Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T18:35:06.393Z Has data issue: false hasContentIssue false
  • English
  • Français

Universal evaporation dynamics of ordered arrays of sessile droplets

Published online by Cambridge University Press:  04 March 2019

Sandeep Hatte ,
Keshav Pandey ,
Khushboo Pandey ,
Suman Chakraborty Open the ORCID record for Suman Chakraborty [Opens in a new window]  and
Saptarshi Basu Open the ORCID record for Saptarshi Basu [Opens in a new window]
Sandeep Hatte
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg 24061, USA
Keshav Pandey
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India
Khushboo Pandey
Affiliation:
Interdisciplinary Center for Energy Research (ICER), Indian Institute of Science, Bangalore 560012, India
Suman Chakraborty
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
Saptarshi Basu*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India Interdisciplinary Center for Energy Research (ICER), Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Manipulation of an array of surface droplets organised in an ordered structure turns out to be of immense consequence in a wide variety of applications ranging from photonics, near field imaging and inkjet printing on the one hand to bio-molecular analysis and DNA sequencing on the other. While evaporation of a single isolated sessile droplet has been well studied, the collective evaporative dynamics of an ordered array of droplets on a solid substrate remains elusive. Physically, the closed region between the centre and side droplets in the ordered array reduces the mobility of the diffusing vapour, resulting in its accumulation along with enhanced local concentration and a consequent increment in the lifetime of the centre droplet. Here, we present a theoretical model to account for evaporation lifetime scaling in closely placed ordered linear droplet arrays. In addition, the present theory predicts the limiting cases of droplet interaction; namely, critical droplet separation for which interfacial interaction ceases to exist and minimum possible droplet separation (droplets on the verge of coalescence) for which the droplet system achieves maximum lifetime scaling. Further experimental evidence demonstrates the applicability of the present scaling theory to extended dimensions of the droplet array, generalising our physical conjecture. It is also worth noting that the theoretical time scale is applicable across a wide variety of drop–substrate combinations and initial droplet volumes. We also highlight that the scaling law proposed here can be extended seamlessly to other forms of confinement such as an evaporating droplet inside a mini-channel, as encountered in countless applications ranging from biomedical engineering to surface patterning.

JFM classification

Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 866 , 10 May 2019 , pp. 61 - 81
Copyright
© 2019 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.)

