No Access Submitted: 01 February 2015 Accepted: 26 August 2015 Published Online: 29 September 2015
Physics of Fluids 27, 092105 (2015); https://doi.org/10.1063/1.4930283
more...View Affiliations
  • 1School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Chemical Engineering, Colorado School of Mines, Golden, Colorado 80401, USA
  • 3School of Engineering, Brown University, Providence, Rhode Island 02912, USA
  • 4Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, Massachusetts 02115, USA
  • 5Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, Massachusetts 02138, USA
  • 6Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
  • 7Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • a)Author to whom correspondence should be addressed. Electronic mail:

View Contributors
  • C. Nadir Kaplan
  • Ning Wu
  • Shreyas Mandre
  • Joanna Aizenberg
  • L. Mahadevan
Drying suspensions often leave behind complex patterns of particulates, as might be seen in the coffee stains on a table. Here, we consider the dynamics of periodic band or uniform solid film formation on a vertical plate suspended partially in a drying colloidal solution. Direct observations allow us to visualize the dynamics of band and film deposition, where both are made of multiple layers of close packed particles. We further see that there is a transition between banding and filming when the colloidal concentration is varied. A minimal theory of the liquid meniscus motion along the plate reveals the dynamics of the banding and its transition to the filming as a function of the ratio of deposition and evaporation rates. We also provide a complementary multiphase model of colloids dissolved in the liquid, which couples the inhomogeneous evaporation at the evolving meniscus to the fluid and particulate flows and the transition from a dilute suspension to a porous plug. This allows us to determine the concentration dependence of the bandwidth and the deposition rate. Together, our findings allow for the control of drying-induced patterning as a function of the colloidal concentration and evaporation rate.
This research was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-09-1-0669-DOD35CAP, the Harvard-MRSEC DMR-1420570, and the Kavli Institute for Bionano Science and Technology at Harvard University.
  1. 1. J. B. Bones, J. V. Sanders, E. R. Segnit, and F. Hulliger, “Structure of opal,” Nature 204, 990 (1964). https://doi.org/10.1038/204990a0, Google ScholarCrossref
  2. 2. R. O. Prum and R. Torres, “Structural coloration of avian skin: Convergent evolution of coherently scattering dermal collagen arrays,” J. Exp. Biol. 206, 2409 (2003). https://doi.org/10.1242/jeb.00431, Google ScholarCrossref
  3. 3. A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, “Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature 405, 437 (2000). https://doi.org/10.1038/35013024, Google ScholarCrossref
  4. 4. S. A. Rinnie, F. Garcia-Santamaria, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52 (2008). https://doi.org/10.1038/nphoton.2007.252, Google ScholarCrossref
  5. 5. K. Eun Sik, L. Wonmok, P. Nam-Gyu, K. Junkyung, and L. Hyunjung, “Compact inverse-opal electrode using non-aggregated TiO2 nanoparticles for dye-sensitized solar cells,” Adv. Funct. Mater. 19, 1093 (2009). https://doi.org/10.1002/adfm.200801540, Google ScholarCrossref
  6. 6. C. Sung-Wook, X. Jingwei, and X. Younan, “Chitosan-based inverse opals: Three-dimensional scaffolds with uniform pore structures for cell culture,” Adv. Mater. 21, 2997 (2009). https://doi.org/10.1002/adma.200803504, Google ScholarCrossref
  7. 7. B. Hatton, L. Mishchenko, S. Davis, K. H. Sandhage, and J. Aizenberg, “Assembly of large-area, highly ordered, crack-free inverse opal films,” Proc. Natl. Acad. Sci. U. S. A. 107, 10354 (2010). https://doi.org/10.1073/pnas.1000954107, Google ScholarCrossref
