Validity of Capillary Imbibition Models in Paper-Based Microfluidic Applications

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.

A simple method for the assessment of electrophoretic mobility in porous media

Developing paper-based electrophoretic methods involve dealing with significant uncertainty levels when compared to their capillary counterparts. Critical information for developing these kinds of methods are the electrophoretic mobility of background electrolytes and samples. This work presents the design and characterization of a device for measuring the electrophoretic mobilities of dyes in porous media. The device was developed with the aim of validating a previously presented model and also proposing a protocol for the straightforward determination of electrophoretic mobilities in porous media when open-channel values are already known. Whatman #1 paper was used as a model substrate as far as it is the most common porous medium substrate for paper-based electrophoresis. The device was designed using a numerical simulation-assisted approach, utilizing OpenFOAM® and specific solvers for capillary transport and electromigration, namely porousMicroTransport and electroMicroTransport, respectively. The electrophoretic mobilities of five dyes were analyzed experimentally with the proposed device. To establish appropriate comparative values at different pHs, experiments in fused silica capillaries were also performed. An effective parameter model for describing the electrophoretic behavior of dyes in porous media, that is, the constriction factor, was found consistent with previous reports for the Whatman #1 paper. This consistency was found after considering (via direct measurements) the chromatographic effect of the medium over each dye. Consequently, the recorded values hold significant worth due to their potential for direct application in designing new experiments or devices in Whatman #1 paper. With the validation of the model through the experiments with the proposed device, those researchers interested on developing electrophoretic methods in porous substrates can make use of the open-channel electrophoretic mobilities reported in the literature, or in the well-known software databases, and correct them for the media of interest just by performing two simple characterization steps.

Effects of Relative Humidity and Paper Geometry on the Imbibition Dynamics and Reactions in Lateral Flow Assays

Lateral flow assays and paper microfluidics have the potential to replace benchtop instrumented medical diagnostic systems with instrument-free systems that rely on passive transport of liquid through micro-porous paper substrates. Predicting the imbibition dynamics of liquid through dry paper substrates is mostly modeled through the Lucas-Washburn (LW) equations. However, the LW framework assumes that the fluid front exhibits a sharp boundary between the dry and wet phases across the liquid imbibition interface. Additionally, the relative humidity in the environment results in moisture trapped within the pores of the paper substrates as the paper attains an equilibrium with the ambient air. Here, we apply a two-phase transport framework based on Brooks and Corey's model to capture imbibition dynamics on partially saturated paper substrates. The model is experimentally validated and is then used to predict the liquid-paper imbibition dynamics in simulated environments with 1-70% relative humidity. The model was also used to determine the saturation gradient of liquid along the imbibition interface of the paper substrate. Insights from these studies enabled us to determine the mechanism of the liquid transport in partially saturated porous paper substrates. The model also enabled us to evaluate the optimal paper shapes and relative humidity of the environment that maximize imbibition rates and minimize imbibition front broadening. Finally, we evaluate the effect of moisture content of paper on the rate of paper-based biochemical reaction by amplifying a sequence of the SARS-CoV-2 RNA target via reverse transcriptase loop-mediated isothermal amplification. Taken together, this study provides some important guidelines to academic and applied researchers working in point-of-care diagnostics to develop paper-based testing platforms that are capable of functioning in a robust manner across multiple environmental conditions.