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Dynamics of water imbibition through paper with swelling

Published online by Cambridge University Press:  14 April 2020

Sooyoung Chang  and
Wonjung Kim Open the ORCID record for Wonjung Kim [Opens in a new window]
Sooyoung Chang
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul04107, Korea
Wonjung Kim*
Affiliation:
Department of Mechanical Engineering, Sogang University, Seoul04107, Korea
*
†Email address for correspondence: wonjungkim@sogang.ac.kr
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Abstract

We present a combined experimental and theoretical investigation of the dynamics of water imbibition through paper with swelling. The Washburn equation has been widely used to describe the dynamics of the liquid absorption in paper, but its prediction of liquid imbibition speed has been reported to be inaccurate. Our recent study (Chang et al., J. Fluid Mech., vol. 845, 2018, pp. 36–50) demonstrated that the internal cavity of cellulose fibres composing the paper is partially responsible for the limited accuracy of the Washburn equation based on oil imbibition experiments. Here we extend the investigation to water absorption through paper with swelling. We demonstrate that the swelling of the cellulose fibre network in addition to the internal voids of the cellulose fibres crucially affects the imbibition dynamics. Based on the microscopic observation that paper swelling is caused by the expansion of inter-fibre space, we suggest a mathematical model for water imbibition which considers both intra-fibre voids and swelling. By introducing parameters that characterize the swelling speed and volume of paper, our model markedly improves prediction of the water imbibition speed. The results provide not only a theoretical background for designing paper-based microfluidic systems, but also new insights into capillary flow through expandable porous media.

