Transport in Porous Media

, Volume 100, Issue 1, pp 143–157 | Cite as

Mechanical Stresses Induced by Evaporation in Consolidated Colloidal Suspensions of Hard Particles. Poroelasticity Theory Versus Experiments

Article

Abstract

Drying of colloidal suspensions often yields intriguing, complex and generally undesirable crack patterns. Despite a consensus on the main underlying physical mechanisms that lead to their formation, quantitative prediction seems at present out of reach. Notably, a prerequisite for this is the determination of the mechanical stress field. Here, our point of view is to provide a sound and well-established continuum mechanics model that can be used safely and easily by a large community and particularly by the fracture mechanics one. We show by comparison with beam deflection experiments, that (i) the use of Biot’s linear poroelasticity theory allows for the prediction of the stresses that lead to the crack formation and that (ii) the setup allows for the identification of some poroelastic constants. This evidenced that the hypothesis of incompressible constituents is reasonable for the nanolatex suspensions considered here, greatly simplifying the constitutive equations and reducing the number of material constants from four to two.

Keywords

Drying of colloidal dispersion Shrinkage crack patterns Poroelasticity 

Notes

Acknowledgments

The work was partially supported by the ANR Program JC-JC ANR-05-JCJC-0029 Morphologies. It is issued from Chekchaki (2011) Ph.D. thesis. We thank L. Dormieux, G. Gauthier, E. Herbert, J. P. Hulin, D. Kondo, D. Or for fruitful discussions. We thank E. Bourgeat-Lami and Rhodia Recherche (Aubervilliers, France) to have provide us some colloidal suspensions. Last and not least, we thank L. Pauchard to provide us indentation and beam deflection setups.

