https://doi.org/10.1140/epjs/s11734-025-01900-9
Regular Article
Super-fast bullet bubbles transported in cylindrical capillaries under pressure-driven flow
1
Transfers, Interfaces and Processes (TIPs), Université Libre de Bruxelles, 1050, Brussels, Belgium
2
University of Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, 69622, Villeurbanne, France
3
Escuela de Ingenierías Industriales, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain
Received:
27
August
2025
Accepted:
28
August
2025
Published online:
8
September
2025
When transported by a pressure-driven flow in a cylindrical capillary, bubbles may exhibit very fast velocities. In this paper, we show that when the bubbles are largely deformable, that is, at large capillary numbers Ca, the velocity of the bubble can be larger than the maximal velocity of the flow that transports them. We call this regime “super-fast”. However, the situation changes when inertial effects become significant at higher Reynolds numbers (
), leading to a decrease in the bubble’s relative velocity for sufficiently large values of the Laplace number, defined as 
. In this article, we uncover the conditions for which the super-fast regime exists: the deformability of the bubble is crucial, and hence the capillary number needs to be larger than a critical value, yet smaller than a threshold above which the bubble breaks up. The two limiting capillary numbers are presented in a phase diagram as a function of the bubble size and the Laplace number.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
