1932

Abstract

The evaporation of a sessile droplet of liquid is a complex and multifaceted fundamental topic of enduring scientific interest that is key to numerous physical and biological processes. As a result, in recent decades a considerable multidisciplinary research effort has been directed toward many different aspects of the problem. This review focuses on some of the insights that can be obtained from relatively simple mathematical models and discusses some of the directions in which the field may move in the future.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-031822-013213
2023-01-19
2024-06-18
Loading full text...

Full text loading...

/deliver/fulltext/fluid/55/1/annurev-fluid-031822-013213.html?itemId=/content/journals/10.1146/annurev-fluid-031822-013213&mimeType=html&fmt=ahah

Literature Cited

  1. Adachi E, Dimitrov AS, Nagayama K. 1995. Stripe patterns formed on a glass surface during droplet evaporation. Langmuir 11:41057–60
    [Google Scholar]
  2. Ait Saada M, Chikh S, Tadrist L 2013. Evaporation of a sessile drop with pinned or receding contact line on a substrate with different thermophysical properties. Int. J. Heat Mass Transf. 58:1/2197–208
    [Google Scholar]
  3. Ajaev VS. 2005. Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528:279–96
    [Google Scholar]
  4. Ajaev VS, Kabov OA. 2017. Heat and mass transfer near contact lines on heated surfaces. Int. J. Heat Mass Transf. 108:918–32
    [Google Scholar]
  5. Anderson DM, Davis SH. 1995. The spreading of volatile liquid droplets on heated surfaces. Phys. Fluids 7:2248–65
    [Google Scholar]
  6. Askounis A, Orejon D, Koutsos V, Sefiane K, Shanahan MER. 2011. Nanoparticle deposits near the contact line of pinned volatile droplets: size and shape revealed by atomic force microscopy. Soft Matter 7:94152–55
    [Google Scholar]
  7. Barash LY. 2015. Dependence of fluid flows in an evaporating sessile droplet on the characteristics of the substrate. Int. J. Heat Mass Transf. 84:419–26
    [Google Scholar]
  8. Barash LY, Bigioni TP, Vinokur VM, Shchur LN. 2009. Evaporation and fluid dynamics of a sessile drop of capillary size. Phys. Rev. E 79:046301
    [Google Scholar]
  9. Berteloot G, Hoang A, Daerr A, Kavehpour HP, Lequeux F, Limat L. 2012. Evaporation of a sessile droplet: inside the coffee stain. J. Colloid Interface Sci. 370:1155–61
    [Google Scholar]
  10. Bhardwaj R, Fang X, Attinger D. 2009. Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study. New J. Phys. 11:075020
    [Google Scholar]
  11. Bhardwaj R, Fang X, Somasundaran P, Attinger D. 2010. Self-assembly of colloidal particles from evaporating droplets: role of DLVO interactions and proposition of a phase diagram. Langmuir 26:117833–42
    [Google Scholar]
  12. Birdi KS, Vu DT. 1993. Wettability and the evaporation rates of fluids from solid surfaces. J. Adhes. Sci. Technol. 7:6485–93
    [Google Scholar]
  13. Birdi KS, Vu DT, Winter A. 1989. A study of the evaporation rates of small water drops placed on a solid surface. J. Phys. Chem. 93:93702–3
    [Google Scholar]
  14. Bouchenna C, Ait Saada M, Chikh S, Tadrist L 2017. Generalized formulation for evaporation rate and flow pattern prediction inside an evaporating pinned sessile drop. Int. J. Heat Mass Transf. 109:482–500
    [Google Scholar]
  15. Boulogne F, Ingremeau F, Stone HA. 2017. Coffee-stain growth dynamics on dry and wet surfaces. J. Phys. Condens. Matter 29:074001
    [Google Scholar]
  16. Bourgès-Monnier C, Shanahan MER. 1995. Influence of evaporation on contact angle. Langmuir 11:72820–29
    [Google Scholar]
  17. Bou Zeid W, Brutin D. 2013. Influence of relative humidity on spreading, pattern formation and adhesion of a drying drop of whole blood. Colloids Surf. A 430:1–7
    [Google Scholar]
  18. Brutin D 2015. Droplet Wetting and Evaporation San Diego, CA: Academic
    [Google Scholar]
