固体中的诱发位移或粘性流体中小尺度流动在这样一个边缘附近的特性。为此，我们求解了线弹性且可能是可压缩的固体的控制弹性方程，以及不可压缩流体的低雷诺数流动方程。从技术上讲，我们推导了在由两个平面边界所限定的约束下，这两个边界在一条直线边缘处相交时的相关格林函数。这两个边界都具有无滑移或自由滑移条件，或者每个边界单独满足其中之一。 之前，我们解决了力的方向平行于直线边缘的较简单情况。在这里，我们通过更具挑战性的力指向与边缘垂直方向的情况来补充这一解决方案。这两者结合在一起提供了通用解。 我们的分析在定量理论描述中的具体应用情况包括：受限胶体悬浮液中的粒子运动、边缘附近活性微泳者的动力学行为，或者由于激活的功能化颗粒引起的弹性材料的受控变形。 显示英文摘要

摘要： Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this purpose, we solve the governing elasticity equations for linearly elastic, potentially compressible solids, as well as the low-Reynolds-number flow equations for incompressible fluids. Technically speaking, we derive the associated Green's functions under confinement by two planar boundaries that meet at a straight edge. The two boundaries both feature no-slip or free-slip conditions, or one of these two conditions per boundary. Previously, we solved the simpler case of the force being oriented parallel to the straight edge. Here, we complement this solution by the more challenging case of the force pointing into a direction perpendicular to the edge. Together, these two cases provide the general solution. Specific situations in which our analysis may find application in terms of quantitative theoretical descriptions are particle motion in confined colloidal suspensions, dynamics of active microswimmers near edges, or actuated distortions of elastic materials due to activated contained functionalized particles.