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Abstract
The viscous froth model is used to predict rheological behaviour of a twodimensional (2D) liquidfoam 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 socalled infinite staircase structure, the system does not undergo topological bubble neighbourexchange 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 socalled lens system, topological transformations do occur for high enough imposed back pressures. The threebubble 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, steadystate propagating threebubble solutions are obtained for a range of bubble sizes and imposed back pressures. As an imposed back pressure increases quasistatically from equilibrium, complex dynamics are exhibited as the systems undergo either topological transformations, reach saddlenode bifurcation points, or asymptote to a geometrically invariant structure which ceases to change as the back pressure is further increased.
Original language  English 

Article number  20210642 
Number of pages  27 
Journal  Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 
Volume  478 
Issue number  2258 
Early online date  9 Feb 2022 
DOIs  
Publication status  Published  9 Feb 2022 
Keywords
 physics of bubbles
 foam rheology
 multiphase fluids
 nonNewtonian fluids
 viscous froth model
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 1 Active

Foam Improved Oil Recovery: Effects of Flow Reversal
EPSRC (Engineering and Physical Sciences Research Council)
1/08/21 → 30/09/23
Project: Research