  19. Brutin D, Sefiane K, eds. 2022. Drying of Complex Fluid Drops London: R. Soc. Chem.
    [Google Scholar]
  20. Brutin D, Starov V. 2018. Recent advances in droplet wetting and evaporation. Chem. Soc. Rev. 47:2558–85
    [Google Scholar]
  21. Burelbach JP, Bankoff SG, Davis SH. 1988. Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195:463–94
    [Google Scholar]
  22. Cachile M, Bénichou O, Cazabat AM. 2002a. Evaporating droplets of completely wetting fluids. Langmuir 18:217985–90
    [Google Scholar]
  23. Cachile M, Bénichou O, Poulard C, Cazabat AM 2002b. Evaporating droplets. Langmuir 18:218070–78
    [Google Scholar]
  24. Carle F, Sobac B, Brutin D. 2012. Hydrothermal waves on ethanol droplets evaporating under terrestrial and reduced gravity levels. J. Fluid Mech. 712:614–23
    [Google Scholar]
  25. Carle F, Sobac B, Brutin D. 2013. Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation. Appl. Phys. Lett. 102:061603
    [Google Scholar]
  26. Carrier O, Shahidzadeh-Bonn N, Zargar R, Aytouna M, Habibi M et al. 2016. Evaporation of water: evaporation rate and collective effects. J. Fluid Mech. 798:774–86
    [Google Scholar]
  27. Castanet G, Perrin L, Caballina O, Lemoine F. 2016. Evaporation of closely-spaced interacting droplets arranged in a single row. Int. J. Heat Mass Transf. 93:788–802
    [Google Scholar]
  28. Cazabat A-M, Guéna G. 2010. Evaporation of macroscopic sessile droplets. Soft Matter 6:122591–612
    [Google Scholar]
  29. Charitatos V, Kumar S. 2020. A thin-film model for droplet spreading on soft solid substrates. Soft Matter 16:358284–98
    [Google Scholar]
  30. Charitatos V, Kumar S. 2021. Droplet evaporation on soft solid substrates. Soft Matter 17:419339–52
    [Google Scholar]
  31. Charitatos V, Pham T, Kumar S. 2021. Droplet evaporation on inclined substrates. Phys. Rev. Fluids 6:084001
    [Google Scholar]
  32. Chen C-T, Tseng F-G, Chieng C-C. 2006. Evaporation evolution of volatile liquid droplets in nanoliter wells. Sens. Actuators A 130/131:12–19
    [Google Scholar]
  33. Chen C-T, Chieng C-C, Tseng F-G. 2007. Uniform solute deposition of evaporable droplet in nanoliter wells. J. Microelectromech. Syst. 16:51209–18
    [Google Scholar]
  34. Chen L, Evans JRG. 2009. Arched structures created by colloidal droplets as they dry. Langmuir 25:1911299–301
    [Google Scholar]
  35. Chen X, Chen PG, Ouazzani J, Liu Q. 2017a. Numerical simulations of sessile droplet evaporating on heated substrate. Eur. Phys. J. Spec. Top. 226:61325–35
    [Google Scholar]
  36. Chen X, Wang X, Chen PG, Liu Q. 2017b. Thermal effects of substrate on Marangoni flow in droplet evaporation: response surface and sensitivity analysis. Int. J. Heat Mass Transf. 113:354–65
    [Google Scholar]
  37. Chen YH, Hu WN, Wang J, Hong FJ, Cheng P. 2017. Transient effects and mass convection in sessile droplet evaporation: the role of liquid and substrate thermophysical properties. Int. J. Heat Mass Transf. 108:2072–87
    [Google Scholar]
  38. Cho H, Kim S-M, Liang H, Kim S 2020. Electric-potential-induced uniformity in graphene oxide deposition on porous alumina substrates. Ceram. Int. 46:10A14828–39
    [Google Scholar]
  39. Chong KL, Li Y, Ng CS, Verzicco R, Lohse D. 2020. Convection-dominated dissolution for single and multiple immersed sessile droplets. J. Fluid Mech. 892:A21
    [Google Scholar]
  40. Crivoi A, Duan F. 2013. Evaporation-induced branched structures from sessile nanofluid droplets. J. Phys. Chem. C 117:157835–43
    [Google Scholar]
  41. D'Ambrosio H-M, Colosimo T, Duffy BR, Wilson SK, Yang L et al. 2021. Evaporation of a thin droplet in a shallow well: theory and experiment. J. Fluid Mech. 927:A43
    [Google Scholar]
  42. Dash S, Garimella SV. 2013. Droplet evaporation dynamics on a superhydrophobic surface with negligible hysteresis. Langmuir 29:3410785–95
    [Google Scholar]
  43. Debuisson D, Merlen A, Senez V, Arscott S. 2016. Stick–jump (SJ) evaporation of strongly pinned nanoliter volume sessile water droplets on quick drying, micropatterned surfaces. Langmuir 32:112679–86
    [Google Scholar]
  44. Deegan RD. 2000. Pattern formation in drying drops. Phys. Rev. E 61:1475–85
    [Google Scholar]
  45. Deegan RD, Bakajin O, Dupont TF, Huber G, Nagel SR, Witten TA. 1997. Capillary flow as the cause of ring stains from dried liquid drops. Nature 389:6653827–29
