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Evaporation effects in elastocapillary aggregation

Published online by Cambridge University Press:  01 March 2016

Andreas Hadjittofis ,
John R. Lister ,
Kiran Singh  and
Dominic Vella
Andreas Hadjittofis
Affiliation:
Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
John R. Lister
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Kiran Singh
Affiliation:
Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
Dominic Vella*
Affiliation:
Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK
*
†Email address for correspondence: dominic.vella@maths.ox.ac.uk
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Abstract

We consider the effect of evaporation on the aggregation of a number of elastic objects due to a liquid’s surface tension. In particular, we consider an array of spring–block elements in which the gaps between blocks are filled by thin liquid films that evaporate during the course of an experiment. Using lubrication theory to account for the fluid flow within the gaps, we study the dynamics of aggregation. We find that a non-zero evaporation rate causes the elements to aggregate more quickly and, indeed, to contact within finite time. However, we also show that the final number of elements within each cluster decreases as the evaporation rate increases. We explain these results quantitatively by comparison with the corresponding two-body problem and discuss their relevance for controlling pattern formation in elastocapillary systems.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 792 , 10 April 2016 , pp. 168 - 185
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Copyright
© 2016 Cambridge University Press 

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References

Aristoff, J. M., Duprat, C. & Stone, H. A. 2011 Elastocapillary imbibition. Intl J. Non-Linear Mech. 46, 648–656.Google Scholar
Bico, J., Roman, B., Moulin, L. & Boudaoud, A. 2004 Adhesion: elastocapillary coalescence in wet hair. Nature 432, 690.Google Scholar
Boudaoud, A., Bico, J. & Roman, B. 2007 Elastocapillary coalescence: aggregation and fragmentation with a maximal size. Phys. Rev. E 76, 060102.Google ScholarPubMed
Cazabat, A.-M. & Guena, G. 2010 Evaporation of macroscopic sessile droplets. Soft Matt. 6, 2591–2612.CrossRefGoogle Scholar
Chakrapani, N., Wei, B., Carrillo, A., Ajayan, P. M. & Kane, R. S. 2004 Capillarity-driven assembly of two-dimensional cellular carbon nanotube foams. Proc. Natl Acad. Sci. USA 101, 4009–4012.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, 827–829.Google Scholar
Dufresne, E. R., Stark, D. J., Greenblatt, N. A., Cheng, J. X., Hutchinson, J. W., Mahadevan, L. & Weitz, D. A. 2006 Dynamics of fracture in drying suspensions. Langmuir 22, 7144–7147.Google Scholar
Dunn, G. J., Wilson, S. K., Duffy, B. R., David, S. & Sefiane, K. 2009 The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623, 329–351.CrossRefGoogle Scholar
Duprat, C., Aristoff, J. M. & Stone, H. 2011 Dynamics of elastocapillary rise. J. Fluid Mech. 679, 641–654.CrossRefGoogle Scholar
Duprat, C., Protiére, S., Beebe, A. & Stone, H. 2012 Wetting of flexible fibre arrays. Nature 482, 510–513.CrossRefGoogle ScholarPubMed
Gat, A. & Gharib, M. 2013 Elasto-capillary coalescence of multiple parallel sheets. J. Fluid. Mech. 723, 692–705.Google Scholar
Jung, S., Clanet, C. & Bush, J. W. M. 2014 Capillary instability on an elastic helix. Soft Matt. 10, 3225–3228.CrossRefGoogle Scholar
Kelly-Zion, P. L., Pursell, C., Hasbamrer, N., Cardozo, B., Gaughan, K. & Nickels, K. 2013 Vapor distribution above an evaporating sessile drop. Intl J. Heat Mass Transfer 65, 165–172.CrossRefGoogle Scholar
