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Paper-based microfluidic devices are rapidly becoming popular as a platform for developing point-of-care medical diagnostic tests. However, the design of these devices largely relies on trial and error, owing to a lack of proper understanding of fluid flow through porous membranes. Any porous material having pores of multiple sizes contains partially saturated regions, i.e., regions where less than 100% of the pores are filled with fluid. The capillary pressure and permeability of the material change as a function of the extent of saturation. Although methods to measure these relationships have been developed in other fields of study, these methods have not yet been adapted for paper for use by the larger community of analytical chemists. In the current work, we present a set of experimental methods that can be used to measure the relationships between capillary pressure, permeability, and saturation for any commercially available paper membrane. These experiments can be performed using commonly available lab instruments. We further demonstrate the use of the Richards equation in modeling imbibition into two-dimensional paper networks, thus adding new capability to the field. Predictions of spatiotemporal saturation from the model were in strong agreement with experimental measurements. To make these methods readily accessible to a wide community of chemists, biologists, and clinicians, we present the first report of a simple protocol to measure the flow rates considering the effect of partial saturation. Use of this protocol could drastically reduce the trial and error involved in designing paper-based microfluidic devices.

Higher capture efficiency of biomarkers in heterogeneous immunosensors would enable early detection of diseases. Several strategies are used to improve the capture efficiency of these immunosensors including the geometry of the system along with the transport and reaction parameters. Having a prior knowledge of the behavior of the above parameters would facilitate the design of an efficient immunosensor. While the contributions of the transport and reaction parameters toward understanding of the mechanism involved in capture have been well studied in the literature, their effect in combination with the geometry of the sensors has not been explored until now. In this work, we have experimentally demonstrated that the capture efficiency of the antigen-antibody systems is inversely related to the size of the sensor patch. The experimental system was simulated in order to get an in-depth understanding of the mechanism behind the experimental observation. Further, the extent of heterogeneity in the system was analyzed using the Sips isotherm to obtain the heterogeneity index (α) and the reaction rate constant (K(D)) as fitted parameters for a sensor patch of 1.5 mm radius. The experimental kinetic data obtained for the same sensor patch matched reasonably with the simulation results by considering K(D) as the global affinity constant, which indicated that our system can be considered to be homogeneous. Our simulation results associated with the size dependency of the capture efficiency were in agreement with the trends obtained in our experimental observations where an inverse relation was observed owing to the fact that the mass-transfer limitation decreases with the decrease in the size of the sensor patch. The possible underlying mechanism associated with size dependency of capture efficiency was discussed based on the time-dependent radial variation of captured antigens obtained from our simulation results. A study on the parametric variation was further conducted for the nonmixed and mixed systems on the transport (Deff), reaction (K(D)), and geometric parameters (R). Two different correlations were established for the nonmixed and mixed systems between the capture efficiency (f) and a nondimensional number (t(D)/t(R)) consisting of the above-mentioned parameters. Such unified relations will be useful in designing heterogeneous immunosensors and can be extended to microfluidic immunosensors.