Welch Robert L, Szeto Billy, Morris Stephen W
Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066209. doi: 10.1103/PhysRevE.85.066209. Epub 2012 Jun 26.
A thread of viscous fluid falling onto a moving surface exhibits a spectacular variety of types of motion as the surface speed and nozzle height are varied. For modest nozzle heights, four clear regimes are observed. For large surface speed, the thread is dragged into a stretched centenary configuration which is confined to a plane. As the surface speed is lowered, the thread exhibits a supercritical bifurcation to a meandering state. At very low surface speeds, the state resembles the usual coiling motion of a viscous thread falling on a stationary surface. In between the meandering and coiling regimes, a window containing a novel multifrequency state, previously called "figures of eight," is found. Using an improved visualization technique and a fully automated apparatus, we made detailed measurements of the longitudinal and transverse motion of the thread in all these states. We found that the multifrequency state is characterized by a complex pattern of motion whose main frequencies are locked in a 3:2 ratio. This state appears and disappears with finite amplitude at sharp bifurcations without measurable hysteresis.
当表面速度和喷嘴高度变化时，一股粘性流体落到移动表面上会呈现出各种各样引人注目的运动类型。对于适度的喷嘴高度，可以观察到四种清晰的状态。在表面速度较大时，流体丝被拉成一种拉伸的百年形构型，且该构型局限于一个平面内。随着表面速度降低，流体丝会经历超临界分岔进入蜿蜒状态。在极低的表面速度下，该状态类似于粘性流体丝落在静止表面上时通常的盘绕运动。在蜿蜒和盘绕状态之间，发现了一个包含一种新型多频状态的窗口，该状态先前被称为“8字形”。使用改进的可视化技术和全自动设备，我们对处于所有这些状态下的流体丝的纵向和横向运动进行了详细测量。我们发现，多频状态的特征是一种复杂的运动模式，其主要频率以3:2的比例锁定。这种状态在尖锐分岔处以有限振幅出现和消失，没有可测量的滞后现象。
