1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Condensed Matter Physics
  4. Volume 8, 2017
  5. Article

Annual Review of Condensed Matter Physics

Volume 8, 2017

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

Abstract

It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play a central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses cause dramatic departures from classic theories for wetting (Young–Dupré), adhesion (Johnson–Kendall–Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

Keyword(s): analytical methods, numerical methods, capillarity, elastomers, gels, soft interfaces, surface stress
Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031016-025326
2017-03-31
2024-04-19
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/8/1/annurev-conmatphys-031016-025326.html?itemId=/content/journals/10.1146/annurev-conmatphys-031016-025326&mimeType=html&fmt=ahah

Literature Cited

  1. Shepherd RF, Ilievski F, Choi W, Morin SA, Stokes AA. 1.  et al. 2011. PNAS 108:20400–3
  2. Morin SA, Shepherd RF, Kwok SW, Stokes AA, Nemiroski A, Whitesides GM. 2.  2012. Science 337:828–32
  3. Wood R, Walsh C. 3.  2013. Sci. Transl. Med. 5:210210ed19
  4. Suo Z, Ma E, Gleskova H, Wagner S. 4.  1999. Appl. Phys. Lett. 74:1177–79
  5. Lingley AR, Ali M, Liao Y, Mirjalili R, Klonner M. 5.  et al. 2011. J. Micromech. Microeng. 21:125014
  6. Keplinger C, Sun JY, Foo CC, Rothemund P, Whitesides GM, Suo Z. 6.  2013. Science 341:984–87
  7. Sun JY, Keplinger C, Whitesides GM, Suo Z. 7.  2014. Adv. Mater. 26:7608–14
  8. Shin H, Jo S, Mikos AG. 8.  2003. Biomaterials 24:4353–64
  9. Gordon JE. 9.  1978. Structures: Or Why Things Don't Fall Down. Cambridge, MA: Da Capo
  10. Chen D, Cai S, Suo Z, Hayward RC. 10.  2012. Phys. Rev. Lett. 109:038001
  11. Jagota A, Paretkar D, Ghatak A. 11.  2012. Phys. Rev. E 85:051602
  12. Mora S, Phou T, Fromental JM, Pismen LM, Pomeau Y. 12.  2010. Phys. Rev. Lett. 105:214301
  13. Style RW, Boltyanskiy R, Allen B, Jensen KE, Foote HP. 13.  et al. 2015. Nat. Phys. 11:82–87
  14. Style RW, Dufresne ER. 14.  2012. Soft Matter 8:7177
  15. Marchand A, Das S, Snoeijer JH, Andreotti B. 15.  2012. Phys. Rev. Lett. 109:236101
  16. Style RW, Che Y, Wettlaufer JS, Wilen LA, Dufresne ER. 16.  2013. Phys. Rev. Lett. 110:066103
  17. Johnson K, Kendall K, Roberts A. 17.  1971. Proc. R. Soc. A 324:301
  18. Carrillo JMY, Dobrynin AV. 18.  2012. Langmuir 28:10881–90
  19. Style RW, Hyland C, Boltyanskiy R, Wettlaufer JS, Dufresne ER. 19.  2013. Nat. Commun. 4:2728
  20. de Gennes PG, Brochard-Wyart F, Quere D. 20.  2010. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. New York: Springer
  21. Shuttleworth R. 21.  1950. Proc. Phys. Soc. A 63:444
  22. Nicolson MM. 22.  1955. Proc. R. Soc. A 228:490–510
  23. Gurtin ME, Murdoch AI. 23.  1975. Arch. Rational Mech. Anal. 57:291–323
  24. Gurtin ME, Murdoch AI. 24.  1978. Int. J. Solid. Struct. 14:431–40
  25. Cammarata R, Sieradzki K. 25.  1994. Annu. Rev. Mater. Sci. 24:215–34
  26. Spaepen F. 26.  2000. Acta Mater. 48:31–42
  27. Haiss W. 27.  2001. Rep. Prog. Phys. 64:591
  28. Sander D. 28.  2003. Curr. Opin. Solid State Mater. Sci. 7:51–57
  29. Chen T, Chiu MS, Weng CN. 29.  2006. J. Appl. Phys. 100:074308
  30. Javili A, McBride A, Steinmann P, Reddy B. 30.  2014. Comp. Mech. 54:745–62
