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

Enhanced Imbibition in Liquid-Infused Coated Microchannels

Spontaneous capillary imbibition has the potential to improve the performance of many micro and nanodevices since it does not require an external energy source to drive a fluid flow. Despite this advantage, controlling and reducing the friction exerted by the channel walls, which limits the speed of the liquid, remains a challenge. Here, we demonstrate experimentally that infusing the walls of a channel with a liquid lubricant substantially speeds up the imbibition process and reduces the overall viscous friction. By varying the viscosity of the lubricant, we observe a substantial reduction of the imbibition time of up to 50%. Our experimental results are in good agreement with previous theoretical predictions, providing a solid framework to study low-resistance spontaneous imbibition processes.

Multi-dimensional microfluidic paper-based analytical devices (μPADs) for noninvasive testing: A review of structural design and applications

The rapid emergence of microfluidic paper-based devices as point-of-care testing (POCT) tools for early disease diagnosis and health monitoring, particularly in resource-limited areas, holds immense potential for enhancing healthcare accessibility. Leveraging the numerous advantages of paper, such as capillary-driven flow, porous structure, hydrophilic functional groups, biodegradability, cost-effectiveness, and flexibility, it has become a pivotal choice for microfluidic substrates. The repertoire of microfluidic paper-based devices includes one-dimensional lateral flow assays (1D LFAs), two-dimensional microfluidic paper-based analytical devices (2D μPADs), and three-dimensional (3D) μPADs. In this comprehensive review, we provide and examine crucial information related to paper substrates, design strategies, and detection methods in multi-dimensional microfluidic paper-based devices. We also investigate potential applications of microfluidic paper-based devices for detecting viruses, metabolites and hormones in non-invasive samples such as human saliva, sweat and urine. Additionally, we delve into capillary-driven flow alternative theoretical models of fluids within the paper to provide guidance. Finally, we critically examine the potential for future developments and address challenges for multi-dimensional microfluidic paper-based devices in advancing noninvasive early diagnosis and health monitoring. This article showcases their transformative impact on healthcare, paving the way for enhanced medical services worldwide.

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.

Fluid Flow Dynamics in Partially Saturated Paper

This study presents an integrated approach to understanding fluid dynamics in Microfluidic Paper-Based Analytical Devices (µPADs), combining empirical investigations with advanced numerical modeling. Paper-based devices are recognized for their low cost, portability, and simplicity and are increasingly applied in health, environmental monitoring, and food quality analysis. However, challenges such as lack of flow control and the need for advanced detection methods have limited their widespread adoption. To address these challenges, our study introduces a novel numerical model that incorporates factors such as pore size, fiber orientation, and porosity, thus providing a comprehensive understanding of fluid dynamics across various saturation levels of paper. Empirical results focused on observing the wetted length in saturated paper substrates. The numerical model, integrating the Highly Simplified Marker and Cell (HSMAC) method and the High Order accuracy scheme Reducing Numerical Error Terms (HORNET) scheme, successfully predicts fluid flow in scenarios challenging for empirical observation, especially at high saturation levels. The model effectively mimicked the Lucas-Washburn relation for dry paper and demonstrated the increasing time requirement for fluid movement with rising saturation levels. It also accurately predicted faster fluid flow in Whatman Grade 4 filter paper compared with Grade 41 due to its larger pore size and forecasted an increased flow rate in the machine direction fiber orientation of Whatman Grade 4. These findings have significant implications for the design and application of µPADs, emphasizing the need for precise control of fluid flow and the consideration of substrate microstructural properties. The study's combination of empirical data and advanced numerical modeling marks a considerable advancement in paper-based microfluidics, offering robust frameworks for future development and optimization of paper-based assays.

