TY - JOUR
T1 - How viscous bubbles collapse
T2 - Topological and symmetry-breaking instabilities in curvature-driven hydrodynamics
AU - Davidovitch, Benny
AU - Klein, Avraham
N1 - Publisher Copyright:
© 2024 the Author(s).
PY - 2024/8/6
Y1 - 2024/8/6
N2 - The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetrybreaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium"physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength"of surface wrinkles.
AB - The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetrybreaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium"physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength"of surface wrinkles.
KW - topological instabilities
KW - viscous hydrodynamics
KW - wrinkling
UR - http://www.scopus.com/inward/record.url?scp=85200525477&partnerID=8YFLogxK
U2 - 10.1073/pnas.2310195121
DO - 10.1073/pnas.2310195121
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C2 - 39093945
AN - SCOPUS:85200525477
SN - 0027-8424
VL - 121
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 32
M1 - e2310195121
ER -