  31. Mora S, Abkarian M, Tabuteau H, Pomeau Y. 31.  2011. Soft Matter 7:10612
  32. Jerison ER, Xu Y, Wilen LA, Dufresne ER. 32.  2011. Phys. Rev. Lett. 106:186103
  33. Mora S, Maurini C, Phou T, Fromental JM, Audoly B, Pomeau Y. 33.  2013. Phys. Rev. Lett. 111:114301
  34. Karpitschka S, Das S, van Gorcum M, Perrin H, Andreotti B, Snoeijer J. 34.  2015. Nat. Commun. 67891
  35. Andreotti B, Baumchen O, Boulogne F, Daniels KE, Dufresne ER. 35.  et al. 2016. Soft Matter 12:2993–96
  36. Gordan OD, Persson BN, Cesa CM, Mayer D, Hoffmann B. 36.  et al. 2008. Langmuir 24:6636–39
  37. Paretkar D, Xu X, Hui CY, Jagota A. 37.  2014. Soft Matter 10:4084–90
  38. Wang Q, Zhao X. 38.  2014. J. Appl. Mech. 81:051004
  39. Wang Q, Zhao X. 39.  2013. Phys. Rev. E 88:042403
  40. Biot MA. 40.  1963. Appl. Sci. Res. A 12:168–82
  41. Chakrabarti A, Chaudhury MK. 41.  2013. Langmuir 29:6926–35
  42. Chaudhury MK, Chakrabarti A, Ghatak A. 42.  2015. Euro. Phys. J. E 38:1–26
  43. Plateau J. 43.  1873. Statique Expérimentale et Théorique des Liquides Soumis aux Seules Forces Moléculaires. 2 Paris: Gauthier-Villars
  44. Eshelby JD. 44.  1957. Proc. R. Soc. Lond. A 241:376–96
  45. Ducloue L, Pitois O, Goyon J, Chateau X, Ovarlez G. 45.  2014. Soft Matter 10:5093–98
  46. Sharma P, Ganti S. 46.  2004. J. Appl. Mech. 71:663–71
  47. Yang F. 47.  2004. J. Appl. Phys. 95:3516–20
  48. Brisard S, Dormieux L, Kondo D. 48.  2010. Comp. Mater. Sci. 50:403–10
  49. Duan HL, Wang J, Huang ZP, Karihaloo BL. 49.  2005. Proc. R. Soc. A 461:3335–53
  50. Duan HL, Yi X, Huang ZP, Wang J. 50.  2007. Mech. Mater. 39:81–93
  51. Style RW, Wettlaufer JS, Dufresne ER. 51.  2015. Soft Matter 11:672–79
  52. Wang Y, Henann DL. 52.  2016. Extreme Mech. Lett. 9147–57
  53. Kundu S, Crosby AJ. 52a.  2009. Soft Matter 53963–68
  54. Creton C, Ciccotti M. 53.  2016. Rep. Prog. Phys. 79:046601
  55. Liu T, Long R, Hui CY. 54.  2014. Soft Matter 10:7723–29
  56. Hui CY, Liu T, Schwaab ME. 55.  2016. Extreme Mech. Lett. 6:31–36
  57. Young T. 56.  1805. Philos. Trans. R. Soc. Lond. 95:65
  58. Dupré A, Dupré P. 57.  1869. Théorie Mécanique de la Chaleur. Paris: Gauthier-Villars
  59. Neumann F. 58.  1894. Vorlesungen ber die Theorie der Capillaritt. Leipzig, Ger.: B.G. Teubner
  60. Maxwell JC. 59.  1878. Encylopaedia Britannica 556–71 New York: Samuel L. Hall. 9th ed.
  61. Shanahan M, de Gennes PG. 60.  1986. C. R. Acad. Sci. Paris 302:517
  62. Shanahan M. 61.  1987. J. Phys. D: Appl. Phys. 20:945–50
  63. Rusanov AI. 62.  1975. Colloid J. USSR 37:614–22
  64. Rusanov AI. 63.  1978. J. Colloid Interface Sci. 63:330–45
  65. White LR. 64.  2003. J. Colloid Interface Sci. 258:82–96
  66. Hui CY, Jagota A. 65.  2014. Proc. R. Soc. A 470:20140085
  67. Marchand A, Das S, Snoeijer JH, Andreotti B. 66.  2012. Phys. Rev. Lett. 108:094301
  68. Pericet-Cmara R, Best A, Butt HJ, Bonaccurso E. 67.  2008. Langmuir 24:10565–68
  69. Pericet-Camara R, Auernhammer GK, Koynov K, Lorenzoni S, Raiteri R, Bonaccurso E. 68.  2009. Soft Matter 5:3611
  70. Park SJ, Weon BM, San Lee J, Lee J, Kim J, Je JH. 69.  2014. Nat. Commun. 5:4369
  71. Olives J. 70.  2010. J. Phys. Condens. Matter 22:085005
  72. Lubbers LA, Weijs JH, Botto L, Das S, Andreotti B, Snoeijer JH. 71.  2014. J. Fluid Mech. 747:R1
