Hostname: page-component-f554764f5-fr72s Total loading time: 0 Render date: 2025-04-21T15:48:36.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Imbibition and collapse between swelling fibres

Published online by Cambridge University Press:  27 December 2023

Pierre Van de Velde Open the ORCID record for Pierre Van de Velde [Opens in a new window] ,
Julien Dervaux Open the ORCID record for Julien Dervaux [Opens in a new window] ,
Camille Duprat Open the ORCID record for Camille Duprat [Opens in a new window]  and
Suzie Protière
Pierre Van de Velde*
Affiliation:
LadHyX, Ecole Polytechnique, UMR 7646, Palaiseau, France
Julien Dervaux
Affiliation:
Matiere et Systèmes Complexes, CNRS UMR 7057, Université de Paris, Paris, France
Camille Duprat
Affiliation:
LadHyX, Ecole Polytechnique, UMR 7646, Palaiseau, France
Suzie Protière
Affiliation:
Institut Jean Le Rond d'Alembert, Sorbonne Université, CNRS, UMR 7190, Paris, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

While capillary imbibition in tubes or porous materials has been studied extensively in the past, less attention has been paid to imbibition into a swellable porous material. However, swelling is commonly observed when a polymeric network, such as the cellulose composing paper fibres or sponges, absorbs a solvent. The incompressibility of the fluid leads to an elastic expansion of the polymeric matrix. In a porous material, swelling can affect the geometry of the pores, thus affecting the capillary flow. To describe this complex problem, we propose a model experiment, namely the capillary imbibition in a model pore composed of two parallel and stretched elastomeric fibres. In this configuration, one can observe both the progression of a capillary meniscus and the swelling of the fibres. We show that swelling enables a capillary imbibition for fibres placed further apart than the critical distance existing for non-swelling fibres. In this swelling-dominated regime, we identify a new imbibition dynamic at constant velocity which we rationalize using a linear poro-elastic theory. Finally, we describe the elastocapillary collapse of our model pore which is observed when capillary forces overcome the restoring tension force within the fibres.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 978 , 10 January 2024 , A2
Check for updates
Copyright
© The Author(s), 2023. 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.)

