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Edited by Osman A. Basaran, Purdue University, West Lafayette, IN, and accepted by Editorial Board Member John D. Weeks May 13, 2019 (received for review November 19, 2018)
Significance
We observe the formation of bubbles and drops on a daily basis, from dripping faucets to raindrops entraining bubbles on the surface of a lake. The ubiquity of the phenomenon masks the fascinating underlying nonlinear dynamics that is such an important aspect of modern physics. Here, we report on the surprising observation that confinement makes the pinch-off of a bubble a universal process, as opposed to the unconfined case, where pinch-off is sensitive to the details of the experimental setting. We explain how the motion of the contact line, where the liquid, gas, and solid phases meet, leads to self-similar dynamics that effectively erase the memory of the system. Our observations have implications for immiscible flow phenomena from microfluidics to geophysical flows, where confinement, together with fluid–solid physicochemical interactions, play a key role.
Abstract
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.
Footnotes
- ↵1To whom correspondence may be addressed. Email: pahlavan{at}princeton.edu or juanes{at}mit.edu.
Author contributions: A.A.P. and R.J. designed research; A.A.P. performed research; A.A.P., H.A.S., G.H.M., and R.J. analyzed data; and A.A.P., H.A.S., G.H.M., and R.J. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. O.A.B. is a Guest Editor invited by the Editorial Board.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1819744116/-/DCSupplemental.
Published under the PNAS license.
Restoring universality to the pinch-off of a bubble
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