Hostname: page-component-f554764f5-c4bhq Total loading time: 0 Render date: 2025-04-12T00:23:42.465Z Has data issue: false hasContentIssue false
  • English
  • Français

The contact line of an evaporating droplet over a solid wedge and the pinned–unpinned transition

Published online by Cambridge University Press:  23 February 2016

Seok Hyun Hong ,
Marco A. Fontelos  and
Hyung Ju Hwang
Seok Hyun Hong
Affiliation:
Department of Mathematics, POSTECH, 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk 37673, Korea
Marco A. Fontelos*
Affiliation:
Instituto de Ciencias Matemáticas (ICMAT), C/Nicolás Cabrera, Madrid 28049, Spain
Hyung Ju Hwang
Affiliation:
Department of Mathematics, POSTECH, 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk 37673, Korea
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We compute the equilibrium contact angles for an evaporating droplet whose contact line lies over a solid wedge. The stability of the liquid interface is also considered and an integro-differential equation for small perturbations is deduced. The analysis of this equation yields criteria for stability and instability of the contact line, where the instability represents transition from the pinned to unpinned contact line representative of stick–slip motion.

JFM classification

Interfacial Flows (free surface): Capillary flows Phase change: Condensation/evaporation Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , pp. 519 - 538
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abkarian, M., Nunes, J. & Stone Howard, A. 2004 Colloidal crystallization and banding in a cylindrical geometry. J. Am. Chem. Soc. 126 (19), 5978–5979.CrossRefGoogle Scholar
Adachi, E., Dimitrov, A. S. & Nagayama, K. 1995 Stripe patterns formed on a glass-surface during droplet evaporation. Langmuir 11 (4), 1057–1060.CrossRefGoogle Scholar
Bodiguel, H., Doumenc, F. & Guerrier, B. 2009 Pattern formation during the drying of a colloidal suspension. Eur. Phys. J. 166 (1), 29–32.Google Scholar
Bodiguel, H., Doumenc, F. & Guerrier, B. 2010 Stick–slip patterning at low capillary numbers for an evaporating colloidal suspension. Langmuir 26 (13), 10758–10763.CrossRefGoogle ScholarPubMed
Deegan, R. D. 2000 Pattern formation in drying drops. Phys. Rev. E 61 (1), 475–485.Google 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 (6653), 827–829.CrossRefGoogle Scholar
Eggers, J. & Pismen, L. M. 2010 Nonlocal description of evaporating drops. Phys. Fluids 22 (11), 112101.Google Scholar
Fontelos, M. A., Hong, S. H. & Hwang, H. J. 2015 A stable self-similar singularity of evaporating drops: ellipsoidal collapse to a point. Arch. Ration. Mech. Anal. 217 (2), 373–411.CrossRefGoogle Scholar
Gelderblom, H., Bloemen, O. & Snoeijer, J. H. 2012 Stokes flow near the contact line of an evaporating drop. J. Fluid Mech. 709, 69–84.CrossRefGoogle Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35 (1), 85–101.Google 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 (4), 044503.CrossRefGoogle ScholarPubMed
Moffat, J. R., Sefiane, K. & Shanahan, M. E. R. 2009 Effect of $\text{TiO}_{2}$ nanoparticles on contact line stick–slip behavior of volatile drops. J. Phys. Chem. B 113 (26), 8860–8866.CrossRefGoogle Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18 (1), 1–18.Google Scholar
Morales, V. L., Parlange, J.-Y., Wu, M., Perez-Reche, F. J., Zhang, W., Sang, W. & Steenhuis, T. S. 2013 Surfactant-mediated control of colloid pattern assembly and attachment strength in evaporating droplets. Langmuir 29 (6), 1831–1840.Google Scholar
Orejon, D., Sefiane, K. & Shanahan, M. E. R. 2011 Stick–slip of evaporating droplets: substrate hydrophobicity and nanoparticle concentration. Langmuir 27 (21), 12834–12843.CrossRefGoogle ScholarPubMed
Popov, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71 (3), 036313.Google ScholarPubMed
Rio, E., Daerr, A., Lequeux, F. & Limat, L. 2006 Moving contact lines of a colloidal suspension in the presence of drying. Langmuir 22 (7), 3186–3191.CrossRefGoogle ScholarPubMed
Ristenpart, W., Kim, P., Domingues, C., Wan, J. & Stone, H. A. 2007 Influence of substrate conductivity on circulation reversal in evaporating drops. Phys. Rev. Lett. 99 (23), 234502.Google Scholar
Snoeijer, J. H. & Andreotti, B. 2013 Moving contact lines: scales, regimes, and dynamical transitions. Annu. Rev. Fluid Mech. 45 (1), 269–292.Google Scholar
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2014 On the lifetimes of evaporating droplets. J. Fluid Mech. 744, R2.Google Scholar
Weon, B. M. & Je, J. H. 2013 Self-pinning by colloids confined at a contact line. Phys. Rev. Lett. 110 (2), 028303.CrossRefGoogle Scholar
Zheng, R. 2009 A study of the evaporative deposition process: pipes and truncated transport dynamics. Eur. Phys. J. E 29 (2), 205–218.Google ScholarPubMed