Viscous froth model applied to the motion and topological transformations of two-dimensional bubbles in a channel: three-bubble case

Author:

Torres-Ulloa C.1ORCID,Grassia P.1ORCID

Affiliation:

1. Department of Chemical and Process Engineering, University of Strathclyde, James Weir Building, 75 Montrose St, Glasgow G1 1XJ, UK

Abstract

The viscous froth model is used to predict rheological behaviour of a two-dimensional (2D) liquid-foam system. The model incorporates three physical phenomena: the viscous drag force, the pressure difference across foam films and the surface tension acting along them with curvature. In the so-called infinite staircase structure, the system does not undergo topological bubble neighbour-exchange transformations for any imposed driving back pressure. Bubbles then flow out of the channel of transport in the same order in which they entered it. By contrast, in a simple single bubble staircase or so-called lens system, topological transformations do occur for high enough imposed back pressures. The three-bubble case interpolates between the infinite staircase and simple staircase/lens. To determine at which driving pressures and at which velocities topological transformations might occur, and how the bubble areas influence their occurrence, steady-state propagating three-bubble solutions are obtained for a range of bubble sizes and imposed back pressures. As an imposed back pressure increases quasi-statically from equilibrium, complex dynamics are exhibited as the systems undergo either topological transformations, reach saddle-node bifurcation points, or asymptote to a geometrically invariant structure which ceases to change as the back pressure is further increased.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2024-07

2. Viscous froth model applied to multiple topological transformations of bubbles flowing in a channel: three-bubble case;2023-11-15

3. 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;2023-07

4. Yield stress of foam flow in porous media: The effect of bubble trapping;Colloids and Surfaces A: Physicochemical and Engineering Aspects;2022-12

5. Viscous froth model applied to the dynamic simulation of bubbles flowing in a channel: three-bubble case;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2022-11

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