The mechanics of poro-elastic capillary flow

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Absorption of liquid into paper towel is a complex process: it involves a surface tension driven flow in aporous and elastic network that swells and deforms when in contact with liquid. Analysis of surface tensiondriven flow in a capillary dates back a century to the work of Lucas and Washburn on capillary rise. Whileearly work on capillary driven flow focused primarily on the regime where capillary forces balance viscousforces, if the walls of the pore (or of the porous media) are flexible then elastic forces arise due to thedeformation of the pore. The dynamics of elasto-capillary rise have only recently been explored, and it has beenshown that for sufficiently flexible channels the fluid penetration is retarded compared to rigid channels. Inpaper towel, plies are not only elastic, but also porous and so we propose here to extend recent work onelasto-capillary flow to include porous walls. We aim to determine the relative importance of surface tension,elasticity and porosity over length and time scales which are relevant to paper towel and tissue absorption in aneffort to improve the performance of these products.