  8. 8. Á. G Marín, H. Gelderblom, D. Lohse, and J. H. Snoeijer, “Order-to-disorder transition in ring-shaped colloidal stains,” Phys. Rev. Lett. 107, 085502 (2011). https://doi.org/10.1103/PhysRevLett.107.085502, Google ScholarCrossref
  9. 9. T. P. Bigioni, X. M. Lin, T. T. Nguyen, E. I. Corwin, T. A. Witten, and H. M. Jaeger, “Kinetically driven self assembly of highly ordered nanoparticle monolayers,” Nat. Mater. 5, 265 (2006). https://doi.org/10.1038/nmat1611, Google ScholarCrossref
  10. 10. R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, “Capillary flow as the cause of ring stains from dried liquid drops,” Nature 389, 827 (1997). https://doi.org/10.1038/39827, Google ScholarCrossref, ISI
  11. 11. R. D. Deegan, O. Bakajin, T. F. Dupont, G. Huber, S. R. Nagel, and T. A. Witten, “Contact line deposits in an evaporating drop,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 62, 756 (2000). https://doi.org/10.1103/PhysRevE.62.756, Google ScholarCrossref
  12. 12. R. D. Deegan, “Pattern formation in drying drops,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 61, 475 (2000). https://doi.org/10.1103/PhysRevE.61.475, Google ScholarCrossref
  13. 13. Y. O. Popov, “Evaporative deposition patterns: Spatial dimensions of the deposit,” Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 71, 036313 (2005). https://doi.org/10.1103/PhysRevE.71.036313, Google ScholarCrossref
  14. 14. H. S. Kim, C. H. Lee, P. K. Sudeep, T. Emrick, and A. J. Crosby, “Nanoparticle stripes, grids, and ribbons produced by flow coating,” Adv. Mater. 22, 4600 (2010). https://doi.org/10.1002/adma.201001892, Google ScholarCrossref
  15. 15. H. Bodiguel and J. Leng, “Imaging the drying of a colloidal suspension,” Soft Matter 6, 5451 (2010). https://doi.org/10.1039/c0sm00323a, Google ScholarCrossref
  16. 16. E. Adachi, A. S. Dimitrov, and K. Nagayama, “Stripe patterns formed on a glass surface during droplet evaporation,” Langmuir 11, 1057 (1995). https://doi.org/10.1021/la00004a003, Google ScholarCrossref
  17. 17. L. Shmuylovich, A. Q. Shen, and H. A. Stone, “Surface morphology of drying latex films: Multiple ring formation,” Langmuir 18, 3441 (2002). https://doi.org/10.1021/la011484v, Google ScholarCrossref
  18. 18. S. Maheshwari, L. Zhang, Y. Zhu, and H. C. Chang, “Coupling between precipitation and contact-line dynamics: Multiring stains and stick-slip motion,” Phys. Rev. Lett. 100, 044503 (2008). https://doi.org/10.1103/PhysRevLett.100.044503, Google ScholarCrossref
  19. 19. M. Abkarian, J. Nunes, and H. A. Stone, “Colloidal crystallization and banding in a cylindrical geometry,” J. Am. Chem. Soc. 126, 5978 (2004). https://doi.org/10.1021/ja049775o, Google ScholarCrossref
  20. 20. S. Watanabe, K. Inukai, S. Mizuta, and M. T. Miyahara, “Mechanism for stripe pattern formation on hydrophilic surfaces by using convective self-assembly,” Langmuir 25, 7287 (2009). https://doi.org/10.1021/la900315h, Google ScholarCrossref
  21. 21. H. Bodiguel, F. Doumenc, and E. Guerrier, “Stick-slip patterning at low capillary numbers for an evaporating colloidal suspension,” Langmuir 26, 10758 (2010). https://doi.org/10.1021/la100547j, Google ScholarCrossref
  22. 22. G. Jing, H. Bodiguel, F. Doumenc, E. Sultan, and E. Guerrier, “Drying of colloidal suspensions and polymer solutions near the contact line: Deposit thickness at low capillary number,” Langmuir 26, 2288 (2009). https://doi.org/10.1021/la9027223, Google ScholarCrossref
  23. 23. P. J. Yunker, T. Still, M. A. Lohr, and A. G. Yodh, “Suppression of the coffee-ring effect by shape-dependent capillary interactions,” Nature 476, 308 (2011). https://doi.org/10.1038/nature10344, Google ScholarCrossref
  24. 24. J. Li, B. Cabane, M. Sztucki, J. Gummel, and L. Goehring, “Drying dip-coated colloidal films,” Langmuir 28, 200 (2011). https://doi.org/10.1021/la203549g, Google ScholarCrossref
