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Evaporation-driven ring and film deposition from colloidal droplets

Published online by Cambridge University Press:  16 September 2015

C. Nadir Kaplan
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
L. Mahadevan*
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA 02115, USA Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA 02138, USA Department of Physics, Harvard University, Cambridge, MA 02138, USA
*
Email address for correspondence: lm@seas.harvard.edu

Abstract

Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between rings and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop. This includes the liquid flow, local variations of the particle concentration leading to a cross-over between dilute and dense suspensions, and the resulting propagation of the deposition front. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types while correctly accounting for the transition from Stokes flow to Darcy flow at high solute concentrations.

Type
Rapids
Copyright
© 2015 Cambridge University Press 

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References

Abkarian, M., Nunes, J. & Stone, H. A. 2004 Colloidal crystallization and banding in a cylindrical geometry. J. Am. Chem. Soc. 126, 59785979.Google Scholar
Adachi, E., Dimitrov, A. S. & Nagayama, K. 1995 Stripe patterns formed on a glass surface during droplet evaporation. Langmuir 11, 10571060.CrossRefGoogle Scholar
Berteloot, G., Hoang, A., Daerr, A., Kavehpour, H. P., Lequeux, F. & Limat, L. 2012 Evaporation of a sessile droplet: inside the coffee stain. J. Colloid Interface Sci. 370, 155161.Google Scholar
Bigioni, T. P., Lin, X. M., Nguyen, T. T., Corwin, E. I., Witten, T. A. & Jaeger, H. M. 2006 Kinetically driven self assembly of highly ordered nanoparticle monolayers. Nat. Mater. 5, 265270.CrossRefGoogle ScholarPubMed
Brinkman, H. C. 1949 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 2734.Google Scholar
Cohen, S. I. A. & Mahadevan, L. 2013 Hydrodynamics of hemostasis in sickle-cell disease. Phys. Rev. Lett. 110, 138104.CrossRefGoogle ScholarPubMed
ComsolMultiphysics 4.3a, Burlington, MA, USA. http://www.comsol.com/products/4.3a.Google Scholar
Cook, B. P., Bertozzi, A. L. & Hosoi, A. E. 2008 Shock solutions for particle-laden thin films. SIAM J. Appl. Math. 68, 760783.Google Scholar
Craster, R. V., Matar, O. K. & Sefiane, K. 2009 Pinning, retraction, and terracing of evaporating droplets containing nanoparticles. Langmuir 25, 36013609.Google Scholar
Deegan, R. D. 2000 Pattern formation in drying drops. Phys. Rev. E 61, 475485.CrossRefGoogle ScholarPubMed
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 1997 Capillary flow as the cause of ring stains from dried liquid drops. Nature 389, 827829.CrossRefGoogle Scholar
Deegan, R. D., Bakajin, O., Dupont, T. F., Huber, G., Nagel, S. R. & Witten, T. A. 2000 Contact line deposits in an evaporating drop. Phys. Rev. E 62, 756765.Google Scholar
Frastia, L., Archer, A. J. & Thiele, U. 2011 Dynamical model for the formation of patterned deposits at receding contact lines. Phys. Rev. Lett. 106, 077801.Google Scholar
Frastia, L., Archer, A. J. & Thiele, U. 2012 Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions. Soft Matt. 8, 1136311386.CrossRefGoogle Scholar
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.Google Scholar
de Gennes, P. G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena. Springer.Google Scholar
Hu, H. & Larson, R. G. 2005 Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21, 39723980.Google Scholar
Hu, H. & Larson, R. G. 2006 Marangoni effect reverses coffee-ring depositions. J. Phys. Chem. B 110, 70907094.Google Scholar
Kaplan, C. N., Wu, N., Mandre, S., Aizenberg, J. & Mahadevan, L.2015 Dynamics of evaporative colloidal patterning. arXiv:1412.1813.Google Scholar
