Kvick, M; Martinez, DM; Hewitt, DR; Balmforth, NJ; (2017) Imbibition with swelling: Capillary rise in thin deformable porous media. Physical Review Fluids , 2 (7) , Article 074001. 10.1103/PhysRevFluids.2.074001.

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Abstract

The imbibition of a liquid into a thin deformable porous substrate driven by capillary suction is considered. The substrate is initially dry and has uniform porosity and thickness. Two-phase flow theory is used to describe how the liquid flows through the pore space behind the wetting front when out-of-plane deformation of the solid matrix is considered. Neglecting gravity and evaporation, standard shallow-layer scalings are used to construct a reduced model of the dynamics. The model predicts convergence to a self-similar behavior in all regions except near the wetting front, where a boundary layer arises whose structure narrows with the advance of the front. Over time, the rise height approaches the similarity scaling of t^{1/2}, as in the classical Washburn or BCLW law. The results are compared with a series of laboratory experiments using cellulose paper sheets, which provide qualitative agreement.

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