Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-23T07:39:56.747Z Has data issue: false hasContentIssue false
  • English
  • Français

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: hmasoud@mtu.edu, hastone@princeton.edu
†Email addresses for correspondence: hmasoud@mtu.edu, hastone@princeton.edu
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© The Author(s), 2021. Published by 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

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