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Drying by pervaporation in elementary channel networks

Published online by Cambridge University Press:  09 November 2020

Benjamin Dollet Open the ORCID record for Benjamin Dollet [Opens in a new window] ,
Kennedy Nexon Chagua Encarnación ,
Romain Gautier  and
Philippe Marmottant
Benjamin Dollet*
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, 38000Grenoble, France
Kennedy Nexon Chagua Encarnación
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, 38000Grenoble, France
Romain Gautier
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, 38000Grenoble, France
Philippe Marmottant
Affiliation:
Univ. Grenoble Alpes, CNRS, LIPhy, 38000Grenoble, France
*
†Email address for correspondence: [email protected]
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Abstract

The drying dynamics inside a network of interconnected channels driven by pervaporation, e.g. by diffusion of water through a permeable material surrounding the channels, is studied. The channels are initially filled with water and a single air/water meniscus is initiated at the entrance of the network; drying proceeds as menisci progressively invade the network. The study is focused on elementary networks: simple branched networks without reconnections, or simple loops, in order to get a clear physical picture on which an understanding of drying on more complex networks, such as those encountered in leaves, could be built in the near future. Experiments are compared with models which elaborate on a previously published single-channel model (Dollet et al., J. R. Soc. Interface, vol. 16, 2019, 20180690). In branched networks, experiments reveal velocity discontinuities of the menisci as they split at the nodes. In loops, it is found that the drying rate depends on the number of menisci bounding a given connected water region; when there are two such menisci, a prediction of the dynamics of each of them is proposed, based on the pervaporation-induced hydrodynamics inside the channels. Experiments and model predictions compare favourably for the global drying rate. Some deviations are found for the dynamics of individual menisci, which are ascribed to the sensitivity of the dynamics to small fluctuations in wetting conditions.

