Numerical simulation of liquid absorption in paper‐like swelling porous media

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

Spontaneous imbibition of liquids in glass‐fiber wicks. Part I: Usefulness of a sharp‐front approach

“…The relatively recent method to model the wicking flow using Darcy's law are built on the assumption that a clearly identifiable liquid front travels in the porous medium during wicking, and that saturation in the region behind the liquid‐front is 100% (i.e., all the pore space is occupied by the wicking liquid) . Pillai et al continue to develop the Darcy's law–based model for predicting and modeling liquid absorption in porous media . Furthermore, the application of Darcy's law allows researchers to model and predict the 2D and 3D wicking flows in intricately shaped wicks .…”

Enhanced Absorbent Products Incorporating Cellulose and Its Derivatives: A Review

“…Numerical simulation of capillary-induced absorption into paper-like media was carried out by Masoodi et al (2012). Their model included the swelling of the medium as well as the time-varying permeability.…”

“…In the case of ordinary paper products (not superabsorbent), several key studies have focused on theoretical issues (Bristow 1967;Aspler et al 1987;Schuchardt and Berg 1991). Related numerical simulation work has been reported (Masoodi et al 2012). The following articles have considered rates of absorption in the case of hydrogels (Kabra and Gehrke 1994;Zohariaan-Mehr et al 2010;Wang et al 2011c).…”

“…In particular, the addition the fluff pulp can prevent gel blocking, which is the blocking of liquids by a complete wall of saturated SAP particles that are not separated sufficiently by the fibers. Masoodi et al (2012) carried out studies directed at examining the combined effects of cellulose fiber and CMC hydrogel powder with respect to the wicking and uptake of water. Numerical simulation was used to model the phenomenon observed in the experiment.…”

Flow along and across glass‐fiber wicks: Testing of permeability models through experiments and simulations

“…The imbibitional flow of a liquid in wicks due to capillary suction has been modeled using several different approaches . Among the many methods available to model the wicking phenomenon mathematically, the Washburn equation based approach, the sharp‐front approach based on Darcy's law for single‐phase flow, and the diffusive‐front approach based on Richard's equation are perhaps the most popular and widely used. These mathematical models require porous‐medium (wick) properties such as hydraulic radius, fiber radius, porosity, and so forth, to be useful in prediction and optimization studies.…”