Experimental and numerical investigation of wicking dynamics of water on thin paper strips: Effect of orientation and geometry

This study investigates the dynamics of water wicking in porous media, using Whatman filter paper (grade 1) as a model porous substrate. Both experimental and numerical approaches were employed to explore the influence of orientation (vertical and horizontal) and geometric variations (rectangular and trapezoidal shapes) on the wicking process. Capillary rise experiments were compared with predictions from the modified Lucas–Washburn model and COMSOL simulations. A key advancement is a refined theoretical framework extending Darcy's law to include variable cross-sectional areas. This framework revealed that trapezoidal geometries with narrower top widths achieve faster capillary rise due to the reduced viscous pressure loss, which is captured using a factor f in the momentum equation. fz,s has been written as a function of the wicking front location z and a shape factor, s, defined as the ratio of the top width to base for the trapezoidal geometries. Interestingly, f exhibited a maximum when 0≤s≤e−1 condition is met, while for geometries having s>e−1, f increased monotonically, emphasizing the critical role of geometry in determining capillary penetration and pressure loss dynamics. The findings highlight geometry as a critical parameter in modulating wicking performance. Additionally, horizontal wicking was found to be independent of gravity, while vertical wicking exhibited gravity-induced dynamics, underscoring the orientation-dependent nature of capillary transport. Trapezoidal geometries achieved up to ∼40% higher wicking velocity and ∼8% and ∼20% higher penetration height in vertical and horizontal orientations, respectively. The experimental, theoretical, and numerical results largely agree, except for deviations in narrower top-width cases.