References

  1. Allain, C., Limat, L.: Regular patterns of cracks formed by directional drying of a colloidal suspension. Phys. Rev. Lett. 74, 2981–2984 (1995)Google Scholar
  2. Bahr, H., Fischer, G., Weiss, H.: Thermal-shock crack patterns explained by single and multiple crack-propagation. J. Mater. Sci. 21(8), 2716–2720 (1986)CrossRefGoogle Scholar
  3. Biot, M.A.: General theory of 3-dimensional consolidation. J. Appl. Phys. 12, 155–164 (1941)CrossRefGoogle Scholar
  4. Boulogne, F., Pauchard, L., Giorgiutti-Dauphine, F.: Effect of a non-volatile cosolvent on crack patterns induced by desiccation of a colloidal gel. Soft Matter 8, 8505–8510 (2012)CrossRefGoogle Scholar
  5. Brinker, C.J., Scherer, G.W.: Sol–Gel Science: The Physics and Chemistry of Sol–Gel Processing. Academic Press, Boston (1990)Google Scholar
  6. Caupin, F., Herbert, E.: Cavitation in water: a review. Comptes Rendus Physique 7(9–10), 1000–1017 (2006)CrossRefGoogle Scholar
  7. Chekchaki, M.: Détermination théorique et expérimentale des contraintes mécaniques induisant les fractures lors du séchage de suspensions colloïdales, PhD thesis, UPMC Université Pierre et Marie Curie, Paris 6, http://tel.archives-ouvertes.fr/tel-00626937/ (2011)
  8. Chekchaki, M., Frelat, J., Lazarus, V.: Analytical and 3D finite element study of the deflection of an elastic cantilever bilayer plate. Transactions of the ASME. J. Appl. Mech. 78(1), 011008 (2011)CrossRefGoogle Scholar
  9. Colina, H., Roux, S.: Experimental model of cracking induced by drying shrinkage. Eur. Phys. J. E 1(2–3), 189–194 (2000)CrossRefGoogle Scholar
  10. Corcoran, E.: Determining stresses in organic coatings using plate beam deflection. J. Paint Technol. 41(538), 635–640 (1969)Google Scholar
  11. Darcy, H.: Les fontaines de la ville de Dijon. Victor Dalmont, Paris (1856)Google Scholar
  12. Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Nagel, S.R., Witten, T.A.: Capillary flow as the cause of ring stains from dried liquid drops. Nature 389(6653), 827–829 (1997)CrossRefGoogle Scholar
  13. Detournay, E., Cheng, A.-D.: Fundamentals of poroelasticity. In: Fairhurst, C. (ed.) Comprehensive Rock Engineering: Principles, Practice and Projects, pp. 113–171. Pergamon Press, Oxford (1993)Google Scholar
  14. Dormieux, L., Kondo, D., Ulm, F.-J.: Microporomechanics. Wiley, Chichester (2006)CrossRefGoogle Scholar
  15. Dufresne, E.R., Corwin, E.I., Greenblatt, N.A., Ashmore, J., Wang, D.Y., Dinsmore, A.D., Cheng, J.X., Xie, X.S., Hutchinson, J.W., Weitz, D.A.: Flow and fracture in drying nanoparticle suspensions. Phys. Rev. Lett. 91(22), 224501 (2003)CrossRefGoogle Scholar
  16. Gauthier, G., Lazarus, V., Pauchard, L.: Alternating crack propagation during directional drying. Langmuir 23(9), 4715–4718 (2007)CrossRefGoogle Scholar
  17. Gauthier, G., Lazarus, V., Pauchard, L.: Shrinkage star-shaped cracks: explaining the transition from 90 to 120 degrees. Europhys. Lett. 89, 26002 (2010)CrossRefGoogle Scholar
  18. Geyer, J.F., Nematnasser, S.: Experimental investigation of thermally induced interacting cracks in brittle solids. Int. J. Solids Struct. 18(4), 349–356 (1982)CrossRefGoogle Scholar
  19. Giuseppe, E., Davaille, A., Mittelstaedt, E., François, M.: Rheological and mechanical properties of silica colloids: from newtonian liquid to brittle behaviour. Rheologica Acta 51(5), 451–465 (2012)CrossRefGoogle Scholar
  20. Goehring, L., Clegg, W.J., Routh, A.F.: Wavy cracks in drying colloidal films. Soft Matter 7, 7984 (2011)CrossRefGoogle Scholar
  21. Goehring, L., Morris, S.W., Lin, Z.: Experimental investigation of the scaling of columnar joints. Phys. Rev. E 74(3), 036115 (2006)CrossRefGoogle Scholar
  22. Groisman, A., Kaplan, E.: An experimental-study of cracking induced by desiccation. Europhys. Lett. 25(6), 415–420 (1994)CrossRefGoogle Scholar
  23. Huang, G., Lu, H.: Measurements of two independent viscoelastic functions by nanoindentation. Exp. Mech. 47(1), 87–98 (2007)CrossRefGoogle Scholar
  24. Hull, D., Caddock, B.D.: Simulation of prismatic cracking of cooling basalt lava flows by the drying of sol–gels. J. Mater. Sci. 34, 5707–5720 (1999). doi: 10.1023/A:1004793731308 CrossRefGoogle Scholar
  25. Inasawa, S., Yamaguchi, Y.: Self-organized pattern formation of cracks perpendicular to the drying direction of a colloidal suspension. Soft Matter 8, 2416 (2012)CrossRefGoogle Scholar
  26. Keddie, J., Routh, A.F.: Fundamentals of Latex Film Formation. Springer, NewYork (2010)CrossRefGoogle Scholar
  27. Kendall, K., Alford, N.M., Birchall, J.D.: Elasticity of particle assemblies as a measure of the surface energy of solids. Proc. R. Soc. Lond. A Math. Phys. Sci. 412(1843), 269–283 (1987)CrossRefGoogle Scholar