    [Google Scholar]
  46. Deegan RD, Bakajin O, Dupont TF, Huber G, Nagel SR, Witten TA. 2000. Contact line deposits in an evaporating drop. Phys. Rev. E 62:1756–65
    [Google Scholar]
  47. Dhar P, Dwivedi RK, Harikrishnan AR. 2020. Surface declination governed asymmetric sessile droplet evaporation. Phys. Fluids 32:112010
    [Google Scholar]
  48. Diddens C, Tan H, Lv P, Versluis M, Kuerten JGM et al. 2017. Evaporating pure, binary and ternary droplets: thermal effects and axial symmetry breaking. J. Fluid Mech. 823:470–97
    [Google Scholar]
  49. Dollet B, Lohse D. 2016. Pinning stabilizes neighboring surface nanobubbles against Ostwald ripening. Langmuir 32:4311335–39
    [Google Scholar]
  50. Dunn GJ, Wilson SK, Duffy BR, David S, Sefiane K 2008. A mathematical model for the evaporation of a thin sessile liquid droplet: comparison between experiment and theory. Colloids Surf. A 323:1–350–55
    [Google Scholar]
  51. Dunn GJ, Wilson SK, Duffy BR, David S, Sefiane K. 2009a. The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623:329–51
    [Google Scholar]
  52. Dunn GJ, Wilson SK, Duffy BR, Sefiane K. 2009b. Evaporation of a thin droplet on a thin substrate with a high thermal resistance. Phys. Fluids 21:052101
    [Google Scholar]
  53. Edwards AMJ, Cater J, Kilbride JJ, Le Minter P, Brown CV et al. 2021. Interferometric measurement of co-operative evaporation in 2D droplet arrays. Appl. Phys. Lett. 119:151601
    [Google Scholar]
  54. Eggers J, Pismen LM. 2010. Nonlocal description of evaporating drops. Phys. Fluids 22:112101
    [Google Scholar]
  55. Erbil HY. 2012. Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170:1/267–86
    [Google Scholar]
  56. Fabrikant VI. 1985. On the potential flow through membranes. Z. Angew. Math. Phys. 36:4616–23
    [Google Scholar]
  57. Fischer BJ. 2002. Particle convection in an evaporating colloidal droplet. Langmuir 18:160–67
    [Google Scholar]
  58. Gelderblom H, Bloemen O, Snoeijer JH. 2012. Stokes flow near the contact line of an evaporating drop. J. Fluid Mech. 709:69–84
    [Google Scholar]
  59. Gelderblom H, Marín ÁG, Nair H, van Houselt A, Lefferts L et al. 2011. How water droplets evaporate on a superhydrophobic substrate. Phys. Rev. E 83:026306
    [Google Scholar]
  60. Giorgiutti-Dauphiné F, Pauchard L. 2018. Drying drops. Eur. Phys. J. E 41:332
    [Google Scholar]
  61. Gleason K, Putnam SA. 2014. Microdroplet evaporation with a forced pinned contact line. Langmuir 30:3410548–55
    [Google Scholar]
  62. Gopu M, Rathod S, Namangalam U, Pujala RK, Kumar SS, Mampallil D. 2020. Evaporation of inclined drops: formation of asymmetric ring patterns. Langmuir 36:288137–43
    [Google Scholar]
  63. Guéna G, Poulard C, Cazabat AM. 2007. The leading edge of evaporating droplets. J. Colloid Interface Sci. 312:1164–71
    [Google Scholar]
  64. Hamamoto Y, Christy JRE, Sefiane K. 2011. Order-of-magnitude increase in flow velocity driven by mass conservation during the evaporation of sessile drops. Phys. Rev. E 83:051602
    [Google Scholar]
  65. Harris DJ, Conrad JC, Lewis JA. 2009. Evaporative lithographic patterning of binary colloidal films. Philos. Trans. R. Soc. A 367:19095157–65
    [Google Scholar]
  66. Hatte S, Pandey K, Pandey K, Chakraborty S, Basu S. 2019. Universal evaporation dynamics of ordered arrays of sessile droplets. J. Fluid Mech. 866:61–81
    [Google Scholar]
  67. Hu H, Larson RG. 2002. Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B 106:61334–44
    [Google Scholar]
  68. Hu H, Larson RG. 2005a. Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir 21:93963–71
    [Google Scholar]
  69. Hu H, Larson RG. 2005b. Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21:93972–80
    [Google Scholar]
  70. Hu H, Larson RG. 2006. Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110:147090–94
    [Google Scholar]
  71. Hu D, Wu H. 2015. Numerical study and predictions of evolution behaviors of evaporating pinned droplets based on a comprehensive model. Int. J. Therm. Sci. 96:149–59
    [Google Scholar]
  72. Hu D, Wu H. 2016. Volume evolution of small sessile droplets evaporating in stick–slip mode. Phys. Rev. E 93:042805
    [Google Scholar]
  73. Hu D, Wu H, Liu Z. 2014. Effect of liquid–vapor interface area on the evaporation rate of small sessile droplets. Int. J. Therm. Sci. 84:300–8
    [Google Scholar]