  25. 25. T. A. Witten, “Robust fadeout profile of an evaporation stain,” Europhys. Lett. 86, 64002 (2009). https://doi.org/10.1209/0295-5075/86/64002, Google ScholarCrossref
  26. 26. D. Kaya, V. A. Belyi, and M. Muthukumar, “Pattern formation in drying droplets of polyelectrolyte and salt,” J. Chem. Phys. 133, 114905 (2010). https://doi.org/10.1063/1.3493687, Google ScholarScitation, ISI
  27. 27. G. Berteloot, C.-T. Pham, A. Daerr, F. Lequeux, and L. Limat, “Evaporation-induced flow near a contact line: Consequences on coating and contact angle,” Europhys. Lett. 83, 14003 (2008). https://doi.org/10.1209/0295-5075/83/14003, Google ScholarCrossref
  28. 28. G. Berteloot, A. Daerr, F. Lequeux, and L. Limat, “Dip coating with colloids and evaporation,” Chem. Eng. Process. 68, 69 (2013). https://doi.org/10.1016/j.cep.2012.09.001, Google ScholarCrossref
  29. 29. See supplementary material at http://dx.doi.org/10.1063/1.4930283 for the movies of deposition and meniscus break-up. Google Scholar
  30. 30. M. Egen and R. Zentel, “Surfactant-free emulsion polymerization of various methacrylates: Towards monodisperse colloids for polymer opals,” Macromol. Chem. Phys. 205, 1479 (2004). https://doi.org/10.1002/macp.200400087, Google ScholarCrossref
  31. 31. P. G. de Gennes, F. Brochard-Wyart, and D. Quéré, Capillarity and Wetting Phenomena (Springer Science+Business Media, New York, 2004). Google ScholarCrossref
  32. 32. P. G. de Gennes, “Wetting: Statics and dynamics,” Rev. Mod. Phys. 57, 827 (1985). https://doi.org/10.1103/RevModPhys.57.827, Google ScholarCrossref, ISI
  33. 33. P. G. de Gennes, “Deposition of Langmuir-Blodget layers,” Colloid Polym. Sci. 264, 463 (1986). https://doi.org/10.1007/BF01419552, Google ScholarCrossref
  34. 34. J. Eggers, “Hydrodynamic theory of forced dewetting,” Phys. Rev. Lett. 93, 094502 (2004). https://doi.org/10.1103/PhysRevLett.93.094502, Google ScholarCrossref, ISI
  35. 35. J. Eggers, “Existence of receding and advancing contact lines,” Phys. Fluids 17, 082106 (2005). https://doi.org/10.1063/1.2009007, Google ScholarScitation, ISI
  36. 36. J. H. Snoeijer, B. Andreotti, G. Delon, and M. Fermigier, “Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation,” J. Fluid. Mech. 579, 63 (2006). https://doi.org/10.1017/S0022112007005216, Google ScholarCrossref
  37. 37. J. H. Snoeijer and B. Andreotti, “Moving contact lines: Scales, regimes, and dynamical transitions,” Annu. Rev. Fluid Mech. 45, 269 (2013). https://doi.org/10.1146/annurev-fluid-011212-140734, Google ScholarCrossref, ISI
  38. 38. B. Scheid, J. Delacotte, B. Dollet, E. Rio, F. Restagno, E. A. van Nierop, I. Cantat, D. Langevin, and H. A. Stone, “The role of surface rheology in liquid film formation,” Europhys. Lett. 90, 24002 (2010). https://doi.org/10.1209/0295-5075/90/24002, Google ScholarCrossref
  39. 39. C. E. Colosqui, J. F. Morris, and H. A. Stone, “Hydrodynamically driven colloidal assembly in dip coating,” Phys. Rev. Lett. 110, 188302 (2013). https://doi.org/10.1103/PhysRevLett.110.188302, Google ScholarCrossref
  40. 40. S. D. R. Wilson, “The drag-out problem in film coating theory,” J. Eng. Math. 16, 209 (1982). https://doi.org/10.1007/BF00042717, Google ScholarCrossref
  41. 41. A. Oron, S. H. Davis, and S. G. Bankoff, “Long-scale evolution of thin liquid films,” Rev. Mod. Phys. 69, 931 (1997). https://doi.org/10.1103/RevModPhys.69.931, Google ScholarCrossref, ISI
  42. 42. H. C. Brinkman, “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,” Appl. Sci. Res. 1, 27 (1949). https://doi.org/10.1007/BF02120313, Google ScholarCrossref
  43. 43. S. I. A. Cohen and L. Mahadevan, “Hydrodynamics of hemostasis in sickle-cell disease,” Phys. Rev. Lett. 110, 138104 (2013). https://doi.org/10.1103/PhysRevLett.110.138104, Google ScholarCrossref
  44. 44. See http://www.comsol.com for COMSOL 4.3a, Burlington, MA, USA. Google Scholar
  1. © 2015 AIP Publishing LLC.