  28. Lazarus, V., Pauchard, L.: From craquelures to spiral crack patterns: influence of layer thickness on the crack patterns induced by desiccation. Soft Matter 7(6), 2552–2559 (2011)CrossRefGoogle Scholar
  29. Man, W., Russel, W.B.: Direct measurements of critical stresses and cracking in thin films of colloid dispersions. Phys. Rev. Lett. 100(19), 198302 (2008)CrossRefGoogle Scholar
  30. Martinet, J.: Thermocinétique. Technique et documentation edn, Lavoisier, Paris (1989)Google Scholar
  31. Muller, G.: Starch columns: analog model for basalt columns. J. Geophys. Res. 103(B7), 15239–15253 (1998)CrossRefGoogle Scholar
  32. Ngo, D., Feng, X., Huang, Y., Rosakis, A.J., Brown, M.A.: Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: analysis for obtaining film stress from non-local curvature information. Int. J. Solids Struct. 44(6), 1745–1754 (2007)CrossRefGoogle Scholar
  33. Oliver, W.C., Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564 (1992)CrossRefGoogle Scholar
  34. Pantina, J.P., Furst, E.M.: Elasticity and critical bending moment of model colloidal aggregates. Phys. Rev. Lett. 94, 138301 (2005)CrossRefGoogle Scholar
  35. Pantina, J.P., Furst, E.M.: Colloidal aggregate micromechanics in the presence of divalent ions. Langmuir 22(12), 5282–5288 (2006)CrossRefGoogle Scholar
  36. Petersen, C., Heldmann, C., Johannsmann, D.: Internal stresses during film formation of polymer latices. Langmuir 15(22), 7745–7751 (1999)CrossRefGoogle Scholar
  37. Ronsin, O., Heslot, F., Perrin, B.: Experimental study of quasistatic brittle crack propagation. Phys. Rev. Lett. 75(12), 2352–2355 (1995)CrossRefGoogle Scholar
  38. Routh, A.F., Russel, W.B.: Horizontal drying fronts during solvent evaporation from latex films. AIChE J. 44(9), 2088–2098 (1998)CrossRefGoogle Scholar
  39. Routh, A., Russel, W.: A process model for latex film formation: limiting regimes for individual driving forces. Langmuir 15(22), 7762–7773 (1999)CrossRefGoogle Scholar
  40. Russel, W., Wu, N., Man, W.: Generalized hertzian model for the deformation and cracking of colloidal packings saturated with liquid. Langmuir 24(5), 1721–1730 (2008)CrossRefGoogle Scholar
  41. Scherer, G.W.: Drying gels :VIII. Revision and review. J. Non-Cryst. Solids 109(2–3), 171–182 (1989)CrossRefGoogle Scholar
  42. Shao, Y., Xu, X., Meng, S., Bai, G., Jiang, C., Song, F.: Crack patterns in ceramic plates after quenching. J. Am. Ceram. Soc. 93(10), 3006–3008 (2010)CrossRefGoogle Scholar
  43. Sobac, B., Brutin, D.: Structural and evaporative evolutions in desiccating sessile drops of blood. Phys. Rev. E 84(1), 011603 (2011)CrossRefGoogle Scholar
  44. Stoney, G.G.: The tension of metallic films deposited by electrolysis. Proc. R. Soc. Lond. A, Contain. Pap. Math. Phys. Char. 82(553), 172–175 (1909)CrossRefGoogle Scholar
  45. Tirumkudulu, M.S., Russel, W.B.: Role of capillary stresses in film formation. Langmuir 20(7), 2947–2961 (2004)CrossRefGoogle Scholar
  46. Toramaru, A., Matsumoto, T.: Columnar joint morphology and cooling rate: a starch–water mixture experiment. J. Geophys. Res. 109(B2), B02205 (2004)CrossRefGoogle Scholar
  47. Wang, H.F.: Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology. Princeton University Press, Princeton (2000)Google Scholar
  48. Xu, Y., Engla, W.C., Jerison, E.R., Wallenstein, K.J., Hyland, C., Wilene, L.A., Dufresne, E.R.: Imaging in-plane and normal stresses near an interface crack using traction force microscopy. Proc. Natl. Acad. Sci. 107, 14964–14967 (2010)CrossRefGoogle Scholar
  49. Xu, Y., German, G.K., Mertz, A.F., Dufresne, E.R.: Imaging stress and strain in the fracture of drying colloidal films. Soft Matter 9, 3735–3740 (2013)CrossRefGoogle Scholar
  50. Yang, B., Ravi-Chandar, K.: Crack path instabilities in a quenched glass plate. J. Mech. Phys. Solids 49(1), 91–130 (2001)CrossRefGoogle Scholar
  51. Yow, H.N., Goikoetxea, M., Goehring, L., Routh, A.F.: Effect of film thickness and particle size on cracking stresses in drying latex films. J. Colloid Interface Sci. 352(2), 542–548 (2010)CrossRefGoogle Scholar
  52. Yuse, A., Sano, M.: Transition between crack patterns in quenched glass plates. Nature 362(6418), 329–331 (1993)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Fatigue and Fracture Mechanics Laboratory, Department of Mechanical EngineeringPontifical Catholic University of Rio de JaneiroRio de JaneiroBrazil
  2. 2.UPMC Univ Paris 6, UMR 7608, FASTOrsayFrance
  3. 3.Univ Paris-Sud, UMR 7608, FASTOrsayFrance
  4. 4.CNRS, UMR 7608, FASTOrsayFrance

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