Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T01:01:07.844Z Has data issue: false hasContentIssue false
  • English
  • Français

Microstructural effects in aqueous foam fracture

Published online by Cambridge University Press:  23 November 2015

Peter S. Stewart ,
Stephen H. Davis  and
Sascha Hilgenfeldt
Peter S. Stewart*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, UK
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Sascha Hilgenfeldt
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We examine the fracture of a quasi-two-dimensional surfactant-laden aqueous foam under an applied driving pressure, using a network modelling approach developed for metallic foams by Stewart & Davis (J. Rheol., vol. 56, 2012, p. 543). In agreement with experiments, we observe two distinct mechanisms of failure analogous to those observed in a crystalline solid: a slow ductile mode when the driving pressure is applied slowly, where the void propagates as bubbles interchange neighbours through the T1 process; and a rapid brittle mode for faster application of pressures, where the void advances by successive rupture of liquid films driven by Rayleigh–Taylor instability. The simulations allow detailed insight into the mechanics of the fracturing medium and the role of its microstructure. In particular, we examine the stress distribution around the crack tip and investigate how brittle fracture localizes into a single line of breakages. We also confirm that pre-existing microstructural defects can alter the course of fracture.

JFM classification

Interfacial Flows (free surface): Fingering instability Complex Fluids: Foams Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 425 - 461
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arciniaga, M., Kuo, C.-C. & Dennin, M. 2011 Size dependent brittle to ductile transition in bubble rafts. Colloids Surf. A 382 (1), 36–41.Google Scholar
Arif, S., Tsai, J. C. & Hilgenfeldt, S. 2010 Speed of crack propagation in dry aqueous foam. Eur. Phys. Lett. 92 (3), 38001.Google Scholar
Arif, S., Tsai, J. C. & Hilgenfeldt, S. 2012 Spontaneous brittle-to-ductile transition in aqueous foam. J. Rheol. 56, 485–499.Google Scholar
Aubouy, M., Jiang, Y., Glazier, J. A. & Graner, F. 2003 A texture tensor to quantify deformations. Granul. Matt. 5 (2), 67–70.Google Scholar
Banhart, J. 2001 Manufacture, characterisation and application of cellular metals and metal foams. Prog. Mater. Sci. 46 (6), 559–632.Google Scholar
Ben-Amar, M. & Poire, E. C. 1999 Pushing a non-Newtonian fluid in a Hele-Shaw cell: from fingers to needles. Phys. Fluids 11 (7), 1757–1767.Google Scholar
Ben Salem, I., Cantat, I. & Dollet, B. 2013a Response of a two-dimensional liquid foam to air injection: influence of surfactants, critical velocities and branched fracture. Colloids Surf. A 438, 41–46.Google Scholar
Ben Salem, I., Cantat, I. & Dollet, B. 2013b Response of a two-dimensional liquid foam to air injection: swelling rate, fingering and fracture. J. Fluid Mech. 714, 258–282.Google Scholar
Bragg, L. & Nye, J. F. 1947 A dynamical model of a crystal structure. Proc. R. Soc. Lond. A 190 (1023), 474–481.Google Scholar
Bremond, N. & Villermaux, E. 2005 Bursting thin liquid films. J. Fluid Mech. 524, 121–130.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.Google Scholar
Buehler, M. J., Abraham, F. F. & Gao, H. 2003 Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426 (6963), 141–146.Google Scholar
Buehler, M. J., Tang, H., van Duin, A. C. T. & Goddard, W. A. III 2007 Threshold crack speed controls dynamical fracture of silicon single crystals. Phys. Rev. Lett. 99 (16), 165502.CrossRefGoogle ScholarPubMed
Cantat, I. 2013 Liquid meniscus friction on a wet plate: bubbles, lamellae, and foams. Phys. Fluids 25 (3), 031303.Google Scholar
Cantat, I. & Delannay, R. 2003 Dynamical transition induced by large bubbles in two-dimensional foam flows. Phys. Rev. E 67 (3), 031501.Google Scholar
Cantat, I. & Delannay, R. 2005 Dissipative flows of 2D foams. Eur. Phys. J. E 18 (1), 55–67.Google Scholar
Deshpande, V. S., Needleman, A. & Van der Giessen, E. 2002 Discrete dislocation modeling of fatigue crack propagation. Acta Mater. 50 (4), 831–846.Google Scholar
Dollet, B. & Cantat, I. 2010 Deformation of soap films pushed through tubes at high velocity. J. Fluid Mech. 652, 529–539.Google Scholar
Dollet, B. & Graner, F. 2007 Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow. J. Fluid Mech. 585, 181–211.Google Scholar
Edwards, S. F. & Grinev, D. V. 1999 Statistical mechanics of stress transmission in disordered granular arrays. Phys. Rev. Lett. 82 (26), 5397.Google Scholar
Farajzadeh, R., Andrianov, A., Krastev, R., Hirasaki, G. J. & Rossen, W. R. 2012 Foam–oil interaction in porous media: implications for foam assisted enhanced oil recovery. Adv. Colloid Interface Sci. 183, 1–13.Google Scholar
