Modeling Unsaturated Flow in Absorbent Swelling Porous Media: Part 1. Theory |
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| Authors: | Hans-Jörg G. Diersch Volker Clausnitzer Volodymyr Myrnyy Rodrigo Rosati Mattias Schmidt Holger Beruda Bruno J. Ehrnsperger Raffaele Virgilio |
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| Affiliation: | (1) Weldon School of Biomedical Engineering, Purdue University, 46202 West Lafayette, IN, USA;(2) Department of Mathematical Sciences, IUPUI, 46202 Indianapolis, IN, USA;(3) Department of Biomedical Engineering, Surgery, and Cellular and Integrative Physiology, IUPUI, 46202 Indianapolis, IN, USA;(4) Department of Biomedical Engineering, IUPUI, 46202 Indianapolis, IN, USA;(5) Weldon School of Biomedical Engineering, Purdue University, 47906 West Lafayette, IN, USA;(6) Department of Biomedical Engineering Department of Surgery Department of Cellular and Integrative Physiology Indiana Center for Vascular Biology and Medicine, IUPUI, 46202 Indianapolis, IN, USA |
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| 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. |
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