  74. Jackson JD. 1988. Classical Electrodynamics New York: Wiley. , 3rd ed..
    [Google Scholar]
  75. Kajiya T, Nishitani E, Yamaue T, Doi M. 2006. Piling-to-buckling transition in the drying process of polymer solution drop on substrate having a large contact angle. Phys. Rev. E 73:011601
    [Google Scholar]
  76. Kang SJ, Vandadi V, Felske JD, Masoud H. 2016. Alternative mechanism for coffee-ring deposition based on active role of free surface. Phys. Rev. E 94:063104
    [Google Scholar]
  77. Kaplan CN, Mahadevan L. 2015. Evaporation-driven ring and film deposition from colloidal droplets. J. Fluid Mech. 781:R2
    [Google Scholar]
  78. Karapetsas G, Matar OK, Valluri P, Sefiane K. 2012. Convective rolls and hydrothermal waves in evaporating sessile drops. Langmuir 28:3111433–39
    [Google Scholar]
  79. Khilifi D, Foudhil W, Fahem K, Harmand S, Ben Jabrallah S 2019. Study of the phenomenon of the interaction between sessile drops during evaporation. Therm. Sci. 23:2B1105–14
    [Google Scholar]
  80. Kim JY, Hwang IG, Weon BM. 2017. Evaporation of inclined water droplets. Sci. Rep. 7:42848
    [Google Scholar]
  81. Kokalj T, Cho H, Jenko M, Lee LP. 2010. Biologically inspired porous cooling membrane using arrayed-droplets evaporation. Appl. Phys. Lett. 96:163703
    [Google Scholar]
  82. Kolegov KS, Barash LY. 2020. Applying droplets and films in evaporative lithography. Adv. Colloid Interface Sci. 285:102271
    [Google Scholar]
  83. Kovalchuk NM, Trybala A, Starov VM. 2014. Evaporation of sessile droplets. Curr. Opin. Colloid Interface Sci. 19:4336–42
    [Google Scholar]
  84. Kuang M, Wang L, Song Y 2014. Controllable printing droplets for high-resolution patterns. Adv. Matter 26:406950–58
    [Google Scholar]
  85. Kumar PL, Thampi SP, Basavaraj MG. 2021. Patterns from drops drying on inclined substrates. Soft Matter 17:337670–81
    [Google Scholar]
  86. Lacasta AM, Sokolov IM, Sancho JM, Sagués F. 1998. Competitive evaporation in arrays of droplets. Phys. Rev. E 57:56198–201
    [Google Scholar]
  87. Larson RG. 2014. Transport and deposition patterns in drying sessile droplets. AIChE J. 60:51538–71
    [Google Scholar]
  88. Lebedev NN. 1965. Special Functions and Their Applications transl. RA Silverman Englewood Cliffs, NJ: Prentice-Hall (from Russian)
    [Google Scholar]
  89. Li Y, Diddens C, Lv P, Wijshoff H, Versluis M, Lohse D. 2019. Gravitational effect in evaporating binary microdroplets. Phys. Rev. Lett. 122:114501
    [Google Scholar]
  90. Li Y, Diddens C, Segers T, Wijshoff H, Versluis M, Lohse D. 2020. Evaporating droplets on oil-wetted surfaces: suppression of the coffee-stain effect. PNAS 117:2916756–63
    [Google Scholar]
  91. Li Y-F, Sheng Y-J, Tsao H-K. 2013. Evaporation stains: suppressing the coffee-ring effect by contact angle hysteresis. Langmuir 29:257802–11
    [Google Scholar]
  92. Liu Y, Zhang X. 2018. A review of recent theoretical and computational studies on pinned surface nanobubbles. Chin. Phys. B 27:014401
    [Google Scholar]
  93. Lohse D, Zhang X. 2015. Surface nanobubbles and nanodroplets. Rev. Mod. Phys. 87:3981–1035
    [Google Scholar]
  94. Lohse D, Zhang X. 2020. Physicochemical hydrodynamics of droplets out of equilibrium. Nat. Rev. Phys. 2:8426–43
    [Google Scholar]
  95. Maatar A, Chikh S, Ait Saada M, Tadrist L 2015. Transient effects on sessile droplet evaporation of volatile liquids. Int. J. Heat Mass Transf. 86:212–20
    [Google Scholar]
  96. Maki KL, Kumar S. 2011. Fast evaporation of spreading droplets of colloidal suspensions. Langmuir 27:1811347–63
    [Google Scholar]
  97. Malinowski R, Volpe G, Parkin IP, Volpe G. 2018. Dynamic control of particle deposition in evaporating droplets by an external point source of vapor. J. Phys. Chem. Lett. 9:3659–64
    [Google Scholar]
  98. Mampallil D, Eral HB. 2018. A review on suppression and utilization of the coffee-ring effect. Adv. Colloid Interface Sci. 252:38–54
    [Google Scholar]
  99. Man X, Doi M. 2016. Ring to mountain transition in deposition pattern of drying droplets. Phys. Rev. Lett. 116:066101
