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Evaporation of multiple droplets

Published online by Cambridge University Press:  29 September 2021

Hassan Masoud Open the ORCID record for Hassan Masoud [Opens in a new window] ,
Peter D. Howell Open the ORCID record for Peter D. Howell [Opens in a new window]  and
Howard A. Stone Open the ORCID record for Howard A. Stone [Opens in a new window]
Hassan Masoud*
Affiliation:
Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Houghton, MI 49931, USA
Peter D. Howell
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

We derive an accurate estimate for the diffusive evaporation rates of multiple droplets of different sizes and arbitrary contact angles placed on a horizontal substrate. The derivation, which is based on a combination of Green's second identity and the method of reflections, simply makes use of the solution for the evaporation of a single droplet. The theoretical results can serve as a guide for future computational and experimental studies on the collective evaporation of arrays of droplets, as well as similar multi-body, diffusion-dominated transport problems.

JFM classification

Drops and Bubbles: Drops Phase change: Condensation/evaporation Interfacial Flows (free surface): Contact lines
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , R4
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bao, L., Spandan, V., Yang, Y., Dyett, B., Verzicco, R., Lohse, D. & Zhang, X. 2018 Flow-induced dissolution of femtoliter surface droplet arrays. Lab Chip 18 (7), 1066–1074.CrossRefGoogle ScholarPubMed
Brenner, H. 1963 Forced convection heat and mass transfer at small Peclet numbers from a particle of arbitrary shape. Chem. Engng Sci. 18 (2), 109–122.CrossRefGoogle Scholar
Brutin, D. & Starov, V. 2018 Recent advances in droplet wetting and evaporation. Chem. Soc. Rev. 47 (2), 558–585.CrossRefGoogle ScholarPubMed
Carrier, O., Shahidzadeh-Bonn, N., Zargar, R., Aytouna, M., Habibi, M., Eggers, J. & Bonn, D. 2016 Evaporation of water: evaporation rate and collective effects. J. Fluid Mech. 798, 774–786.CrossRefGoogle Scholar
Castanet, G., Perrin, L., Caballina, O. & Lemoine, F. 2016 Evaporation of closely-spaced interacting droplets arranged in a single row. Intl J. Heat Mass Transfer 93, 788–802.CrossRefGoogle Scholar
Cazabat, A.-M. & Guena, G. 2010 Evaporation of macroscopic sessile droplets. Soft Matt. 6 (12), 2591–2612.CrossRefGoogle Scholar
Chong, K.L., Li, Y., Ng, C.S., Verzicco, R. & Lohse, D. 2020 Convection-dominated dissolution for single and multiple immersed sessile droplets. J. Fluid Mech. 892, A21.CrossRefGoogle Scholar
Dollet, B. & Lohse, D. 2016 Pinning stabilizes neighboring surface nanobubbles against Ostwald ripening. Langmuir 32 (43), 11335–11339.CrossRefGoogle ScholarPubMed
Erbil, H.Y. 2012 Evaporation of pure liquid sessile and spherical suspended drops: a review. Adv. Colloid Interface Sci. 170 (1-2), 67–86.CrossRefGoogle ScholarPubMed
Fabrikant, V.I. 1985 On the potential flow through membranes. Z. Angew. Math. Phys. 36 (4), 616–623.CrossRefGoogle Scholar
Giorgiutti-Dauphiné, F. & Pauchard, L. 2018 Drying drops. Eur. Phys. J. E 41 (3), 32.CrossRefGoogle ScholarPubMed
Hatte, S., Pandey, K., Pandey, K., Chakraborty, S. & Basu, S. 2019 Universal evaporation dynamics of ordered arrays of sessile droplets. J. Fluid Mech. 866, 61–81.CrossRefGoogle Scholar
Khilifi, D., Foudhil, W., Fahem, K., Harmand, S. & Ben, J.S. 2019 Study of the phenomenon of the interaction between sessile drops during evaporation. Therm. Sci. 23 (2B), 1105–1114.CrossRefGoogle Scholar
Kim, S. & Karilla, S.J. 2005 Microhydrodynamics: Principles and Selected Applications. Dove.Google Scholar
Laghezza, G., Dietrich, E., Yeomans, J.M., Ledesma-Aguilar, R., Kooij, E.S., Zandvliet, H.J.W. & Lohse, D. 2016 Collective and convective effects compete in patterns of dissolving surface droplets. Soft Matt. 12 (26), 5787–5796.CrossRefGoogle ScholarPubMed
Lebedev, N.N. 1965 Special Functions and Their Applications. Prentice-Hall.CrossRefGoogle Scholar
Masoud, H. & Stone, H.A. 2019 The reciprocal theorem in fluid dynamics and transport phenomena. J. Fluid Mech. 879, P1.CrossRefGoogle Scholar
Michelin, S., Guérin, E. & Lauga, E. 2018 Collective dissolution of microbubbles. Phys. Rev. Fluids 3 (4), 043601.CrossRefGoogle Scholar
Popov, Y.O. 2005 Evaporative deposition patterns: spatial dimensions of the deposit. Phys. Rev. E 71 (3), 036313.CrossRefGoogle ScholarPubMed
Schäfle, C., Bechinger, C., Rinn, B., David, C. & Leiderer, P. 1999 Cooperative evaporation in ordered arrays of volatile droplets. Phys. Rev. Lett. 83 (25), 5302.CrossRefGoogle Scholar
Shaikeea, A., Jyoti, D. & Basu, S. 2016 Insight into the evaporation dynamics of a pair of sessile droplets on a hydrophobic substrate. Langmuir 32 (5), 1309–1318.CrossRefGoogle ScholarPubMed
Sokuler, M., Auernhammer, G.K., Liu, C.J., Bonaccurso, E. & Butt, H.-J. 2010 Dynamics of condensation and evaporation: effect of inter-drop spacing. Europhys. Lett. 89 (3), 36004.CrossRefGoogle Scholar
Stauber, J.M., Wilson, S.K., Duffy, B.R. & Sefiane, K. 2014 On the lifetimes of evaporating droplets. J. Fluid Mech. 744, R2.CrossRefGoogle Scholar
Vandadi, V., Jafari Kang, S. & Masoud, H. 2016 Reciprocal theorem for convective heat and mass transfer from a particle in Stokes and potential flows. Phys. Rev. Fluids 1 (2), 022001.CrossRefGoogle Scholar
Wray, A.W., Duffy, B.R & Wilson, S.K. 2020 Competitive evaporation of multiple sessile droplets. J. Fluid Mech. 884, A45.CrossRefGoogle Scholar
Zhu, X., Verzicco, R., Zhang, X. & Lohse, D. 2018 Diffusive interaction of multiple surface nanobubbles: shrinkage, growth, and coarsening. Soft Matt. 14 (11), 2006–2014.CrossRefGoogle ScholarPubMed