Capillary transport in paper porous materials at low saturation levels: Normal, fast or superfast?: Normal, fast or superfast diffusion?

Alex V. Lukyanov, Vladimir V. Mitkin, Tristan Pryer, Penpark Sirimark, Theo G. Theofanous

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1 Citation (SciVal)


The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated that the process of liquid spreading in this type of porous material at low saturation can be described macroscopically by a similar super-fast, nonlinear diffusion model to that which had been previously identified in experiments and simulations in particulate porous media. The macroscopic diffusion model has been underpinned by simulations using a microscopic network model. The theoretical results have been qualitatively compared with available experimental observations within the witness card technique using persistent liquids. The long-term evolution of the wetting spots was found to be truly universal and fully in line with the mathematical model developed. The result has important repercussions for the witness card technique used in field measurements of the dissemination of various low-volatility agents in imposing severe restrictions on collection and measurement times.

Original languageEnglish
Article number20200491
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2244
Early online date23 Dec 2020
Publication statusPublished - 23 Dec 2020

Bibliographical note

Funding Information:
Data accessibility. This article has no additional data. Authors’ contributions. All authors were involved in the preparation of the manuscript. A.V.L. and T.G.T. conceived of the study, designed the study, coordinated the study and helped draft the manuscript. P.S. and T.P. carried out the numerical analysis and analytical studies of the model, participated in data analysis and critically revised the manuscript. V.V.M. carried out the experimental work, participated in the design of the study and in data analysis and critically revised the manuscript. All authors have read and approved the final manuscript. All authors gave final approval for publication and agree to be held accountable for the work performed therein. Competing interests. We declare we have no competing interests. Funding. The research was partially supported through a Royal Thai Government scholarship and EPSRC grant no. EP/P000835/1. Acknowledgements. The authors thank the referees for their valuable comments. We are grateful for their constructive remarks, which led to a significant improvement to the manuscript.

Publisher Copyright:
© 2020 The Author(s).

Copyright 2021 Elsevier B.V., All rights reserved.


  • capillary flows
  • fibrous materials
  • porous media
  • superfast diffusion

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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