Viscous froth model applied to multiple topological transformations of bubbles flowing in a channel : three-bubble case

Torres-Ulloa, Carlos and Grassia, Paul (2023) Viscous froth model applied to multiple topological transformations of bubbles flowing in a channel : three-bubble case. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 479 (2275). 20220785. ISSN 1471-2946 (https://doi.org/10.1098/rspa.2022.0785)

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Abstract

A two-dimensional foam system comprised of three bubbles is studied via dynamic simulations with the viscous froth model. The bubbles are arranged in a staircase configuration and move along a channel due to an imposed driving back pressure. Depending on the bubble size relative to channel size, the three-bubble system can undergo topological transformations (as for a simpler staircase structure, known as the simple lens) or it can reach a geometrically invariant migrating state (as for an infinite staircase structure). A methodology used previously determined the system evolution up to the first topological transformation, but evolution beyond this was not studied before. To address this, unsteady state three-bubble simulations are realised here, extending beyond the first transformation. For sufficiently high imposed back pressures, a sequence of topological transformations occurs before a steadily migrating shape is reached, typically in a topology such that an equal number of films connect to both channel walls.

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