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Galvani N, Pasquet M, Mukherjee A, Requier A, Cohen-Addad S, Pitois O, Höhler R, Rio E, Salonen A, Durian DJ, Langevin D. Hierarchical bubble size distributions in coarsening wet liquid foams. Proc Natl Acad Sci U S A 2023; 120:e2306551120. [PMID: 37708201 PMCID: PMC10515135 DOI: 10.1073/pnas.2306551120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Accepted: 08/07/2023] [Indexed: 09/16/2023] Open
Abstract
Coarsening of two-phase systems is crucial for the stability of dense particle packings such as alloys, foams, emulsions, or supersaturated solutions. Mean field theories predict an asymptotic scaling state with a broad particle size distribution. Aqueous foams are good model systems for investigations of coarsening-induced structures, because the continuous liquid as well as the dispersed gas phases are uniform and isotropic. We present coarsening experiments on wet foams, with liquid fractions up to their unjamming point and beyond, that are performed under microgravity to avoid gravitational drainage. As time elapses, a self-similar regime is reached where the normalized bubble size distribution is invariant. Unexpectedly, the distribution features an excess of small roaming bubbles, mobile within the network of jammed larger bubbles. These roaming bubbles are reminiscent of rattlers in granular materials (grains not subjected to contact forces). We identify a critical liquid fraction [Formula: see text], above which the bubble assembly unjams and the two bubble populations merge into a single narrow distribution of bubbly liquids. Unexpectedly, [Formula: see text] is larger than the random close packing fraction of the foam [Formula: see text]. This is because, between [Formula: see text] and [Formula: see text], the large bubbles remain connected due to a weak adhesion between bubbles. We present models that identify the physical mechanisms explaining our observations. We propose a new comprehensive view of the coarsening phenomenon in wet foams. Our results should be applicable to other phase-separating systems and they may also help to control the elaboration of solid foams with hierarchical structures.
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Affiliation(s)
- Nicolò Galvani
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, Paris75005, France
- Lab Navier, Univ Gustave Eiffel, Ecole Nationale des Ponts et Chaussées, CNRS, Champs-sur-Marne77420, France
| | - Marina Pasquet
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay91405, France
| | - Arnab Mukherjee
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, Paris75005, France
| | - Alice Requier
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay91405, France
| | - Sylvie Cohen-Addad
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, Paris75005, France
- Université Gustave Eiffel, Champs-sur-Marne77420, France
| | - Olivier Pitois
- Lab Navier, Univ Gustave Eiffel, Ecole Nationale des Ponts et Chaussées, CNRS, Champs-sur-Marne77420, France
| | - Reinhard Höhler
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, Paris75005, France
- Université Gustave Eiffel, Champs-sur-Marne77420, France
| | - Emmanuelle Rio
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay91405, France
| | - Anniina Salonen
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay91405, France
| | - Douglas J. Durian
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA19104
- Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY10010
| | - Dominique Langevin
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay91405, France
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