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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]
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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 

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