Journal of Nanoparticle Research

, Volume 13, Issue 1, pp 59–68 | Cite as

Computational approach to drying a nanoparticle-suspended liquid droplet

Technology and Applications


We suggest a computational approach for estimating the ring-like deposition of nanoparticles contained in a drying liquid droplet. The proposed method involves a Monte Carlo scheme, based on three independent probabilistic processes: (a) evaporation at the liquid surface, (b) convective motion of nanoparticles to the contact line, and (c) treatment of the nanoparticles floating in the air. According to the computational results, while the liquid is evaporating in nanoparticle-suspended liquid droplet (NSLD), the nanoparticles are moved to the contact line as the mass of droplet decreases linearly with time. Since the resulting ring-like deposition can be accounted for in terms of nanoparticle mobility and liquid evaporation from the droplet, our computational approach achieves a morphological and kinematical description of NSLD drying. Some other important features, such as self-pinning of the contact line, reduction of the droplet radius, and pattern formation, are also obtained from this simulation.


Drying Evaporation Nanoparticle-suspended liquid Monte Carlo simulation 


  1. Anderson MP, Srolovitz DJ, Grest GS, Sahni PS (1984) Computer simulation of grain growth—I. Kinetics. Acta Metall 32:783–791CrossRefGoogle Scholar
  2. Blossey R, Bosio A (2002) Contact line deposits on cDNA microarrays: a twin-spot effect. Langmuir 18:2952–2954CrossRefGoogle Scholar
  3. Cheng G, Puntes VF, Guo T (2006) Synthesis and self-assembled ring structures of Ni nanocrystals. J Colloid Interface Sci 293:430–436CrossRefGoogle Scholar
  4. Conway J, Korns H, Fisch MR (1997) Evaporation kinematics of polystyrene bead suspensions. Langmuir 13:426–431CrossRefGoogle Scholar
  5. De Gans B-J, Duineveld PC, Schubert US (2004) Inkjet printing of polymers: state of the art and future developments. Adv Mater 16:203–213CrossRefGoogle Scholar
  6. Deegan RD (2000) Pattern formation in drying drops. Phys Rev E 61:475–485CrossRefGoogle Scholar
  7. 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 389:827–829CrossRefGoogle Scholar
  8. Deegan RD, Bakajin O, Dupont TF, Huber G, Nagel SR, Witten TA (2000) Contact line deposits in an evaporating drop. Phys Rev E 62:756–765CrossRefGoogle Scholar
  9. Ge G, Brus LE (2001) Fast surface diffusion of large disk-shaped nanocrystal aggregates. Nano Lett 1:219–222CrossRefGoogle Scholar
  10. Gelbart WM, Ben-Shaul A (1996) The new science of complex fluids. J Phys Chem 100:13169–13189CrossRefGoogle Scholar
  11. Govor LV, Reiter G, Parisi J, Bauer GH (2004) Self-assembled nanoparticle deposits formed at the contact line of evaporating micrometer-size droplets. Phys Rev E 69:061609CrossRefGoogle Scholar
  12. Hu H, Larson RG (2002) Evaporation of a sessile droplet on a substrate. J Phys Chem B 106:1334–1344CrossRefGoogle Scholar
  13. Hu H, Larson RG (2005a) Analysis of the microfluid flow in an evaporating sessile droplet. Langmuir 21:3963–3971CrossRefGoogle Scholar
  14. Hu H, Larson RG (2005b) Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21:3972–3980CrossRefGoogle Scholar
  15. Jang J, Oh JH (2004) Morphogenesis of evaporation-induced self-assemblies of polypyrrole nanoparticles dispersed in a liquid medium. Langmuir 20:8419–8422CrossRefGoogle Scholar
  16. Kagan CR, Murray CB, Nirmal M, Bawendi MG (1996) Electronic energy transfer in CdSe quantum dot solids. Phys Rev Lett 76:1517–1520CrossRefGoogle Scholar
  17. Kletenik-Edelman O, Ploshnik E, Salant A, Shenhar R, Banin U, Rabani E (2008) Drying-mediated hierarchical self-assembly of nanoparticles: a dynamical coarse-grained approach. J Phys Chem C 112:4498–4506CrossRefGoogle Scholar
  18. Kletenik-Edelman O, Sztrum-Vartash CG, Rabani E (2009) Coarse-grained lattice models for drying-mediated self-assembly of nanoparticles. J Mater Chem 19:2872–2876CrossRefGoogle Scholar
  19. Magdassi S, Bassa A, Vinetsky Y, Kamyshny A (2003) Silver nanoparticles as pigments for water-based ink-jet inks. Chem Mater 15:2208–2217CrossRefGoogle Scholar
