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Wendy Zhang : Drop breakup: asymmetric cones in viscous flow

Dynamic singularities are ubiquitous. They arise in mathematical models of phenomena as grand as star formation or as familiar as the breakup of a thread of honey as it is being added to tea. Drop breakup allows one to study dynamics close to a singularity in a simple context which is also accessible to experiments. Recent works have revealed that a viscous liquid drop close to breakup looks self-similar---the drop profile looks the same if the length scales are rescaled appropriately. A new numerical strategy is developed to capture the drop breakup dynamics and show good agreement with experimental measurements. Surprisingly, the presence of even small amounts of viscous dissipation in the surrounding can dramatically alter the self-similar profile. In particular, when no exterior viscous dissipation is present, the thread profile is symmetric about the point of pinch-off. When small amounts of exterior viscous dissipation are present, the thread profile becomes severely asymmetric. An understanding of the final breakup process is crucial in elucidating the mechanisms underlying the formation of satellite drops, an issue relevant to the development of ink-jet printing technologies and emulsification processes.

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