A comparison of different geometrical elements to model fluid wicking in paper-based microfluidic devices

Recently, microfluidic paper-based analytical devices (μPADs) have outstripped polymeric microfluidic devices in the ease of fabrication and simplicity. Surface tension-based fluid motion in the paper's porous structure has made the paper a suitable substrate for multiple biological assays by directing fluid into multiple assay zones. The widespread assumption in most works for modeling wicking in a paper is that the paper is a combination of capillaries with the same diameter equal to the effective pore diameter. Although assuming paper as a bundle of capillaries gives a good insight into pressure force that drives the fluid inside the paper, there are some difficulties using the effective pore radius. The effective pore radius is totally different from the average geometrical pore radius which makes it impossible to predict wicking in μPADs based on geometrical parameters. In this article, we introduce different analytical and numerical models to investigate the possibility of determining the permeability of the paper, based on geometrical parameters rather than effective parameters. The lattice Boltzmann method is used for numerical simulations. The permeability of each of the proposed models was compared with the experimental permeability. Results indicated that assuming paper as a combination of capillaries and annuluses leads to accurate results that totally depend on average geometrical values rather than effective values. This paves the way for prediction of the fluid wicking only by considering average geometrical pore and fiber diameters.