    [Google Scholar]
  100. Mangel RF, Baer E. 1962. The evaporation of water drops from a “Teflon” surface. Chem. Eng. Sci. 17:9705–6
    [Google Scholar]
  101. Marín ÁG, Gelderblom H, Lohse D, Snoeijer JH. 2011. Rush-hour in evaporating coffee drops. Phys. Fluids 23:091111
    [Google Scholar]
  102. Marin A, Karpitschka S, Noguera-Marín D, Cabrerizo-Vílchez MA, Rossi M et al. 2019. Solutal Marangoni flow as the cause of ring stains for drying salty colloidal drops. Phys. Rev. Fluids 4:041601(R)
    [Google Scholar]
  103. Masoud H, Felske JD. 2009a. Analytical solution for inviscid flow inside an evaporating sessile drop. Phys. Rev. E 79:016301
    [Google Scholar]
  104. Masoud H, Felske JD. 2009b. Analytical solution for Stokes flow inside an evaporating sessile drop: spherical and cylindrical cap shapes. Phys. Fluids 21:042102
    [Google Scholar]
  105. Masoud H, Howell PD, Stone HA. 2021. Evaporation of multiple droplets. J. Fluid Mech. 927:R4
    [Google Scholar]
  106. Masoud H, Stone HA. 2019. The reciprocal theorem in fluid mechanics and transport phenomena. J. Fluid Mech. 879:P1
    [Google Scholar]
  107. McHale G, Aqil S, Shirtcliffe NJ, Newton MI, Erbil HY. 2005. Analysis of droplet evaporation on a superhydrophobic surface. Langmuir 21:2411053–60
    [Google Scholar]
  108. Michelin S, Guérin E, Lauga E. 2018. Collective dissolution of microbubbles. Phys. Rev. Fluids 3:043601
    [Google Scholar]
  109. Moffat JR, Sefiane K, Shanahan MER. 2009. Effect of TiO2 nanoparticles on contact line stick–slip behavior of volatile drops. J. Phys. Chem. B 113:268860–66
    [Google Scholar]
  110. Moore MR, Vella D, Oliver JM. 2021. The nascent coffee ring: how solute diffusion counters advection. J. Fluid Mech. 920:A54
    [Google Scholar]
  111. Murisic M, Kondic L. 2011. On evaporation of sessile drops with moving contact lines. J. Fluid Mech. 679:219–46
    [Google Scholar]
  112. Nguyen TAH, Biggs SR, Nguyen AV. 2017. Manipulating colloidal residue deposit from drying droplets: air/liquid interface capture competes with coffee-ring effect. Chem. Eng. Sci. 167:78–87
    [Google Scholar]
  113. Nguyen TAH, Biggs SR, Nguyen AV. 2018. Analytical model for diffusive evaporation of sessile droplets coupled with interfacial cooling effect. Langmuir 34:236955–62
    [Google Scholar]
  114. Nguyen TAH, Nguyen AV. 2014. Transient volume of evaporating sessile droplets: 2/3, 1/1, or another power law?. Langmuir 30:226544–47
    [Google Scholar]
  115. Nguyen TAH, Nguyen AV, Hampton MA, Xu ZP, Huang L, Rudolph V. 2012. Theoretical and experimental analysis of droplet evaporation on solid surfaces. Chem. Eng. Sci. 69:1522–29
    [Google Scholar]
  116. Orejon D, Sefiane K, Shanahan MER. 2011. Stick–slip of evaporating droplets: substrate hydrophobicity and nanoparticle concentration. Langmuir 27:2112834–43
    [Google Scholar]
  117. Ozawa K, Nishitani E, Doi M. 2005. Modeling of the drying process of liquid droplet to form thin film. Jpn. J. Appl. Phys. 44:6A4229–34
    [Google Scholar]
  118. Pan Z, Dash S, Weibel JA, Garimella SV. 2013. Assessment of water droplet evaporation mechanisms on hydrophobic and superhydrophobic substrates. Langmuir 29:5115831–41
    [Google Scholar]
  119. Pan Z, Weibel JA, Garimella SV. 2014. Influence of surface wettability on transport mechanisms governing water droplet evaporation. Langmuir 30:329726–30
    [Google Scholar]
  120. Parsa M, Harmand S, Sefiane K. 2018. Mechanisms of pattern formation from dried sessile drops. Adv. Colloid Interface Sci. 254:22–47
    [Google Scholar]
  121. Paul A, Khurana G, Dhar P. 2021. Substrate concavity influenced evaporation mechanisms of sessile droplets. Phys. Fluids 33:082003
    [Google Scholar]
  122. Pham T, Kumar S. 2017. Drying of droplets of colloidal suspensions on rough substrates. Langmuir 33:3810061–76
    [Google Scholar]
  123. Pham T, Kumar S. 2019. Imbibition and evaporation of droplets of colloidal suspensions on permeable substrates. Phys. Rev. Fluids 4:034004
    [Google Scholar]
