Modeling-Guided Design of Paper Microfluidic Networks: A Case Study of Sequential Fluid Delivery

Saturation Equation: An Analytical Expression for Partial Saturation during Wicking Flow in Paper Microfluidic Channels

The design and fabrication of paper-based microfluidic devices is critically dependent on modeling fluid flow through porous paper membranes. A commonly observed phenomenon is partial saturation, i.e., regions of the paper membrane not being filled completely due to pores of different sizes. The most comprehensive model to date of partial saturation during wicking flow in paper is the Richards equation. However, the solution to the Richards equation requires numerical solvers like COMSOL, which makes it largely inaccessible to the paper microfluidics and lateral flow assay community. There is therefore a need for a simple and appropriate model of partial saturation in paper membranes, easily usable by the wider research community. In the current work, we present an approach to model paper membranes as a bundle of parallel capillaries whose radii follow a two-parameter log-normal distribution. Application of the Washburn equation to the bundle provides a distribution of fluid fronts, which can be used to calculate saturation. Using this approach, we developed the "saturation equation"─an explicit analytical expression to calculate saturation as a function of space and time in 1D wicking flow. Experimentally obtained data for spatiotemporal saturation for four different paper materials were fit to this analytical model to obtain parameters for each material. Results obtained from this analytical model match well with both experimental data and numerical results obtained from the Richards equation. The availability of an explicit analytical expression for partial saturation will enable incorporation of the critical phenomenon of partial saturation in the design of paper microfluidic devices.

Unreacted Labeled PCR Primers Inhibit the Signal in a Nucleic Acid Lateral Flow Assay as Elucidated by a Transport Reaction Model

Factors that affect the performance of the nucleic acid lateral flow assay (NALFA) have not been well studied. In this work, we identify two important phenomena that negatively affect signal intensities during the detection of PCR products using NALFA: (i) the presence of unreacted PCR primers, and (ii) the presence of excess PCR amplicons. This is the first report that highlights the negative effect of unreacted PCR primers on NALFA. The negative effect of excess amplicons, while not explicitly reported for NALFAs, emanates from an identical phenomenon in lateral flow immunoassays known as the "hook effect". We show that the above effects may be alleviated by increasing the concentration of capture antibodies at the test line and the concentration of reporter moieties (gold nanoparticles). To demonstrate these, we utilized a PCR assay in which both primers were end-labeled, to generate dually end-labeled (bi-labeled) PCR amplicons of 230 bp length. To provide mechanistic understanding of these phenomena, we present the first transport-reaction model of NALFA, the results of which qualitatively matched all observed phenomena. Based on these results, we provide recommendations for the optimal design of PCR for NALFA detection.

Spontaneous Imbibition in Paper-Based Microfluidic Devices: Experiments and Numerical Simulations

Microfluidic paper-based analytical devices (μPADs) have quickly been an excellent choice for point-of-care diagnostic platforms ever since they appeared. Because capillary force is the main driving force for the transport of analytes in μPADs, low spontaneous imbibition rates may limit the detection sensitivity. Therefore, quantitative understanding of internal spontaneous capillary flow progress is requisite for designing sensitive and accurate μPADs. In this work, experimental and numerical studies have been performed to investigate the capillary flow in a typical filter paper. We use light-transmitting imaging technology to study wetting saturation changes in the paper. Our experimental results show an obvious transition of a saturated wetting front into an unsaturated wetting front as the imbibition proceeds. We find that the single-phase Darcy model considerably overestimates the temporal wetting penetration depths. Alternatively, we use the Richards equation together with the two-phase flow material properties that are obtained from the image-based pore-network modeling of the filter paper. Moreover, we have considered a dynamic term in the capillary pressure due to strong wetting dynamics in spontaneous imbibition. As a result, the numerical predictions of spontaneous imbibition in the paper are significantly improved. Our studies provide insights into the development of a quantitative spontaneous imbibition model for μPADs applications.

Barrier-Free Microfluidic Paper Analytical Devices for Multiplex Colorimetric Detection of Analytes

In recent years, microfluidic paper analytical devices (μPADs) have been extensively utilized to conduct multiplex colorimetric assays. Despite their simple and user-friendly operation, the need for patterning paper with wax or other physical barriers to create flow channels makes large-scale manufacturing cumbersome. Moreover, convection of rehydrated reagents in the test zones leads to nonuniform colorimetric signals, which makes quantification difficult. To overcome these challenges, we present a device called a barrier-free μPAD (BF-μPAD) that consists of a stack of two paper membranes having different wicking rates-the top layer acting as a fluid distributing layer and the bottom layer containing reagents for colorimetric detection. Multiple analytes can be detected using this assembly without the need to pattern either layer with wax or other barriers. In one embodiment, a device is capable of delivering the sample fluid to 20 distinct dried reagent spots stored on an 8 cm × 2 cm membrane in as few as 30 s. The multiplexing feature of the BF-μPAD is demonstrated for colorimetric detection of salivary thiocyanate, protein, glucose, and nitrite. Most importantly, the device improves the limit of detection of colorimetric assays performed on conventional μPADs by more than 3.5×. To understand fluid imbibition in the paper assembly, the device geometry is modeled in COMSOL Multiphysics using the Richards equation; the results obtained provide insights into the nonintuitive flow pattern producing perfectly uniform signals in the barrier-free assembly.

Recent developments in flow modeling and fluid control for paper-based microfluidic biosensors

Over the last 10 years, researchers have shown that paper is a promising substrate for affordable biosensors. The field of paper-microfluidics has evolved rapidly in that time, with simple colorimetric assays giving way to more complex electrochemical devices that can handle multiple samples at a given time. As paper devices become more complex, the ability to precisely control different fluids simultaneously becomes a challenge. Specifically, automated flow control is a necessary attribute to make paper-based devices more useable in resource-limited settings. Flow control strategies on paper are typically developed experimentally through trial-and-error, with little focus on theory. This is because flow behavior in paper is not well understood and sometimes difficult to predict precisely. Additionally, popular theoretical models are too simplistic, making them unsuitable for complex device designs and application conditions. A better understanding of flow theory would allow devices conceived straight from theoretical models. This could save time and resources by reducing experimental work. In this review, we provide an overview of different theoretical models used to characterize imbibition in paper substrates and document the latest flow control strategies that have been applied to automated fluid control on paper. Additionally, we look at current efforts to commercialize paper-based devices along with challenges facing this industry.