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Keywords:

  • swelling;
  • absorption;
  • permeability;
  • wicking;
  • Darcy's law;
  • finite element method;
  • Washburn equation;
  • imbibition;
  • paper

Abstract

The work is built on a previous research by Wiryana and Berg, in which wicking into four wet-formed paper stripes, consisting of cellulose fibers and four different percentages of the powdered carboxymethyl cellulose (CMC) superabsorbent, was studied experimentally. Because of the swelling of cellulose fibers and CMC powder on contact with water, the wicking was accompanied by a swelling of the matrix. A finite element/control volume (FE/CV)-based computer program is used for the first time to model the wicking in such swelling porous medium. The simulation used a novel form of continuity equation, which included the effects of liquid absorption and matrix swelling, in conjunction with the Darcy's law to model the single-phase flow behind a clearly defined liquid-front. A new method of estimating the time-varying permeability of the paper, based on the absorbed liquid-mass vs. time plots, is also proposed. Later, this time-dependent permeability is used in the numerical simulation to change the permeability in elements behind the moving liquid-front as a function of the time that the element has been wetted by the liquid, since the passage of the liquid-front. The numerical prediction of the wicking-front location as a function of time compares well with the reported experimental data. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2536–2544, 2012