  124. Picknett RG, Bexon R. 1977. The evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci. 61:2336–50
    [Google Scholar]
  125. Popov YO. 2005. Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71:036313
    [Google Scholar]
  126. Poulard C, Guéna G, Cazabat AM. 2005. Diffusion-driven evaporation of sessile drops. J. Phys. Condens. Matter 17:49S4213–27
    [Google Scholar]
  127. Pradhan TK, Panigrahi PK. 2015. Deposition pattern of interacting droplets. Colloids Surf. A 482:562–67
    [Google Scholar]
  128. Rieger B, van den Doel LR, van Vliet LJ. 2003. Ring formation in nanoliter cups: quantitative measurements of flow in micromachined wells. Phys. Rev. E 68:036312
    [Google Scholar]
  129. Ristenpart WD, Kim PG, Domingues C, Wan J, Stone HA 2007. Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99:234502
    [Google Scholar]
  130. Routh AF. 2013. Drying of thin colloidal films. Rep. Prog. Phys. 76:046603
    [Google Scholar]
  131. Sáenz PJ, Sefiane K, Kim J, Matar OK, Valluri P. 2015. Evaporation of sessile drops: a three-dimensional approach. J. Fluid Mech. 772:705–39
    [Google Scholar]
  132. Sáenz PJ, Wray AW, Che Z, Matar OK, Valluri P et al. 2017. Dynamics and universal scaling law in geometrically-controlled sessile drop evaporation. Nat. Commun. 8:14783
    [Google Scholar]
  133. Savva N, Rednikov A, Colinet P. 2017. Asymptotic analysis of the evaporation dynamics of partially wetting droplets. J. Fluid Mech. 824:574–623
    [Google Scholar]
  134. Schäfle C, Bechinger C, Rinn B, David C, Leiderer P. 1999. Cooperative evaporation in ordered arrays of volatile droplets. Phys. Rev. Lett. 83:255302–5
    [Google Scholar]
  135. Schofield FGH, Pritchard D, Wilson SK, Sefiane K 2021. The lifetimes of evaporating sessile droplets of water can be strongly influenced by thermal effects. Fluids 6:4141
    [Google Scholar]
  136. Schofield FGH, Wilson SK, Pritchard D, Sefiane K. 2018. The lifetimes of evaporating sessile droplets are significantly extended by strong thermal effects. J. Fluid Mech. 851:231–44
    [Google Scholar]
  137. Schofield FGH, Wray AW, Pritchard D, Wilson SK. 2020. The shielding effect extends the lifetimes of two-dimensional sessile droplets. J. Eng. Math. 120:189–110
    [Google Scholar]
  138. Sefiane K. 2010. On the formation of regular patterns from drying droplets and their potential use for bio-medical applications. J. Bionic Eng. 7:Suppl.S82–93
    [Google Scholar]
  139. Sefiane K. 2014. Patterns from drying drops. Adv. Colloid Interface Sci. 206:372–81
    [Google Scholar]
  140. Sefiane K, Bennacer R. 2011. An expression for droplet evaporation incorporating thermal effects. J. Fluid Mech. 667:260–71
    [Google Scholar]
  141. Sefiane K, Moffat JR, Matar OK, Craster RV. 2008. Self-excited hydrothermal waves in evaporating sessile drops. Appl. Phys. Lett. 93:074103
    [Google Scholar]
  142. Sefiane K, Steinchen A, Moffat R. 2010. On hydrothermal waves observed during evaporation of sessile droplets. Colloids Surf. A 365:1–395–108
    [Google Scholar]
  143. Sefiane K, Wilson SK, David S, Dunn GJ, Duffy BR. 2009. On the effect of the atmosphere on the evaporation of sessile droplets of water. Phys. Fluids 21:062101
    [Google Scholar]
  144. Snoeijer JH, Andreotti B. 2013. Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45:269–92
    [Google Scholar]
  145. Semenov S, Starov VM, Rubio RG, Velarde MG. 2010. Instantaneous distribution of fluxes in the course of evaporation of sessile liquid droplets: computer simulations. Colloids Surf. A 372:1–3127–34
    [Google Scholar]
  146. Semenov S, Starov VM, Rubio RG, Agogo H, Velarde MG. 2011. Evaporation of sessile water droplets: universal behaviour in presence of contact angle hysteresis. Colloids Surf. A 391:1–3135–44
    [Google Scholar]
  147. Semenov S, Starov VM, Rubio RG, Agogo H, Velarde MG. 2012. Evaporation of sessile water droplets in presence of contact angle hysteresis. Math. Model. Nat. Phenom. 7:482–98
    [Google Scholar]
  148. Semenov S, Starov VM, Rubio RG, Velarde MG. 2012. Computer simulations of evaporation of pinned sessile droplets: influence of kinetic effects. Langmuir 28:4315203–11
