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- W4320233700 abstract "Deformable bubbles propagated by the flow of a viscous liquid in a Hele-Shaw channel of uniform depth tend to travel along the channel's axis. Pairs of neighbouring bubbles will either separate or coalesce because an individual bubble's propagation speed increases monotonically with its size; this means that any group of bubbles will eventually rearrange itself in order of decreasing bubble size and all bubbles will separate. We show that, by introducing a small geometric perturbation to the channel in the form of an axially-uniform depth reduction along its centreline, the system supports a multitude of stable bubble formations and this can disrupt the necessary ordering by bubble size. The constituent bubbles of a stable formation lie in alternation on opposite sides of the depth-perturbation, retain fixed shapes and propagate steadily at the same speed. A stable formation is always led by the smallest of its constituent bubbles, which would be the slowest bubble in isolation. The leading bubble propagates as if it were isolated and the trailing bubbles reduce their speeds by adjusting their shapes and overlap of the depth-perturbation in the perturbation fields of their preceding nearest-neighbours in order to match that of the leading bubble. The trailing bubbles can be arranged in any order and, hence, the number of stable formations increases factorially as the number of bubbles is increased." @default.
- W4320233700 created "2023-02-13" @default.
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- W4320233700 date "2023-02-02" @default.
- W4320233700 modified "2023-10-05" @default.
- W4320233700 title "Stable bubble formations in a Hele-Shaw channel" @default.
- W4320233700 doi "https://doi.org/10.48550/arxiv.2302.01038" @default.
- W4320233700 hasPublicationYear "2023" @default.
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