Solute imbibition in paper strip: Pore-scale insights into the concentration-dependent permeability

Capillary wicking in a thicker gel blot microfluidics paper has been investigated through a combination of an analytical framework, experiments, and numerical simulations. The primary objectives of this work are to investigate the concentration-dependent wicking process inside thicker microfluidic paper and to estimate the concentration-dependent permeability using both theoretical models and experimental data. An additional goal is to estimate the parameters for saturation-dependent flow modeling in thicker microfluidic paper. To comprehend the wicking phenomenon on thicker gel blot paper, a series of experiments employing aqueous food dye solutions at varying concentrations has been conducted. In order to calculate the temporal wicking length analytically, the Brinkman-extended Darcy equation is implemented. By modifying the permeability expression for a simple rectangular unidirectional fiber cell and pure liquid, the expression of effective permeability for the analytical framework has also been introduced. The concentrations of the food dye solutions appear to have a substantial influence on the wicking phenomenon. Effective permeability and wicking length have been found to follow a decreasing pattern at lower concentrations while both increase at higher values. Intriguingly, employing a microfluidics paper with a relatively greater thickness facilitates the visualization of the fluid front. This phenomenon is identified by the formation of an acute angle at intermediate time instants, while the fluid front angle assumes an angle nearly similar to 90 degrees during smaller and higher time instants. In order to evaluate the saturation-dependent capillary pressure and permeability, the empirical correlation of concentration-dependent Brooks and Corey parameters is additionally determined experimentally. These parameters are subsequently employed in numerical simulations to illustrate the saturation-dependent flow field using Richards' equation. Furthermore, numerical simulations based on these estimated model parameters have been conducted, and it turns out that the saturation field has an excellent agreement with the experimental results. The results of the current study can be used to design low-cost paper-based diagnostic devices for usage in healthcare and environmental applications.