  20. Magdassi S, Grouchko M, Toker D, Kamyshny A, Balberg I, Millo O (2005) Ring stain effect at room temperature in silver nanoparticles yields high electrical conductivity. Langmuir 21:10264–10267CrossRefGoogle Scholar
  21. Maillard M, Motte L, Ngo AT, Pileni MP (2000) Rings and hexagons made of nanocrystals: a Marangoni effect. J Phys Chem B 104:11871–11877CrossRefGoogle Scholar
  22. Maillard M, Motte L, Pileni MP (2001) Rings and hexagons made of nanocrystals. Adv Mater 13:200–204CrossRefGoogle Scholar
  23. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AN, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092CrossRefGoogle Scholar
  24. Ohara PC, Gelbart WM (1998) Interplay between hole instability and nanoparticle array formation in ultrathin liquid films. Langmuir 14:3418–3424CrossRefGoogle Scholar
  25. Ohara PC, Heath JR, Gelbart WM (1997) Self-assembly of submicrometer rings of particles from solutions of nanoparticles. Angew Chem Int Ed 36:1078–1080CrossRefGoogle Scholar
  26. Pauliac-Vaujour E, Moriarty P (2007) Meniscus-mediated organization of colloidal nanoparticles. J Phys Chem C 111:16255–16260CrossRefGoogle Scholar
  27. Pauliac-Vaujour E, Stannard A, Martin CP, Blunt MO, Notingher I, Moriarty PJ, Vancea I, Thiele U (2008) Fingering instabilities in dewetting nanofluids. Phys Rev Lett 100:176102CrossRefGoogle Scholar
  28. Rabani E, Reichman DR, Geissler PL, Brus LE (2003) Drying-mediated self-assembly of nanoparticles. Nature 426:271–274CrossRefGoogle Scholar
  29. Shafi KVPM, Felner I, Mastai Y, Gedanken A (1999) Olympic ring formation from newly prepared barium hexaferrite nanoparticle suspension. J Phys Chem A 103:3358–3360Google Scholar
  30. Srolovitz DJ, Grest GS, Anderson MP (1986) Computer simulation of recrystallization—I. Homogeneous nucleation and growth. Acta Metall 34:1833–1845CrossRefGoogle Scholar
  31. Stannard A, Martin CP, Pauliac-Vaujour E, Moriarty P, Thiele U (2008) Dual-scale pattern formation in nanoparticle assemblies. J Phys Chem C 112:15195–15203CrossRefGoogle Scholar
  32. Stowell C, Korgel BA (2001) Self-assembled honeycomb networks of gold nanocrystals. Nano Lett 1:595–600CrossRefGoogle Scholar
  33. Sztrum CG, Hod O, Rabani E (2005) Self-assembly of nanoparticles in three-dimensions: formation of stalagmites. J Phys Chem B 109:6741–6747CrossRefGoogle Scholar
  34. Sztrum CG, Rabani E (2006) Out-of-equilibrium self-assembly of binary mixture of nanoparticles. Adv Mater 18:565–571CrossRefGoogle Scholar
  35. Takagahara T (1992) Quantum dot lattice and enhanced excitonic optical nonlinearity. Surf Sci 267:310–314CrossRefGoogle Scholar
  36. Thiele U, Vancea I, Archer AJ, Robbins MJ, Frastia L, Stannard A, Pauliac-Vaujour E, Martin CP, Blunt MO, Moriarty PJ (2009) Modelling approaches to the dewetting of evaporating thin films of nanoparticle suspensions. J Phys Condens Mater 21:264016CrossRefGoogle Scholar
  37. Tikare V, Cawley JD (1998) Numerical simulation of grain growth in liquid phase sintered materials—I. Model. Acta Mater 46:1333–1342CrossRefGoogle Scholar
  38. Vancea I, Thiele U, Pauliac-Vaujour E, Stannard A, Martin CP, Blunt MO, Moriarty PJ (2008) Front instabilities in evaporatively dewetting nanofluids. Phys Rev E 78:041601CrossRefGoogle Scholar
  39. Yarin AL, Szczech JB, Megaridis CM, Zhang J, Gamota DR (2006) Lines of dense nanoparticle colloidal suspensions evaporating on a flat surface: formation of non-uniform dried deposits. J Colloid Interface Sci 294:343–354CrossRefGoogle Scholar
  40. Yosef G, Rabani E (2006) Self-assembly of nanoparticles into rings: a lattice-gas model. J Phys Chem B 110:20965–20972CrossRefGoogle Scholar
  41. Zhou WL, He J, Fang J, Huynh TA, Kennedy TJ, Stokes KL, O’Connor CJ (2003) Self-assembly of FePt nanoparticles into nanorings. J Appl Phys 93:7340–7342CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Corporate R&D InstituteSamsung Electro-MechanicsYeongtong-Gu, SuwonSouth Korea
  2. 2.Corporate R&D CenterSamsung SDI Co. LTDYongin446-577South Korea
  3. 3.Department of Physics and AstronomyEast Tennessee State UniversityJohnson CityUSA

Personalised recommendations