References

Bansal, L., Hatte, S., Basu, S. & Chakraborty, S. 2017 Universal evaporation dynamics of a confined sessile droplet. Appl. Phys. Lett. 111 (10), 101601.10.1063/1.4996986Google Scholar
Boreyko, J. B., Hansen, R. R., Murphy, K. R., Nath, S., Retterer, S. T. & Collier, C. P. 2016 Controlling condensation and frost growth with chemical micropatterns. Sci. Rep. 6, 1–15.10.1038/srep19131Google Scholar
Brutin, D., Sobac, B., Loquet, B. & Sampol, J. 2011 Pattern formation in drying drops of blood. J. Fluid Mech. 667, 85–95.10.1017/S0022112010005070Google Scholar
Calvert, P. 2001 Inkjet printing for materials and devices. Chem. Mater. 13 (10), 3299–3305.10.1021/cm0101632Google Scholar
Carrier, O., Shahidzadeh-bonn, N. & Zargar, R. 2016 Evaporation of water: evaporation rate and collective effects. J. Fluid Mech. 798, 774–786.10.1017/jfm.2016.356Google Scholar
Cerf, A., Alava, T., Barton, R. A. & Craighead, H. G. 2011 Transfer-printing of single dna molecule arrays on graphene for high-resolution electron imaging and analysis. Nano Lett. 11 (10), 4232–4238.10.1021/nl202219wGoogle Scholar
Chen, X., Ma, R., Li, J. & Wang, Z. 2012 Evaporation of droplets on superhydrophobic surfaces: surface roughness and small droplet size effects. Phys. Rev. Lett. 109 (11), 1–6.Google Scholar
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), 827–829.10.1038/39827Google Scholar
Gans, B. D. & Schubert, U. S. 2003 Inkjet printing of polymer micro-arrays and libraries: instrumentation, requirements, and perspectives. Macromol. Rapid Commun. 22 (11), 659–666.Google Scholar
Hatte, S., Dhar, R., Bansal, L., Chakraborty, S. & Basu, S. 2019 On the lifetime of evaporating confined sessile droplets. Colloids Surf. A 560, 78–83.10.1016/j.colsurfa.2018.10.008Google Scholar
Hu, H. & Larson, R. G. 2002 Evaporation of a sessile droplet on a substrate. J. Phys. Chem B 106 (6), 1334–1344.10.1021/jp0118322Google Scholar
Hu, H. & Larson, R. G. 2005 Analysis of the effects of marangoni stresses on the microflow in an evaporating sessile droplet. Langmuir 21 (9), 3972–3980.10.1021/la0475270Google Scholar
Jyoti, A., Shaikeea, D. & Basu, S. 2016 Insight into the evaporation dynamics of a pair of sessile droplets on a hydrophobic substrate. Langmuir 32 (5), 1309–1318.Google Scholar
Jyoti, A., Shaikeea, D., Basu, S. & Bansal, L. 2017 Universal representations of evaporation modes in sessile droplets. PloS One 12 (9), 1–8.Google Scholar
K.Tang, A. G. 1994 Generation by electrospray of monodisperse water droplets for targeted drug delivery by inhalation. J. Aero. Sci. 25 (6), 1237–1249.10.1016/0021-8502(94)90212-7Google Scholar
Laghezza, G., Dietrich, E., Yeomans, J. M. & Lohse, D. 2016 Collective and convective effects compete in patterns of dissolving surface droplets. Soft Matt. 12 (26), 5787–5796.10.1039/C6SM00767HGoogle Scholar
Mallinson, S., Mcbain, G. D. & Horrocks, G.2016 Viscosity and surface tension of aqueous mixtures. In 20th Australasian Fluid Mechanics Conference Perth, Australia. Australasian Fluid Mechanics Society.Google Scholar
Nguyen, T. A. H. & Nguyen, A. V. 2012 On the lifetime of evaporating sessile droplets. Langmuir 28 (3), 1924–1930.10.1021/la2036955Google Scholar
Nguyen, T. A. H., Nguyen, A. V., Hampton, M. A., Xu, Z. P., Huang, L. & Rudolph, V. 2012 Theoretical and experimental analysis of droplet evaporation on solid surfaces. Chem. Engng Sci. 69 (1), 522–529.10.1016/j.ces.2011.11.009Google Scholar
Picknett, R. G. & Bexon, R. 1977 The evaporation of sessile or pendant drops in still air. J. Colloid Interface Sci. 61 (2), 336–350.10.1016/0021-9797(77)90396-4Google Scholar
Pinheiro, L. B., Coleman, V. A., Hindson, C. M. & Emslie, K. R. 2012 Evaluation of a droplet digital polymerase chain reaction format for DNA copy number quantification. Anal. Chem. 84 (2), 1003–1011.10.1021/ac202578xGoogle Scholar
Song, H., Chen, D. L. & Ismagilov, R. F. 2006 Reactions in droplets in microfluidic channels angewandte. Angew. Chem. Intl Ed. 45 (44), 7336–7356.10.1002/anie.200601554Google Scholar
Style, R. W., Che, Y., Park, S. J., Weon, B. M., Je, J. H., Hyland, C., German, G. K., Power, M. P., Wilen, L. A., Wettlaufer, J. S. & Dufresne, E. R. 2013 Patterning droplets with durotaxis. Proc. Natl Acad. Sci. USA 110 (31), 12541–12544.10.1073/pnas.1307122110Google Scholar
Tian, L., Martin, N., Bassindale, P. G. & Mann, S. 2016 Acoustic wave patterning. Nat. Commun. 7 (May), 1–10.Google Scholar
Yu, Y. S., Wang, Z. & Zhao, Y. P. 2012 Experimental and theoretical investigations of evaporation of sessile water droplet on hydrophobic surfaces. J. Colloid Interface Sci. 365 (1), 254–259.Google Scholar