  73. Bostwick JB, Shearer M, Daniels KE. 72.  2014. Soft Matter 10:7361–69
  74. Weijs JH, Andreotti B, Snoeijer JH. 73.  2013. Soft Matter 9:8494–503
  75. Weijs JH, Snoeijer JH, Andreotti B. 74.  2014. Phys. Rev. E 89:042408
  76. Leonforte F, Muller M. 75.  2011. J. Chem. Phys. 135:214703
  77. Cao Z, Dobrynin AV. 76.  2015. Macromolecules 48:443–51
  78. Style RW, Che Y, Park SJ, Weon BM, Je JH. 77.  et al. 2013. PNAS 110:12541
  79. Nadermann N, Hui CY, Jagota A. 78.  2013. PNAS 110:10541–45
  80. Roman B, Bico J. 79.  2010. J. Phys. Condens. Matter 22:493101
  81. Mastrangelo C, Hsu C. 80.  1993. J. Microelectromech. Syst. 2:33–43
  82. Bico J, Roman B, Moulin L, Boudaoud A. 81.  2004. Nature 432:690
  83. Kim HY, Mahadevan L. 82.  2006. J. Fluid Mech. 548:141–50
  84. Py C, Reverdy P, Doppler L, Bico J, Roman B, Baroud CN. 83.  2007. Phys. Rev. Lett. 98:156103
  85. Duprat C, Protiere S, Beebe AY, Stone HA. 84.  2012. Nature 482:510–13
  86. Wei Z, Schneider T, Kim J, Kim HY, Aizenberg J, Mahadevan L. 85.  2015. Proc. R. Soc. A 471:217520140593
  87. Huang J, Juszkiewicz M, de Jeu WH, Cerda E, Emrick T. 86.  et al. 2007. Science 317:650–53
  88. Vella D, Huang J, Menon N, Russell TP, Davidovitch B. 87.  Phys. Rev. Lett. 114:014301
  89. Hui CY, Jagota A. 88.  2015. Soft Matter 11:8960–67
  90. Schulman RD, Dalnoki-Veress K. 89.  2015. Phys. Rev. Lett. 115:206101
  91. Hertz H. 90.  1882. J. Reine Angew. Math. 92:156–71
  92. Chaudhury MK, Whitesides GM. 91.  1991. Langmuir 7:1013–25
  93. Shull KR. 92.  2002. Mater. Sci. Eng. R: Rep. 36:1–45
  94. Lin YY, Chen HY. 93.  2006. J. Polym. Sci. B 44:2912–22
  95. Xu X, Jagota A, Hui CY. 94.  2014. Soft Matter 10:4625–32
  96. Cao Z, Dobrynin AV. 95.  2015. Langmuir 31:12520–29
  97. Hui C-Y, Liu T, Salez T, Raphael E, Jagota A. 96.  2015. Proc. R. Soc. A 471:217520140727
  98. Carrillo JMY, Raphael E, Dobrynin AV. 97.  2010. Langmuir 26:12973–79
  99. Maugis D. 98.  1992. J. Colloid Interface Sci. 150:243–69
  100. Karpitschka S, van Wijngaarden L, Snoeijer JH. 99.  2016. Soft Matter 12:4463–71
  101. Cao Z, Stevens MJ, Dobrynin AV. 100.  2014. Macromolecules 47:3203–9
  102. Jensen KE, Sarfati R, Style RW, Boltyanskiy R, Chakrabarti A. 101.  et al. 2015. PNAS 112:14490–94
  103. Liu Q, Suo Z. 102.  2016. Extreme Mech. Lett. 7:27–33
  104. Rowlinson JS, Widom B. 103.  2013. Molecular Theory of Capillarity. Oxford, UK: Clarendon
  105. Fuller GG, Vermant J. 104.  2012. Annu. Rev. Chem. Biomol. Eng. 3:519–43
  106. Hermans E, Bhamla MS, Kao P, Fuller GG, Vermant J. 105.  2015. Soft Matter 11:8048–57
  107. Scriven L. 106.  1960. Chem. Eng. Sci. 12:98–108
  108. Cammarata R. 107.  2008. Philos. Mag. 88:927–48
  109. Cahn JW. 108.  1980. Acta Metall. 28:1333–38
  110. Hui CY, Jagota A. 109.  2013. Langmuir 29:11310–16
  111. Lu W, Suo Z. 110.  2001. J. Mech. Phys. Solids 49:1937–50
  112. Benveniste Y, Miloh T. 111.  2007. J. Elastic. 88:87–111
  113. Hajji M. 112.  1978. J. Appl. Mech. 45:320–24
  114. Dervaux J, Limat L. 113.  2015. Proc. R. Soc. A 471:217620140813
  115. Sneddon IN. 114.  1995. Fourier Transforms. New York: Dover
  116. Abramovich M, Stegun IA. 115.  1968. Handbook of Mathematical Functions. New York: Dover
  117. Henann DL, Bertoldi K. 116.  2014. Soft Matter 10:709–17