JFM classification

Phase change: Condensation/evaporation Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A6
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Armstrong, R. T. & Berg, S. 2013 Interfacial velocities and capillary pressure gradients during Haines jumps. Phys. Rev. E 88, 043010.CrossRefGoogle ScholarPubMed
Bejan, A. 1993 Heat Transfer. Wiley.Google Scholar
Bienaimé, D. 2016 Embolies dans les plantes. PhD thesis, Université Grenoble Alpes.Google Scholar
Brodribb, T. J., Bienaimé, D. & Marmottant, P. 2016 a Revealing catastrophic failure of leaf networks under stress. Proc. Natl Acad. Sci. 113, 4865–4869.CrossRefGoogle ScholarPubMed
Brodribb, T. J., Skelton, R., McAdam, S., Bienaimé, D., Lucani, C. & Marmottant, P. 2016 b Visual quantification of embolism reveals leaf vulnerability to hydraulic failure. New Phytol. 209, 1403–1409.CrossRefGoogle ScholarPubMed
Bruus, H. 2007 Theoretical Microfluidics. Oxford University Press.Google Scholar
Choat, B., Brodribb, T. J., Brodersen, C. R., Duursma, R. A., López, R. & Medlyn, B. E. 2018 Triggers of tree mortality under drought. Nature 558, 531–539.CrossRefGoogle ScholarPubMed
Cochard, H. 2006 Cavitation in trees. C. R. Phys. 7, 1018–1026.CrossRefGoogle Scholar
Dollet, B., Louf, J. F., Alonzo, M., Jensen, K. H. & Marmottant, P. 2019 Drying of channels by evaporation through a permeable medium. J. R. Soc. Interface 16, 20180690.CrossRefGoogle ScholarPubMed
Eijkel, J. C. T., Bomer, J. G. & van den Berg, A. 2005 Osmosis and pervaporation in polyimide submicron microfluidic channel structures. Appl. Phys. Lett. 87, 114103.CrossRefGoogle Scholar
Harley, S. J., Glascoe, E. A. & Maxwell, R. S. 2012 Thermodynamic study in dynamic water vapor sorption in sylgard-184. J. Phys. Chem. B 116, 14183–14190.CrossRefGoogle ScholarPubMed
Hochberg, U., Ponomarenko, A., Zhang, Y. J., Rockwell, F. E. & Holbrook, N. M. 2019 Visualizing embolism propagation in gas-injected leaves. Plant Physiol. 180, 874–881.CrossRefGoogle ScholarPubMed
Leng, J., Lonetti, B., Tabeling, P., Joanicot, M. & Ajdari, A. 2006 Microevaporators for kinetic exploration of phase diagrams. Phys. Rev. Lett. 96, 084503.CrossRefGoogle ScholarPubMed
Link, D. R., Anna, S. L., Weitz, D. A. & Stone, H. A. 2004 Geometrically mediated breakup of drops in microfluidic devices. Phys. Rev. Lett. 92, 054503.CrossRefGoogle ScholarPubMed
Merlin, A., Salmon, J. B. & Leng, J. 2012 Microfluidic-assisted growth of colloidal crystals. Soft Matt. 8, 3526–3537.CrossRefGoogle Scholar
Noblin, X., Mahadevan, L., Coomaraswamy, I. A., Weitz, D. A., Holbrook, N. M. & Zwieniecki, M. A. 2008 Optimal vein density in artificial and real leaves. Proc. Natl Acad. Sci. 105, 9140–9144.CrossRefGoogle ScholarPubMed
Randall, G. C. & Doyle, P. S. 2005 Permeation-driven flow in poly(dimethylsiloxane) microfluidic devices. Proc. Natl Acad. Sci. 102, 10813–10818.CrossRefGoogle ScholarPubMed
Sadjadi, Z. & Rieger, H. 2013 Scaling theory for spontaneous imbibition in random networks of elongated pores. Phys. Rev. Lett. 110, 144502.CrossRefGoogle ScholarPubMed
Salkin, L., Schmit, A., Courbin, L. & Panizza, P. 2013 Passive breakups of isolated drops and one-dimensional assemblies of drops inmicrofluidic geometries: experiments and models. Lab Chip 13, 3022–3032.CrossRefGoogle Scholar
Signe Mamba, S., Magniez, J. C., Zoueshtiagh, F. & Baudoin, M. 2018 Dynamics of a liquid plug in a capillary tube under cyclic forcing: memory effects and airway reopening. J. Fluid Mech. 838, 156–191.CrossRefGoogle Scholar
Song, Y., Baudoin, M., Manneville, P. & Baroud, C. N. 2011 The air-liquid flow in a microfluidic airway tree. Med. Engng Phys. 33, 849–856.CrossRefGoogle Scholar
Song, Y., Manneville, P. & Baroud, C. N. 2010 Local interactions and the global organization of a two-phase flow in a branching tree. Phys. Rev. Lett. 105, 134501.CrossRefGoogle Scholar
Tyree, M. T. & Sperry, J. S. 1989 Vulnerability of xylem to cavitation and embolism. Annu. Rev. Plant Physiol. Plant Mol. Biol. 40, 19–36.CrossRefGoogle Scholar
Verneuil, E., Buguin, A. & Silberzan, P. 2004 Permeation-induced flows: consequences for silicone-based microfluidics. Europhys. Lett. 68, 412–418.CrossRefGoogle Scholar
Walker, G. M. & Beebe, D. J. 2002 An evaporation-based microfluidic sample concentration method. Lab Chip 2, 57–61.CrossRefGoogle ScholarPubMed
Watson, J. M. & Baron, M. G. 1996 The behaviour in water in poly(dimethylsiloxane). J. Membr. Sci. 110, 47–57.CrossRefGoogle Scholar
Ziane, N., Guirardel, M., Leng, J. & Salmon, J. B. 2015 Drying with no concentration gradient in large microfluidic droplets. Soft Matt. 11, 3637–3642.CrossRefGoogle ScholarPubMed
Ziemecka, I., Haut, B. & Scheid, B. 2015 Hydrogen peroxide concentration by pervaporation of a ternary liquid solution in microfluidics. Lab Chip 15, 504–511.CrossRefGoogle ScholarPubMed