Article purchase

Temporarily unavailable

References

Aristoff, J.M., Duprat, C. & Stone, H.A. 2011 Elastocapillary imbibition. Intl J. Non-Linear Mech. 46 (4), 648–656.CrossRefGoogle Scholar
Bell, J.M. & Cameron, F.K. 1906 The flow of liquids through capillary spaces. J. Phys. Chem. 10 (8), 658–674.CrossRefGoogle Scholar
Bico, J., Reyssat, É. & Roman, B. 2018 Elastocapillarity: when surface tension deforms elastic solids. Annu. Rev. Fluid Mech. 50 (1), 629–659.CrossRefGoogle Scholar
Bico, J., Roman, B., Moulin, L. & Boudaoud, A. 2004 Elastocapillary coalescence in wet hair. Nature 432 (7018), 690–690.CrossRefGoogle ScholarPubMed
Bintein, P.-B. 2015 Dynamiques de gouttes funambules: applications à la fabrication de laine de verre. PhD thesis, Univ. Paris 6.Google Scholar
Biot, M.A. 1941 General theory of three-dimensional consolidation. J. Appl. Phys. 12 (2), 155–164.CrossRefGoogle Scholar
Chang, S., Jensen, K.H. & Kim, W. 2022 Dynamics of water imbibition through hydrogel-coated capillary tubes. Phys. Rev. Fluids 7 (6), 064301.CrossRefGoogle Scholar
Chang, S. & Kim, W. 2020 Dynamics of water imbibition through paper with swelling. J. Fluid Mech. 892, A39.CrossRefGoogle Scholar
Charpentier, J.-B., de Motta, J.C.B. & Ménard, T. 2020 Capillary phenomena in assemblies of parallel cylindrical fibers: from statics to dynamics. Intl J. Multiphase Flow 129, 103304.CrossRefGoogle Scholar
Dervaux, J. & Ben Amar, M. 2012 Mechanical instabilities of gels. Annu. Rev. Condens. Matter Phys. 3 (1), 311–332.CrossRefGoogle Scholar
Duprat, C. 2022 Moisture in textiles. Annu. Rev. Fluid Mech. 54 (1), 443–467.CrossRefGoogle Scholar
Duprat, C., Aristoff, J.M. & Stone, H.A. 2011 Dynamics of elastocapillary rise. J. Fluid Mech. 679, 641–654.CrossRefGoogle Scholar
Duprat, C. & Protiere, S. 2015 Capillary stretching of fibers. Europhys. Lett. 111 (5), 56006.CrossRefGoogle Scholar
Dyba, R.V. & Miller, B. 1969 Evaluation of wettability from capillary rise between filaments. Textile Res. J. 39 (10), 962–970.CrossRefGoogle Scholar
Ha, J. & Kim, H.-Y. 2020 Capillarity in soft porous solids. Annu. Rev. Fluid Mech. 52, 263–284.Google Scholar
Holmes, D.P., Brun, P.-T., Pandey, A. & Protière, S. 2016 Rising beyond elastocapillarity. Soft Matt. 12 (22), 4886–4890.CrossRefGoogle ScholarPubMed
Hui, C.-Y. & Muralidharan, V. 2005 Gel mechanics: a comparison of the theories of Biot and Tanaka, Hocker, and Benedek. J. Chem. Phys. 123 (15), 154905.CrossRefGoogle Scholar
Kim, H.-Y. & Mahadevan, L. 2006 Capillary rise between elastic sheets. J. Fluid Mech. 548, 141–150.CrossRefGoogle Scholar
Kvick, M., Martinez, D.M., Hewitt, D.R. & Balmforth, N.J. 2017 Imbibition with swelling: capillary rise in thin deformable porous media. Phys. Rev. Fluids 2 (7), 074001.CrossRefGoogle Scholar
Lucas, R. 1918 Ueber das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten. Kolloidn. Z. 23 (1), 15–22.CrossRefGoogle Scholar
Princen, H.M. 1969 Capillary phenomena in assemblies of parallel cylinders. J. Colloid Interface Sci. 30 (1), 69–75.CrossRefGoogle Scholar
Pucci, M.F., Liotier, P.-J. & Drapier, S. 2016 Capillary wicking in flax fabrics – effects of swelling in water. Colloids Surf. A 498, 176–184.CrossRefGoogle Scholar
Reyssat, E. & Mahadevan, L. 2009 Hygromorphs: from pine cones to biomimetic bilayers. J. R. Soc. Interface 6 (39), 951–957.CrossRefGoogle ScholarPubMed
Reyssat, E. & Mahadevan, L. 2011 How wet paper curls. Europhys. Lett. 93 (5), 54001.CrossRefGoogle Scholar
Schuchardtl, D. 1991 Liquid transport in composite cellulose – superabsorbent fiber networks. Wood Fiber Sci. 23 (3), 342–357.Google Scholar
Takahashi, A., Häggkvist, M. & Li, T.-Q. 1997 Capillary penetration in fibrous matrices studied by dynamic spiral magnetic resonance imaging. Phys. Rev. E 56 (2), 2035–2042.CrossRefGoogle Scholar
Testoni, G.A., Kim, S., Pisupati, A. & Park, C.H. 2018 Modeling of the capillary wicking of flax fibers by considering the effects of fiber swelling and liquid absorption. J. Colloid Interface Sci. 525, 166–176.CrossRefGoogle ScholarPubMed
Van de Velde, P. 2022 Swelling and wetting of model elastic fibers. PhD thesis, Institut Polytechnique de Paris.Google Scholar
Van de Velde, P., Dervaux, J., Protière, S. & Duprat, C. 2022 Spontaneous localized fluid release on swelling fibres. Soft Matt. 18 (24), 4565–4571.CrossRefGoogle ScholarPubMed
Van de Velde, P., Protière, S. & Duprat, C. 2021 Dynamics of drop absorption by a swelling fiber. Soft Matt. 17 (25), 6168–6175.CrossRefGoogle ScholarPubMed
Washburn, E.W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273–283.CrossRefGoogle Scholar