Darcy's law‐based model for wicking in paper‐like swelling porous media

The wicking of liquid into a paper-like swelling porous medium made from cellulose and superabsorbent fibers was modeled using Darcy's law. The work is built on a previous study in which the Washburn equation, modified to account for swelling, was used to predict wicking in a composite of cellulose and superabsorbent fibers. In a new wicking model proposed here, Darcy's law for flow in porous media is coupled with the mass conservation equation containing an added sink or source term to account for matrix swelling and liquid absorption. The wicking-rate predicted by the new model compares well with the previous experimental data, as well as the modified Washburn equation predictions. The effectiveness of various permeability models used with the new wicking model is also investigated. © 2010 American Institute of Chemical Engineers AIChE J, 2010

[1]  Richard Lucas,et al.  Ueber das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten , 1918 .

[2]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[3]  B. R. Gebart,et al.  Permeability of Unidirectional Reinforcements for RTM , 1992 .

[4]  Mikko Alava,et al.  Imbibition in disordered media , 2004 .

[5]  J. G. Williams,et al.  Liquid flow through aligned fiber beds , 1974 .

[6]  J. Berg,et al.  The effect of surfactants on wicking flow in fiber networks , 1988 .

[7]  S. Chwastiak,et al.  A wicking method for measuring wetting properties of carbon yarns , 1973 .

[8]  K. Pillai,et al.  Darcy's law‐based models for liquid absorption in polymer wicks , 2007 .

[9]  John C. Berg,et al.  Liquid Transport in Composite Cellulose—Superabsorbent Fiber Networks , 1991 .

[10]  J. Kardos,et al.  Resin flow through fiber beds during composite manufacturing processes. Part I: Review of newtonian flow through fiber beds , 1992 .

[11]  K. Pillai.  Governing equations for unsaturated flow through woven fiber mats. Part 1. Isothermal flows , 2002 .

[12]  S. Whitaker.  The method of volume averaging , 1998 .

[13]  Suresh G. Advani,et al.  Flow of generalized Newtonian fluids across a periodic array of cylinders , 1993 .

[14]  Reza Masoodi,et al.  Role of Hydraulic and Capillary Radii in Improving the Effectiveness of Capillary Model in Wicking , 2008 .

[15]  E. W. Washburn.  The Dynamics of Capillary Flow , 1921 .

[16]  J. Parlange.  Porous Media: Fluid Transport and Pore Structure , 1981 .

[17]  E. Kissa,et al.  Wetting and Wicking , 1996 .

[18]  Suresh G. Advani,et al.  Wicking across a Fiber-Bank , 1996 .

[19]  The influence of fiber swelling on paper wetting , 2001 .

[20]  F. Fowkes.  Role of Surface Active Agents in Wetting , 1953 .

[21]  J. Kardos,et al.  Resin flow through fiber beds during composite manufacturing processes. Part II: Numerical and experimental studies of newtonian flow through ideal and actual fiber beds , 1992 .

[22]  Krishna M. Pillai,et al.  Governing equations for unsaturated flow through woven fiber mats. Part 2. Non-isothermal reactive flows , 2004 .