Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawińskiego 5B, 02-106 Warsaw, Poland.
Soft Matter. 2023 Jul 5;19(26):4829-4846. doi: 10.1039/d3sm00255a.
We study experimentally the dynamics of one and two ball chains settling under gravity in a highly viscous silicon oil at a Reynolds number much smaller than unity. We record the motion and shape deformation using two cameras. We demonstrate that single ball chains in most cases do not tend to be planar and often rotate, not keeping the ends at the same horizontal level. Shorter ball chains usually form shapes resembling distorted U. Longer ones in the early stage of the evolution form a shape resembling distorted W, and later deform non-symmetrically and significantly out of a plane. The typical evolution of shapes observed in our experiments with single ball chains is reproduced in our numerical simulations of a single elastic filament. In the computations, the filament is modelled as a chain of beads. Consecutive beads are connected by springs. Additional springs link consecutive pairs of beads. Elastic forces are assumed to be much smaller than gravity. As a result, the fibre is very flexible. We assume that the fluid sticks to the surfaces of the beads. We perform multipole expansion of the Stokes equations, with a lubrication correction. This method is implemented in the precise HYDROMULTIPOLE numerical codes. In our experiments, two ball chains, initially one above the other, later move away or approach each other, for a larger or smaller initial distance, respectively.
我们在一个具有较大黏性的硅油中，在雷诺数远小于 1 的条件下，对单链和双链在重力作用下的沉降动力学进行了实验研究。我们使用两个摄像机记录运动和形状变形。我们证明，在大多数情况下，单链球往往不是平面的，并且经常旋转，使得两端不在同一水平面上。较短的链球通常形成类似于变形的 U 形的形状，而较长的链球在演化的早期阶段形成类似于变形的 W 形的形状，然后非对称地显著变形到平面之外。我们在单链球实验中观察到的典型形状演化，在我们对单个弹性细丝的数值模拟中得到了重现。在计算中，细丝被建模为一个珠链。连续的珠子由弹簧连接。附加的弹簧连接连续的珠子对。假设弹性力远小于重力。因此，纤维非常灵活。我们假设流体附着在珠子的表面。我们对 Stokes 方程进行了多极展开，并进行了润滑修正。这种方法在精确的 HYDROMULTIPOLE 数值代码中实现。在我们的实验中，两个球链，初始时一个在另一个上面，随后分别以较大或较小的初始距离彼此远离或靠近。