    [Google Scholar]
  149. Semenov S, Trybala A, Rubio RG, Kovalchuk N, Starov V, Velarde MG. 2014. Simultaneous spreading and evaporation: recent developments. Adv. Colloid Interface Sci. 206:382–98
    [Google Scholar]
  150. Shahidzadeh-Bonn N, Rafaï S, Azouni A, Bonn D. 2006. Evaporating droplets. J. Fluid Mech. 549:307–13
    [Google Scholar]
  151. Shahidzadeh N, Schut MFL, Desarnaud J, Prat M, Bonn D. 2015. Salt stains from evaporating droplets. Sci. Rep. 5:10335
    [Google Scholar]
  152. Shaikeea A, Basu S, Hatte S, Bansal L. 2016. Insights into vapor-mediated interactions in a nanocolloidal droplet system: evaporation dynamics and effects on self-assembly topologies on macro- to microscales. Langmuir 32:4010334–43
    [Google Scholar]
  153. Shen Y, Kang F, Cheng Y, Zhang K, Sui Y. 2022. Numerical and theoretical analysis of fast evaporating sessile droplets with coupled fields. Int. J. Therm. Sci. 172:107284
    [Google Scholar]
  154. Smith FR, Brutin D. 2018. Wetting and spreading of human blood: recent advances and applications. Curr. Opin. Colloid Interface Sci. 36:78–83
    [Google Scholar]
  155. Sobac B, Brutin D. 2012. Thermal effects of the substrate on water droplet evaporation. Phys. Rev. E 86:021602
    [Google Scholar]
  156. Sodtke C, Ajaev VS, Stephan P 2008. Dynamics of volatile liquid droplets on heated surfaces: theory versus experiment. J. Fluid Mech. 610:343–62
    [Google Scholar]
  157. Sokuler M, Auernhammer GK, Liu CJ, Bonaccurso E, Butt H-J. 2010. Dynamics of condensation and evaporation: effect of inter-drop spacing. Eur. Phys. Lett. 89:036004
    [Google Scholar]
  158. Sommer AP. 2004. Limits of the impact of gravity on self-organizing nanospheres. J. Phys. Chem. B 108:248096–98
    [Google Scholar]
  159. Soolaman DM, Yu H-Z. 2005. Water microdroplets on molecularly tailored surfaces: correlation between wetting hysteresis and evaporation mode switching. J. Phys. Chem. B 109:3817967–73
    [Google Scholar]
  160. Stauber JM. 2015. On the evaporation of sessile droplets PhD Thesis, Univ. Strathclyde Glasgow, UK:
    [Google Scholar]
  161. Stauber JM, Wilson SK, Duffy BR, Sefiane K. 2014. On the lifetimes of evaporating droplets. J. Fluid Mech. 744:R2
    [Google Scholar]
  162. Stauber JM, Wilson SK, Duffy BR, Sefiane K. 2015a. Evaporation of droplets on strongly hydrophobic substrates. Langmuir 31:123653–60
    [Google Scholar]
  163. Stauber JM, Wilson SK, Duffy BR, Sefiane K. 2015b. On the lifetimes of evaporating droplets with related initial and receding contact angles. Phys. Fluids 27:122101
    [Google Scholar]
  164. Sultan E, Boudaoud A, Ben Amar M 2005. Evaporation of a thin film: diffusion of the vapour and Marangoni instabilities. J. Fluid Mech. 543:183–202
    [Google Scholar]
  165. Ta VD, Carter RM, Esenturk E, Connaughton C, Wasley TJ et al. 2016. Dynamically controlled deposition of colloidal nanoparticle suspension in evaporating drops using laser radiation. Soft Matter 12:204530–36
    [Google Scholar]
  166. Talbot E, Bain C, De Dier R, Sempels W, Vermant J. 2016. Droplets drying on surfaces. Fundamentals of Inkjet Printing: The Science of Inkjet and Droplets SD Hoath 251–79 New York: Wiley
    [Google Scholar]
  167. Tarasevich YY. 2005. Simple analytical model of capillary flow in an evaporating sessile drop. Phys. Rev. E 71:027301
    [Google Scholar]
  168. Timm ML, Dehdashti E, Jarrahi Darban A, Masoud H 2019. Evaporation of a sessile droplet on a slope. Sci. Rep. 9:19803
    [Google Scholar]
  169. Vancauwenberghe V, Di Marco P, Brutin D. 2013. Wetting and evaporation of a sessile drop under an external electrical field: a review. Colloids Surf. A 432:50–56
    [Google Scholar]
  170. van den Doel LR, van Vliet LJ. 2001. Temporal phase-unwrapping algorithm for dynamic interference pattern analysis in interference-contrast microscopy. Appl. Opt. 40:254487–500
    [Google Scholar]
  171. Vlasko-Vlasov VK, Sulwer M, Shevchenko EV, Parker J, Kwok WK. 2020. Ring patterns generated by an expanding colloidal meniscus. Phys. Rev. E 102:052608