Farrokhpay, S. 2011 The significance of froth stability in mineral flotation: a review. Adv. Colloid Interface Sci. 166 (1), 1–7.Google Scholar
Fuerstman, M. J., Lai, A., Thurlow, M. E., Shevkoplyas, S. S., Stone, H. A. & Whitesides, G. M. 2007 The pressure drop along rectangular microchannels containing bubbles. Lab on a Chip 7 (11), 1479–1489.Google Scholar
Gouldstone, A., Van Vliet, K. J. & Suresh, S. 2001 Nanoindentation: simulation of defect nucleation in a crystal. Nature 411, 656.Google Scholar
Grassia, P., Montes-Atenas, G., Lue, L. & Green, T. E. 2008 A foam film propagating in a confined geometry: analysis via the viscous froth model. Eur. Phys. J. E 25 (1), 39–49.CrossRefGoogle Scholar
Green, T. E., Bramley, A., Lue, L. & Grassia, P. 2006 Viscous froth lens. Phys. Rev. E 74 (5), 051403.Google Scholar
Green, T. E., Grassia, P., Lue, L. & Embley, B. 2009 Viscous froth model for a bubble staircase structure under rapid applied shear: an analysis of fast flowing foam. Colloids Surf. A 348 (1), 49–58.Google Scholar
Guozden, T. M., Jagla, E. A. & Marder, M. 2010 Supersonic cracks in lattice models. Intl J. Fracture 162 (1–2), 107–125.Google Scholar
Hilgenfeldt, S., Arif, S. & Tsai, J. C. 2008 Foam: a multiphase system with many facets. Phil. Trans. R. Soc. Lond. A 366, 2145–2159.Google Scholar
Hilgenfeldt, S., Koehler, S. A. & Stone, H. A. 2001 Dynamics of coarsening foams: accelerated and self-limiting drainage. Phys. Rev. Lett. 86 (20), 4704.Google Scholar
Hirsch, P. B. & Roberts, S. G. 1997 Modelling plastic zones and the brittle–ductile transition. Phil. Trans. R. Soc. Lond. A 355 (1731), 1991–2002.Google Scholar
Holian, B. L. & Ravelo, R. 1995 Fracture simulations using large-scale molecular dynamics. Phys. Rev. B 51 (17), 11275.Google Scholar
Keller, J. B. & Kolodner, I. 1954 Instability of liquid surfaces and the formation of drops. J. Appl. Phys. 25 (7), 918–921.Google Scholar
Koehler, S. A., Hilgenfeldt, S. & Stone, H. A. 2001 Flow along two dimensions of liquid pulses in foams: experiment and theory. Eur. Phys. Lett. 54 (3), 335–341.Google Scholar
Kuo, C.-C. & Dennin, M. 2013 Scaling behavior of universal pinch-off in two-dimensional foam. Phys. Rev. E 87 (5), 052308.Google Scholar
Le Merrer, M., Lespiat, R., Höhler, R. & Cohen-Addad, S. 2015 Linear and non-linear wall friction of wet foams. Soft Matt. 11 (2), 368–381.Google Scholar
Livne, A., Bouchbinder, E., Svetlizky, I. & Fineberg, J. 2010 The near-tip fields of fast cracks. Science 327 (5971), 1359–1363.Google Scholar
von Neumann, J. 1952 Discussion to grain shapes and other metallurgical applications of topology. In Metal Interfaces (ed. Smith, C. S.), p. 108. American Society for Metals.Google Scholar
Ro, J. S. & Homsy, G. M. 1995 Viscoelastic free surface flows: thin film hydrodynamics of Hele-Shaw and dip coating flows. J. Non-Newtonian Fluid Mech. 57 (2), 203–225.Google Scholar
Saffman, P. G. 1986 Viscous fingering in Hele-Shaw cells. J. Fluid Mech. 173, 73–94.Google Scholar
Sherman, D. & Be’ery, I. 2004 Dislocations deflect and perturb dynamically propagating cracks. Phys. Rev. Lett. 93 (26), 265501.Google Scholar
Shilo, D., Sherman, D., Be’ery, I. & Zolotoyabko, E. 2002 Large local deflections of a dynamic crack front induced by intrinsic dislocations in brittle single crystals. Phys. Rev. Lett. 89 (23), 235504.Google Scholar
Stebe, K. J., Lin, S. Y. & Maldarelli, C. 1991 Remobilizing surfactant retarded fluid particle interfaces. I. Stress-free conditions at the interfaces of micellar solutions of surfactants with fast sorption kinetics. Phys. Fluids A 3 (1), 3–20.Google Scholar
Stebe, K. J. & Maldarelli, C. 1994 Remobilizing surfactant retarded fluid particle interfaces: controlling the surface mobility at interfaces of solutions containing surface active components. J. Colloid Interface Sci. 163 (1), 177–189.Google Scholar
Stewart, P. S. & Davis, S. H. 2012 Dynamics and stability of metallic foams: network modelling. J. Rheol. 56, 543–574.Google Scholar
Stewart, P. S. & Davis, S. H. 2013 Self-similar coalescence of clean foams. J. Fluid Mech. 722, 645–664.Google Scholar
Stewart, P. S., Davis, S. H. & Hilgenfeldt, S. 2013 Viscous Rayleigh–Taylor instability in aqueous foams. Colloids Surf. A 436, 898–905.Google Scholar
Wang, Y., Papageorgiou, D. T. & Maldarelli, C. 1999 Increased mobility of a surfactant-retarded bubble at high bulk concentrations. J. Fluid Mech. 390, 251–270.Google Scholar
Weertman, J. 1996 Dislocation Based Fracture Mechanics. World Scientific.Google Scholar
Zocchi, G., Shaw, B. E., Libchaber, A. & Kadanoff, L. P. 1987 Finger narrowing under local perturbations in the Saffman–Taylor problem. Phys. Rev. A 36 (4), 1894–1900.Google Scholar