Predicting wicking dynamics of Newtonian liquid droplet in paper channels

Capillary-driven wicking in porous substrates is commonly described by models assuming an infinite liquid reservoir, which is not a valid assumption for point-of-care applications using finite droplets. In addition, wicking depends on multiple factors such as paper microstructure, fluid properties, and fabrication methods. This multi-parameter dependence makes prediction challenging and device design empirical. We hypothesize that including reservoir depletion improves wicking dynamics modelling and enables rational design of distance-based paper sensors.

We developed a minimum-ingredient wicking model with reservoir depletion included through an activity function in conjunction with capillary pressure and viscous dissipation. Automated image analysis and laser-etched paper channels were developed to reproducibly quantify capillary transport on paper. The effect of key variables including paper structure, droplet volume and fluid properties was measured, distance-time profiles plotted and compared against model predictions to evaluate accuracy.

The new model captures deviations due to reservoir depletion and predicts transport dynamics across a wide range of fluid properties and droplet volumes. Paper type significantly affects wicking dynamics highlighting the importance of choosing optimal paper. The model enables rational screening of substrates based on design metrics under realistic conditions, reducing the need for empirical trial-and-error. This is demonstrated through viscosity-modulated distance-based sensing where wicking length serves as the quantitative analytical signal. The model is also valid for other capillary-driven systems where depletion governs wicking dynamics.