Chang Chun-Ti, Bostwick Joshua B, Steen Paul H, Daniel Susan
Theoretical and Applied Mechanics, Cornell University, Ithaca, New York 14853, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):023015. doi: 10.1103/PhysRevE.88.023015. Epub 2013 Aug 14.
In this work, we study the resonance behavior of mechanically oscillated, sessile water drops. By mechanically oscillating sessile drops vertically and within prescribed ranges of frequencies and amplitudes, a rich collection of resonance modes are observed and their dynamics subsequently investigated. We first present our method of identifying each mode uniquely, through association with spherical harmonics and according to their geometric patterns. Next, we compare our measured resonance frequencies of drops to theoretical predictions using both the classical theory of Lord Rayleigh and Lamb for free, oscillating drops, and a prediction by Bostwick and Steen that explicitly considers the effect of the solid substrate on drop dynamics. Finally, we report observations and analysis of drop mode mixing, or the simultaneous coexistence of multiple mode shapes within the resonating sessile drop driven by one sinusoidal signal of a single frequency. The dynamic response of a deformable liquid drop constrained by the substrate it is in contact with is of interest in a number of applications, such as drop atomization and ink jet printing, switchable electronically controlled capillary adhesion, optical microlens devices, as well as digital microfluidic applications where control of droplet motion is induced by means of a harmonically driven substrate.
在这项工作中，我们研究了机械振荡的静止水滴的共振行为。通过在规定的频率和振幅范围内垂直地对静止水滴进行机械振荡，观察到了丰富的共振模式，并随后对其动力学进行了研究。我们首先介绍了通过与球谐函数关联并根据其几何图案唯一识别每种模式的方法。接下来，我们将测得的水滴共振频率与使用瑞利勋爵和兰姆的经典自由振荡水滴理论的理论预测，以及博斯威克和斯汀明确考虑固体基板对液滴动力学影响的预测进行比较。最后，我们报告了对液滴模式混合的观察和分析，即在由单一频率的单个正弦信号驱动的共振静止液滴中多种模式形状的同时共存。在许多应用中，例如液滴雾化和喷墨打印、可切换的电控毛细管粘附、光学微透镜装置以及通过谐波驱动基板诱导液滴运动控制的数字微流控应用中，受与其接触的基板约束的可变形液滴的动态响应是令人感兴趣的。
