Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139;
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540.
Proc Natl Acad Sci U S A. 2019 Jul 9;116(28):13780-13784. doi: 10.1073/pnas.1819744116. Epub 2019 Jun 17.
The pinch-off of a bubble is an example of the formation of a singularity, exhibiting a characteristic separation of length and time scales. Because of this scale separation, one expects universal dynamics that collapse into self-similar behavior determined by the relative importance of viscous, inertial, and capillary forces. Surprisingly, however, the pinch-off of a bubble in a large tank of viscous liquid is known to be nonuniversal. Here, we show that the pinch-off dynamics of a bubble confined in a capillary tube undergo a sequence of two distinct self-similar regimes, even though the entire evolution is controlled by a balance between viscous and capillary forces. We demonstrate that the early-time self-similar regime restores universality to bubble pinch-off by erasing the system's memory of the initial conditions. Our findings have important implications for bubble/drop generation in microfluidic devices, with applications in inkjet printing, medical imaging, and synthesis of particulate materials.
气泡的挤压是奇点形成的一个例子，表现出长度和时间尺度的特征分离。由于这种尺度分离，人们期望出现普遍的动力学，这些动力学会塌缩为自相似行为，由粘性、惯性和毛细力的相对重要性决定。然而，令人惊讶的是，在粘性液体的大容器中气泡的挤压已知是非普适的。在这里，我们表明，即使整个演化过程由粘性和毛细力之间的平衡控制，受限在毛细管中的气泡的挤压动力学也会经历两个不同的自相似状态。我们证明，早期的自相似状态通过消除系统对初始条件的记忆，恢复了气泡挤压的普适性。我们的发现对微流控设备中的气泡/液滴生成具有重要意义，在喷墨打印、医学成像和颗粒材料合成等领域有应用。
