Understanding the breakup of a liquid film is complicated by the fact that there is no obvious instability driving breakup: surface tension favors a film of uniform thickness over a deformed one. Here, we identify two mechanisms driving a film toward (infinite time) pinch-off. In the first problem, we show how the rise of a bubble is arrested in a narrow tube, on account of the lubricating film pinching off. In the second problem, breakup of a free liquid film is driven by a
strong temperature gradient across the pinch region.
J. Eggers is a professor of Applied Mathematics at the University of Bristol. Dr. Eggers' career has been devoted to the understanding of self-similar phenomena. He has made fundamental contributions to our mathematical understanding of free-surface flows, in particular breakup and coalescence of drops. His work is instrumental in establishing the study singularities as a research field fluid dynamics and applied mathematics. With Marco Fontelos, he has recently published a book at Cambridge University Press, which presents a unifying view of singularities in Physics, Mathematics, and Engineering, and aims to make the subject accessible to a wider audience. He is a member of the Academy of Arts and Sciences in Erfurt, Germany, and a Fellow of the American Physical Society, and has been made a Euromech Fellow. Dr. Eggers' most recent work concerns the spatial structure of shock waves in compressible gas dynamics, and singularities in non-linear elasticity.