    [Google Scholar]
  172. Wang Z, Orejon D, Sefiane K, Takata Y. 2019. Coupled thermal transport and mass diffusion during vapor absorption into hygroscopic liquid desiccant droplets. Int. J. Heat Mass Transf. 134:1014–23
    [Google Scholar]
  173. Wang Z, Karapetsas G, Valluri P, Sefiane K, Williams A, Takata Y 2021. Dynamics of hygroscopic aqueous solution droplets undergoing evaporation or vapour absorption. J. Fluid Mech. 912:A2
    [Google Scholar]
  174. Wang F, Wu M, Man X, Yuan Q 2020. Formation of deposition patterns induced by the evaporation of the restricted liquid. Langmuir 36:298520–26
    [Google Scholar]
  175. Widjaja E, Harris MT. 2008. Particle deposition study during sessile drop evaporation. AIChE J. 54:92250–60
    [Google Scholar]
  176. Williams AGL, Karapetsas G, Mamalis D, Sefiane K, Matar OK, Valluri P. 2021. Spreading and retraction dynamics of sessile evaporating droplets comprising volatile binary mixtures. J. Fluid Mech. 907:A22
    [Google Scholar]
  177. Willmer D, Baldwin KA, Kwartnik C, Fairhurst DJ. 2010. Growth of solid conical structures during multistage drying of sessile poly(ethylene oxide) droplets. Phys. Chem. Chem. Phys. 12:163998–4004
    [Google Scholar]
  178. Wilson SK, Duffy BR. 2022. Mathematical models for the evaporation of sessile droplets. See Brutin & Sefiane 2022 47–67
  179. Wray AW, Duffy BR, Wilson SK. 2020. Competitive evaporation of multiple sessile droplets. J. Fluid Mech. 884:A45
    [Google Scholar]
  180. Wray AW, Papageorgiou DT, Craster RV, Sefiane K, Matar OK. 2014. Electrostatic suppression of the “coffee stain effect. .” Langmuir 30:205849–58
    [Google Scholar]
  181. Wray AW, Wray PS, Duffy BR, Wilson SK. 2021. Contact-line deposits from multiple evaporating droplets. Phys. Rev. Fluids 6:073604
    [Google Scholar]
  182. Xu X, Luo J, Guo D. 2010. Criterion for reversal of thermal Marangoni flow in drying drops. Langmuir 26:31918–22
    [Google Scholar]
  183. Xu X, Luo J, Guo D. 2012. Radial-velocity profile along the surface of evaporating liquid droplets. Soft Matter 8:215797–803
    [Google Scholar]
  184. Yang X, Jiang Z, Lyu P, Ding Z, Man X 2021. Deposition pattern of drying droplets. Commun. Theor. Phys. 73:047601
    [Google Scholar]
  185. Yu Y-S, Wang Z, Zhao Y-P. 2012. Experimental and theoretical investigations of evaporation of sessile water droplet on hydrophobic surfaces. J. Colloid Interface Sci. 365:1254–59
    [Google Scholar]
  186. Yunker PJ, Still T, Lohr MA, Yodh AG. 2011. Suppression of the coffee-ring effect by shape-dependent capillary interactions. Nature 476:7360308–11
    [Google Scholar]
  187. Zang D, Tarafdar S, Tarasevich YY, Choudhury MD, Dutta T. 2019. Evaporation of a droplet: from physics to applications. Phys. Rep. 804:1–56
    [Google Scholar]
  188. Zhang X, Lhuissier H, Sun C, Lohse D. 2014. Surface nanobubbles nucleate microdroplets. Phys. Rev. Lett. 112:144503
    [Google Scholar]
  189. Zheng R. 2009. A study of the evaporative deposition process: pipes and truncated transport dynamics. Eur. Phys. J. E 29:2205–18
    [Google Scholar]
  190. Zhong X, Crivoi A, Duan F. 2015. Sessile nanofluid droplet drying. Adv. Colloid Interface Sci. 217:13–30
    [Google Scholar]
  191. Zhu J-L, Shi W-Y. 2021. Hydrothermal waves in sessile droplets evaporating at a constant contact angle mode. Int. J. Heat Mass Transf. 172:121131
    [Google Scholar]
  192. Zhu X, Verzicco R, Zhang X, Lohse D. 2018. Diffusive interaction of multiple surface nanobubbles: shrinkage, growth, and coarsening. Soft Matter 14:112006–14
    [Google Scholar]
  193. Zigelman A, Manor O. 2016. A model for pattern deposition from an evaporating solution subject to contact angle hysteresis and finite solubility. Soft Matter 12:265693–707
    [Google Scholar]
/content/journals/10.1146/annurev-fluid-031822-013213
Loading
/content/journals/10.1146/annurev-fluid-031822-013213
Loading

Data & Media loading...

  • Article Type: Review Article
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