JFM classification

Low-Reynolds-number flows: Porous media Micro-/Nano-fluid dynamics: Microfluidics Interfacial Flows (free surface): Capillary flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , A39
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Ahmed, S., Bui, M. N. & Abbas, A. 2016 Paper-based chemical and biological sensors: engineering aspects. Biosens. Bioelectr. 77, 249–263.CrossRefGoogle ScholarPubMed
Alava, M. & Niskanen, K. 2006 The physics of paper. Rep. Prog. Phys. 69, 669–723.CrossRefGoogle Scholar
Amaral, L., Barabási, A. L., Buldyrev, S. V., Havlin, S. & Stanley, H. E. 1994 New exponent characterizing the effect of evaporation on imbibition experiments. Phys. Rev. Lett. 72, 641–644.CrossRefGoogle ScholarPubMed
Anderson, D. M. 2005 Imbibition of a liquid droplet on a deformable porous substrate. Phys. Fluids 17, 087104.CrossRefGoogle Scholar
Bajpai, P. 2015 Basic overview of pulp and paper manufacturing process. In Green Chemistry and Sustainability in Pulp and Paper Industry (ed. Bajpai, P.), pp. 11–39. Springer International.CrossRefGoogle Scholar
Balankin, A. S., López, H. Z., León, E. P., Matamoros, D. M., Ruiz, L. M., López, D. S. & Rodríguez, M. A. 2013 Depinning and dynamics of imbibition fronts in paper under increasing ambient humidity. Phys. Rev. E 87, 014102.Google ScholarPubMed
Bico, J. & Quéré, D. 2003 Precursors of impregnation. Europhys. Lett. 61, 348–353.CrossRefGoogle Scholar
Böhm, A., Carstens, F., Trieb, C., Schabel, S. & Biesalski, M. 2014 Engineering microfluidic papers: effect of fiber source and paper sheet properties on capillary-driven fluid flow. Microfluid Nanofluid 16, 789–799.CrossRefGoogle Scholar
Cate, D. M., Adkins, J. A., Mettakoonpitak, J. & Henry, C. S. 2014 Recent developments in paper-based microfluidic devices. Anal. Chem. 87, 19–41.CrossRefGoogle ScholarPubMed
Chang, S., Seo, J., Hong, S., Lee, D.-G. & Kim, W. 2018 Dynamics of liquid imbibition through paper with intra-fibre pores. J. Fluid Mech. 845, 36–50.CrossRefGoogle Scholar
Cummins, B. M., Chinthapatla, R., Ligler, F. S. & Walker, G. M. 2017 Time-dependent model for fluid flow in porous materials with multiple pore sizes. Anal. Chem. 89, 4377–4381.CrossRefGoogle ScholarPubMed
Darcy, H. 1856 Les Fontaines publiques de la ville de Dijon. Dalmont.Google Scholar
Enderby, J. A. 1955 Water absorption by polymers. Trans. Faraday Soc. 51, 106–116.CrossRefGoogle Scholar
Hong, S. & Kim, W. 2015 Dynamics of water imbibition through paper channels with wax boundaries. Microfluid Nanofluid 19, 845–853.CrossRefGoogle Scholar
Hong, S., Kwak, R. & Kim, W. 2016 Paper-based flow fractionation system applicable to preconcentration and field-flow separation. Anal. Chem. 88, 1682–1687.CrossRefGoogle ScholarPubMed
Hu, J., Wang, S., Wang, L., Li, F., Pingguan-Murphy, B., Lu, T. J. & Xu, F. 2014 Advances in paper-based point-of-care diagnostics. Biosens. Bioelectr. 54, 585–597.CrossRefGoogle ScholarPubMed
Jahanshahi-Anbuhi, S., Henry, A., Leung, V., Sicard, C., Pennings, K., Pelton, R., Brennan, J. D. & Filipe, C. D. M. 2014 Paper-based microfluidics with an erodible polymeric bridge giving controlled release and timed flow shutoff. Lab on a Chip 14, 229–236.CrossRefGoogle ScholarPubMed
Jurin, J. 1718 An account of some experiments shown before the Royal Society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes. Phil. Trans. R. Soc. Lond. 30, 739–747.Google 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, 074001.CrossRefGoogle Scholar
Lee, M., Kim, S., Kim, H.-Y. & Mahadevan, L. 2016 Bending and buckling of wet paper. Phys. Fluids 28, 042101.CrossRefGoogle Scholar
Lin, Y., Gritsenko, D., Feng, S., Teh, Y. C., Lu, X. & Xu, J. 2016 Detection of heavy metal by paper-based microfluidics. Biosens. Bioelectr. 83, 256–266.CrossRefGoogle ScholarPubMed
MacDonald, B. D. 2018 Flow of liquids through paper. J. Fluid Mech. 852, 1–4.CrossRefGoogle Scholar
Martinez, A. W., Phillips, S. T., Butte, M. J. & Whitesides, G. M. 2007 Patterned paper as a platform for inexpensive, low-volume, portable bioassays. Angew. Chem. Intl Ed. Engl. 46, 1318–1320.CrossRefGoogle ScholarPubMed
Martinez, A. W., Phillips, S. T., Whitesides, G. M. & Carrilho, E. 2009 Diagnostics for the developing world: microfluidic paper-based analytical devices. Anal. Chem. 82, 3–10.CrossRefGoogle Scholar
Masoodi, R. & Pillai, K. M. 2010 Darcy’s law-based model for wicking in paper-like swelling porous media. AIChE J. 56, 2257–2267.Google Scholar
Pillai, K. M. 2014 Single-phase flows in swelling, liquid-absorbing porous media: a derivation of flow governing equations using the volume averaging method with a nondeterministic, heuristic approach to assessing the effect of solid-phase changes. J. Porous Media 17, 915–935.CrossRefGoogle Scholar
Preziosi, L., Joseph, D. D. & Beavers, G. S. 1996 Infiltration of initially dry, deformable porous media. Intl J. Multiphase Flow 22, 1205–1222.CrossRefGoogle Scholar
Reyssat, E. & Mahadevan, L. 2011 How wet paper curls. Europhys. Lett. 93, 54001.CrossRefGoogle Scholar
Schuchardt, D. R. & Berg, J. C. 1991 Liquid transport in composite cellulose-superabsorbent fiber networks. Wood Fiber Sci. 23, 342–357.Google Scholar
Siddique, J., Anderson, D. M. & Bondarev, A. 2009 Capillary rise of a liquid into a deformable porous material. Phys. Fluids 21, 013106.CrossRefGoogle Scholar
Sommer, J. L. & Mortensen, A. 1996 Forced unidirectional infiltration of deformable porous media. J. Fluid Mech. 311, 193–217.CrossRefGoogle Scholar
Topgaard, D. & Söderman, O. 2001 Diffusion of water absorbed in cellulose fibers studied with H-NMR. Langmuir 17, 2694–2702.CrossRefGoogle Scholar
Walji, N. & MacDonald, B. D. 2016 Influence of geometry and surrounding conditions on fluid flow in paper-based devices. Micromachines 7, 73.CrossRefGoogle ScholarPubMed
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273–283.CrossRefGoogle Scholar
Xia, Y., Si, J. & Li, Z. 2016 Fabrication techniques for microfluidic paper-based analytical devices and their applications for biological testing: a review. Biosens. Bioelectr. 77, 774–789.CrossRefGoogle ScholarPubMed
Yetisen, A. K., Akram, M. S. & Lowe, C. R. 2013 Paper-based microfluidic point-of-care diagnostic devices. Lab on a Chip 13, 2210–2251.CrossRefGoogle ScholarPubMed