Modeling Unsaturated Flow in Absorbent Swelling Porous Media: Part 1. Theory

Abstract

The flow and deformation processes in swelling porous media are modeled for absorbent hygiene products (e.g., diapers, wipes, papers etc.). The first part of the article derives the fundamental equations for the hysteretic unsaturated flow, liquid absorption, and large deformation. The final set of model equations consists of balance equations of mobile and absorbed (immobile) liquid combined with a series of constitutive relationships. The resulting equation system is strongly nonlinear and requires advanced numerical strategies for solving. The second part of the article focuses on numerical solution and presents simulation results for 2D and 3D applications.

Cellulosic Substrates for Removal of Pollutants from Aqueous Systems: A Review. 3. Spilled Oil and Emulsified Organic Liquids

“…Various authors have proposed that "capillary action" is a key mechanism by which oil is taken up by sorbent materials (Choi et al 1993(Choi et al , 1994Ribeiro and Rubio 1999;Ribeiro et al 2000;Inagaki et al 2002b;Al-Marzouqi et al 2003;Haussard et al 2003;Lim and Huang 2006;Cojocaru et al 2011;Diersch et al 2010;Masoodi et al , 2011Carrillo et al 2012). In other words, contact angle phenomena govern the wicking of oils into porous substrates.…”

Modeling Unsaturated Flow in Absorbent Swelling Porous Media: Part 2. Numerical Simulation

“…The flow, absorption and deformation processes in AGM swelling porous media are described by the following system of equations as derived in Diersch et al (2010). Written in simplified notation it reads (used symbols are summarized in List of Symbols):…”

“…These relationships are described in Diersch et al (2010) in detail. The reaction term R ψ possesses a sink for mobile liquid due to AGM-driven absorption.…”

“…It is a complex relation and implies dependencies on liquid saturation s (accordingly pressure head ψ) with its derivation, porosity ε with its derivation, solid displacement u and AGM-sorbed liquid concentration C. The reaction R c possesses a kinetic production term of sorbed (immobile) liquid and is controlled by a reaction constant rate and the AGM-sorbed liquid concentration C. Furthermore, R c incorporates dependencies on liquid saturation s (via the solid-liquid interface area) and the solid displacement u. The solid strain d is a function of the AGM-sorbed liquid concentration C. The expressions for R ψ , R c , and d are thoroughly described in Diersch et al (2010). It has to be noted that the first equation of (1) represents a generalized Richards-type flow equation written in a mixed (ψ − s)-form (e.g., Diersch and Perrochet 1999), where both variables of pressure head ψ and saturation s are employed.…”

“…Modeling aims at (1) a better understanding of the inherent physical and chemical processes in those complex porous media characterized by a significant swelling, (2) prediction of liquid dynamics in new composite fiber materials in 2D and 3D, (3) optimization of AGM properties for specific product designs, and (4) optimization of structures (layers and interstitials, thin materials, new configurations) for improving product performances and core designs. The first part of the present article sequence (Diersch et al 2010) develops the theoretical basis for AGM swelling porous media. It concludes in a set of partial differential equations for hysteretic unsaturated flow, AGM absorption of liquid and large deformation.…”