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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: [email protected]
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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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