Multiphysics approach for fluid and charge transport in paper-based microfluidics

Abstract

A multiphysic model that simultaneously describe different transport phenomena in porous media is presented. The porous matrix is regarded as a bundle of periodically constricted tubes, whose pore radius distribution is described by a probability density function (PDF). The mathematical basis and the experimental validation of the model are reported. Two different materials frequently used in paper-based microfluidics were used: Whatman #1 and Muntktell 00A filter papers. These substrates were studied by capillary imbibition, hydrostatic pressure-driven flow, and electrical resistance measurements. Different PDFs were evaluated to represent the output of these experiments, and their predictions were quantified by using a Chi-Square test. The model was able to simultaneously describe the three transport phenomena by using the log-normal PDF with two statistical parameters: mean and variance. The formulation avoids including the tortuosity of the flow path, which is commonly employed as an adjusting parameter. The multiphysics model was also successfully used to calculate the parameters of single-physics models, such as Darcy’s permeability and Lucas-Washburn diffusion coefficient. Furthermore, after obtaining a suitable PDF, the proposed model can be applied to different porous materials, as well as to the design of complex paper-based microfluidic devices that combine several types of papers.