  118. Saksono P, Perić D. 117.  2006. Comp. Mech. 38:265–81
  119. Jagota A, Argento C, Mazur S. 118.  1998. J. Appl. Phys. 83:250–59
  120. Li S, Fan H. 119.  2015. Proc. R. Soc. A 471:20150224
  121. Cao Z, Stevens MJ, Dobrynin AV. 120.  2014. Macromolecules 47:6515–21
  122. Snoeijer JH, Andreotti B. 121.  2008. Phys. Fluids 20:057101
  123. 122. Simulia 2015. Abaqus User Manuals 6.13. Fremont, CA: Dassault Syst.
  124. Rubinstein M, Colby RH. 123.  2003. Polymer Physics. Oxford, UK: Oxford Univ. Press
  125. Dee GT, Sauer BB. 124.  1998. Adv. Phys. 47:161–205
  126. Seifert U. 125.  1997. Adv. Phys. 46:13–137
  127. Helfrich W. 126.  1973. Z. Naturforsch. C Bio. Sci. 28:693–703
  128. Hutchinson J. 127.  1970. Proc. R. Soc. A 319:247–72
  129. Rice JR. 128.  1968. J. Appl. Mech. 35:379–86
  130. Zemel A, Rehfeldt F, Brown AEX, Discher DE, Safran SA. 129.  2010. Nat. Phys. 6:468–73
  131. Schwarz US, Safran SA. 130.  2013. Rev. Mod. Phys. 85:1327–81
  132. German G, Bertola V. 131.  2009. J. Phys.: Condens. Matter 21:375111
  133. Style RW, Isa L, Dufresne ER. 132.  2015. Soft Matter 11:7412–19
  134. Gonzalez-Rodriguez D, Sart S, Babataheri A, Tareste D, Barakat AI. 133.  et al. 2015. Phys. Rev. Lett. 115:088102
  135. Karpitschka S, Pandey A, Lubbers LA, Weijs JH, Botto L. 134.  et al. 2016. PNAS 113:277403–7
  136. Chakrabarti A, Chaudhury MK. 135.  2014. Langmuir 30:4684–93
  137. Chakrabarti A, Chaudhury MK. 136.  2014. Langmuir 31:1911–20
  138. Sokuler M, Auernhammer GK, Roth M, Liu C, Bonaccurso E, Butt HJ. 137.  2010. Langmuir 26:1544–47
  139. Eslami F, Elliott JAW. 138.  2011. J. Phys. Chem. B 115:10646–53
  140. Lopes MC, Bonaccurso E. 139.  2012. Soft Matter 8:7875–81
  141. Mehrabian H, Harting J, Snoeijer JH. 140.  2016. Soft Matter 12:41062–73
  142. Petit J, Bonaccurso E. 141.  2014. Langmuir 30:1160–68
  143. Lopes MC, Bonaccurso E. 142.  2013. Soft Matter 9:7942–50
  144. Weijs JH, Lohse D. 143.  2013. Phys. Rev. Lett. 110:054501
  145. Rose S, Prevoteau A, Elzire P, Hourdet D, Marcellan A, Leibler L. 144.  2014. Nature 505:382–85
  146. Wexler JS, Heard TM, Stone HA. 145.  2014. Phys. Rev. Lett. 112:066102
  147. Li K, Cai S. 146.  2014. Soft Matter 10:8202–9
  148. Labonte D, Federle W. 147.  2015. Philos. Trans. R. Soc. Lond. B 370:20140027
  149. Carre A, Gastel JC, Shanahan MER. 148.  1996. Nature 379:432–34
  150. Chen L, Auernhammer GK, Bonaccurso E. 149.  2011. Soft Matter 7:9084–89
  151. Kajiya T, Daerr A, Narita T, Royon L, Lequeux F, Limat L. 150.  2013. Soft Matter 9:454–61
  152. Chakrabarti A, Chaudhury MK. 151.  2014. Extreme Mech. Lett. 1:47–53
  153. Neukirch S, Antkowiak A, Marigo JJ. 152.  2014. Phys. Rev. E 89:012401
  154. Andreotti B, Snoeijer JH. 153.  2016. Europhys. Lett. 113:66001
/content/journals/10.1146/annurev-conmatphys-031016-025326
Loading
Elastocapillarity: Surface Tension and the Mechanics of Soft Solids
Annual Review of Condensed Matter Physics 8, 99 (2017); https://doi.org/10.1146/annurev-conmatphys-031016-025326
/content/journals/10.1146/annurev-conmatphys-031016-025326
/content/journals/10.1146/annurev-conmatphys-031016-025326
Loading

Data & Media loading...

Supplemental Material

Supplementary Data

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error