Kim, H.-Y. & Mahadevan, L. 2006 Capillary rise between elastic sheets. J. Fluid Mech. 548, 141–150.CrossRefGoogle Scholar
Lecocq, N. & Vandewalle, N. 2002 Experimental study of cracking induced by desiccation in 1-dimensional systems. Eur. Phys. J. E 8, 445–452.Google ScholarPubMed
Ledesma-Aguilar, R., Vella, D. & Yeomans, J. M. 2014 Lattice–Boltzmann simulations of droplet evaporation. Soft Matt. 8, 8267–8275.Google Scholar
Li, J., Cabane, B., Sztucki, M., Gummel, J. & Goehring, L. 2012 Drying dip-coated colloidal films. Langmuir 28, 200–208.Google Scholar
Lyulin, Y. V. & Kabov, O. A. 2013 Measurement of the evaporation mass flow rate in a horizontal liquid layer partly opened into flowing gas. Tech. Phys. Lett. 39, 795–797.CrossRefGoogle Scholar
Machrafi, H., Sadoun, N., Rednikov, A., Dehaeck, S., Dauby, P. C. & Colinet, P. 2013 Evaporation rates and Bénard–Marangoni supercriticality levels for liquid layers under an inert gas flow. Microgravity Sci. Technol. 25, 251–265.Google Scholar
Mchale, G., Aqil, S., Shirtcliffe, N. J., Newton, M. I. & Erbil, H. Y. 2005 Analysis of droplet evaporation on a superhydrophobic surface. Langmuir 21, 11053–11060.Google Scholar
Munro, J. P.2014 Elastocapillary coalescence. Part III essay, University of Cambridge, UK.Google Scholar
Murisic, N. & Kondic, L. 2011 On evaporation of sessile drops with moving contact lines. J. Fluid Mech. 679, 219–246.CrossRefGoogle Scholar
Oliver, J. M., Whiteley, J. P., Saxton, M. A., Vella, D., Zubkov, V. S. & King, J. R. 2015 On contact-line dynamics with mass transfer. Eur. J. Appl. Maths 26, 671–719.Google Scholar
Pokroy, B., Kang, S. H., Mahadevan, L. & Aizenberg, J. 2009 Self-organisation of a mesoscale bristle into ordered hierarchical helical assemblies. Science 323, 237–240.CrossRefGoogle Scholar
Popov, Y. O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71, 036313.Google Scholar
Py, C., Bastien, R., Bico, J., Roman, B. & Boudaoud, A. 2007 3D aggregation of wet fibers. Europhys. Lett. 77, 44005.CrossRefGoogle Scholar
Routh, A. F. 2013 Drying of thin colloidal films. Rep. Prog. Phys. 76, 046603.Google Scholar
Singh, K., Lister, J. R. & Vella, D. 2014 A fluid-mechanical model of elastocapillary coalescence. J. Fluid Mech. 745, 621–646.Google Scholar
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2014 On the lifetime of evaporating drops. J. Fluid Mech. 744, R2.Google Scholar
Tanaka, T., Morigami, M. & Atoda, N. 1993 Mechanism of resist pattern collapse during development process. Japan. J. Appl. Phys. 32, 6059–6064.Google Scholar
Taroni, M. & Vella, D. 2012 Multiple equilibria in a simple elastocapillary system. J. Fluid Mech. 712, 273–294.CrossRefGoogle Scholar
de Volder, M. F. L. & Hart, A. J. 2013 Engineering hierarchical nanostructures by elastocapillary self-assembly. Angew. Chem. Intl Ed. Engl. 52, 2412–2425.CrossRefGoogle ScholarPubMed
de Volder, M. F. L., Park, S. J., Tawfick, S. H., Vidaud, D. O. & Hart, A. J. 2011 Fabrication and electrical integration of robust carbon nanotube micropillars by self-directed elastocapillary densification. J. Micromech. Microengng 21, 045033.Google Scholar
de Volder, M. F. L., Tawfick, S. H., Baughman, R. H. & Hart, A. J. 2013 Carbon nanotubes: present and future commercial applications. Science 339, 535–539.CrossRefGoogle ScholarPubMed
Wei, Z. & Mahadevan, L. 2014 Continuum dynamics of elastocapillary coalescence and arrest. Europhys. Lett. 106, 14002.Google Scholar
Wei, Z., Schneider, T. M., Kim, J., Kim, H.-Y., Aizenberg, J. & Mahadevan, L. 2015 Elastocapillary coalescence of plates and pillars. Proc. R. Soc. Lond. A 471, 20140593.Google Scholar