This study explores the influence of varying cross-sectional geometries on the capillary-driven wicking of water in vertically suspended Whatman filter paper strips. By extending the classical Lucas–Washburn framework through a Darcy-based model with spatially varying cross-sectional area , we analyze how geometry impacts both penetration length and advancing front velocity. The empirical power-law relationship was used to quantify penetration kinetics. Experimentally, the exponent increased from in rectangular strips to and in exponential and hyperbolic geometries, respectively, demonstrating improved wicking due to shape-induced modulation of viscous resistance. Velocity comparisons show that at a height of , front velocities in exponential and hyperbolic cases were and higher than trapezoidal, while at , the trapezoidal geometry outperformed others by and over exponential and hyperbolic shapes, respectively. A central element of this enhancement is the dimensionless viscous resistance term , which captures how geometry influences the wicking. Unlike the constant in rectangular strips, exponential and hyperbolic profiles exhibit a smooth, monotonic increase in , reducing cumulative resistance and supporting sustained wicking. In contrast, the trapezoidal geometry displays a peak in at for an aspect ratio of , leading to a transient benefit. These findings not only align with theoretical predictions but also demonstrate how strategic geometric tapering can substantially enhance capillary transport. The work holds practical significance for wick design in microfluidic diagnostics, passive cooling, and liquid delivery systems.
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