Kaya, D., Belyi, V. A. & Muthukumar, M. 2010 Pattern formation in drying droplets of polyelectrolyte and salt. J. Chem. Phys. 133, 114905.Google Scholar
Kobayashi, M., Makino, M., Okuzono, T. & Doi, M. 2010 Interference effects in the drying of polymer droplets on substrate. J. Phys. Soc. Japan 79, 044802.Google Scholar
Landau, L. D. & Lifshitz, E. M. 2004 Fluid Mechanics, 2nd edn. Elsevier.Google Scholar
Lebovka, N. I., Gigiberiya, V. A., Lytvyn, O. S., Tarasevich, Y. Y., Vodolazskaya, I. V. & Bondarenko, O. P. 2014 Drying of sessile droplets of laponite-based aqueous nanofluids. Colloids Surf. A 462, 5263.Google Scholar
Lin, X. M., Jaeger, H. M., Sorensen, C. M. & Klabunde, K. J. 2001 Formation of long-range-ordered nanocrystal superlattices on silicon nitride substrates. J. Phys. Chem. B 105, 33533357.CrossRefGoogle Scholar
Maheshwari, S., Zhang, L., Zhu, Y. & Chang, H. C. 2008 Coupling between precipitation and contact-line dynamics: multiring stains and stick-slip motion. Phys. Rev. Lett. 100, 044503.Google Scholar
Marín, Á. G., Gelderblom, H., Lohse, D. & Snoeijer, J. H. 2011 Order-to-disorder transition in ring-shaped colloidal stains. Phys. Rev. Lett. 107, 085502.Google Scholar
Marín, Á. G., Gelderblom, H., Susarrey-Arce, A., van Houselt, A., Lefferts, L., Gardeniers, J. G. E., Lohse, D. & Snoeijer, J. H. 2012 Building microscopic soccer balls with evaporating colloidal fakir drops. Proc. Natl Acad. Sci. USA 109, 1645516458.CrossRefGoogle ScholarPubMed
Narayanan, S., Wang, J. & Lin, X. M. 2004 Dynamical self-assembly of nanocrystal superlattices during colloidal droplet evaporation by in situ small angle x-ray scattering. Phys. Rev. Lett. 93, 135503.Google Scholar
Okuzono, T., Kobayashi, M. & Doi, M. 2009 Final shape of a drying thin film. Phys. Rev. E 80, 021603.CrossRefGoogle ScholarPubMed
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931980.CrossRefGoogle Scholar
Parisse, F. & Allain, C. 1996 Shape changes of colloidal suspension droplets during drying. J. Phys. II 6, 11111119.Google Scholar
Parisse, F. & Allain, C. 1997 Drying of colloidal suspension droplets: experimental study and profile renormalization. Langmuir 13, 35983602.Google Scholar
Popov, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71, 036313.Google Scholar
Shmuylovich, L., Shen, A. Q. & Stone, H. A. 2002 Surface morphology of drying latex films: multiple ring formation. Langmuir 18, 34413445.Google Scholar
Stickel, J. J. & Powell, R. L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129149.Google Scholar
Tarasevich, Y. Y., Vodolazskaya, I. V. & Bondarenko, O. P. 2013 Modeling of spatial-temporal distribution of the components in the drying sessile droplet of biological fluid. Colloids Surf. A 432, 99103.Google Scholar
Tarasevich, Y. Y., Vodolazskaya, I. V. & Isakova, O. P. 2011 Desiccating colloidal sessile drop: dynamics of shape and concentration. Colloid Polym. Sci. 289, 10151023.Google Scholar
Thiele, U. 2014 Patterned deposition at moving contact lines. Adv. Colloid Interface Sci. 206, 399413.CrossRefGoogle ScholarPubMed
Witten, T. A. 2009 Robust fadeout profile of an evaporation stain. Euro. Phys. Lett. 86, 64002.Google Scholar
Yang, X., Li, C. Y. & Sun, Y. 2014 From multi-ring to spider web and radial spoke: competition between the receding contact line and particle deposition in a drying colloidal drop. Soft Matt. 10, 44584463.Google Scholar
Yunker, P. J., Still, T., Lohr, M. A. & Yodh, A. G. 2011 Suppression of the coffee-ring effect by shape-dependent capillary interactions. Nature 476, 308311.Google Scholar
Zhang, L., Maheshwari, S., Chang, H. C. & Zhu, Y. 2008 Evaporative self-assembly from complex DNA-colloid suspensions. Langmuir 24, 39113917.Google Scholar
Zheng, R. 2009 A study of the evaporative deposition process: pipes and truncated transport dynamics. Eur. Phys. J. E 29, 205218.Google Scholar

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