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Martin, David W.; Blanchette, François
Journal of engineering mathematics, 12/2022, Letnik: 137, Številka: 1Journal Article
We present a theoretical and numerical study of the time evolution of the film of a soap bubble. Bubbles are assumed to remain approximately spherical with axisymmetric evolution. Inertia is neglected, and the surfactant is assumed insoluble. Applying lubrication theory, we simplify the equations governing the film thickness evolution, surfactant concentration, and tangential fluid velocity. Solving the simplified equations numerically, we examine the long-term behavior of the film and find that most features follow a power law of the form α T β where T is a dimensionless time parameter. We also predict the location (angle from the top) at which the film is thinnest and thus most likely to initiate bursting and present a similarity solution that predicts the decay rate of the minimum film thickness near the pinch-off location.
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