Viscoelastic Effects on Spontaneous Imbibition in Unsaturated Porous Membranes of Complex Shapes

Richards equation is a robust mathematical model for predicting spontaneous imbibition in unsaturated porous materials, whether granular or fibrous. The main restriction of this imbibition model is that it is valid only for Newtonian fluids. In the present work, we extend the classic Richards equation to viscoelastic fluids using a modified version of the single-phase Darcy's law reported in the literature for several polymer solutions. In two-dimensional flows, the viscoelastic Richards model obtained this way turns out to be in the form of a system of three highly nonlinear coupled partial differential equations for the moisture content and the velocity field. The model is numerically validated against published experimental data for a shear-thinning polymer solution imbibed in a tight sandstone core sample extracted from a typical oil reservoir. The viscoelastic Richards model is then used to investigate the effect of a fluid's elasticity on the quasi-stationary regime in a two-dimensional porous membrane of complex shape typically used in diagnostic kits. The obtained numerical results suggest that elasticity has a retarding effect on spontaneous imbibition in capillary-driven, paper-based kits. Based on this new imbibition model, it is predicted that viscoelasticity of the displacing liquid can extend the duration of the quasi-stationary regime on the test line of diagnostic kits. The conclusion is that, for extending the quasi-steady regime in capillary-driven kits, it might prove useful to enhance the degree of elasticity of the test fluids using appropriate rheology modifiers.

Spontaneous Imbibition in Nanomatrix-Fracture of Low Permeability Using Multiscale Nanofluidic Chips

Spontaneous imbibition has garnered increasing attention as an attractive mechanism for developing tight reservoirs. Despite valuable insights from previous experiments, there remains a lack of understanding regarding the imbibition process within multiscale nanopore-fracture networks. In this work, we devised an innovative multiscale model incorporating over 105 nanochannels and integrating a microfracture network to explore the complex imbibition behavior in tight formations. Additionally, fracture-free nanomatrix models with low permeability were developed for comparative discussions. The results show that the Lucas-Washburn equation remains valid at the tremendous fracture-free nanopore networks under the confinement of 500 nm, with a relative deviation of ±6%. The nanomatrix's heterogeneity hinders the imbibition rate, resulting in a reduction of 4.6 to 10.8% in the imbibition slope. The viscosity plays a dominant role in the change of imbibition slope as temperature varies. Our experiments also found that the interactions between the nanomatrix and bulk fracture complicate the imbibition process. A single wetting front no longer applies in the nanomatrix-fracture networks. Differing fracture/microchannel connectivity leads to disparities in macroscopic patterns, saturation rates, and flow directions. The spatial arrangement of fractures significantly impacts the imbibition time. Overall, this work based on nanofluidic techniques systematically explores the effects of matrix heterogeneity, temperature, and fractures on the imbibition process. The real-time in situ visualization of fluid distribution in multiscale matrix-fracture systems has been achieved, which offers theoretical guidance for practical engineering applications.

Bifurcation and Transposition of the Wicking Front of Binary Solutions Infiltrating into Chromatography Paper Associated with Their Evaporation

Nonequilibrium fluid patterns, such as Marangoni contraction, coffee rings, and tears of wine, are generated in binary solutions spread on a substrate during their evaporation. In this study, we observed another type of nonequilibrium behavior exhibited by binary solutions as they infiltrate porous materials and undergo evaporation. A binary solution comprising hexane and ethanol was brought into contact with the chromatography paper to facilitate infiltration into the paper's pores. Because the experimental setup was in an open environment, infiltration and evaporation occurred simultaneously. The wicking front exhibited an initial rapid advancement, followed by subsequent receding and readvancing. Additionally, the bifurcation of the wicking front after the onset of its readvancement was confirmed by monitoring the temporal evolution of the spatial luminance distribution and temperature distribution on the surface of the chromatography paper. Chromatographic development of a hydrophilic dye was conducted in this experimental setup in an open environment. Additionally, it was confirmed that the receding and readvancing of the wicking front represented the transposition of the bifurcated wicking fronts.

Paper based microfluidic devices: a review of fabrication techniques and applications

A wide range of applications are possible with paper-based analytical devices, which are low priced, easy to fabricate and operate, and require no specialized equipment. Paper-based microfluidics offers the design of miniaturized POC devices to be applied in the health, environment, food, and energy sector employing the ASSURED (Affordable, Sensitive, Specific, User-friendly, Rapid and Robust, Equipment free and Deliverable to end users) principle of WHO. Therefore, this field is growing very rapidly and ample research is being done. This review focuses on fabrication and detection techniques reported to date. Additionally, this review emphasises on the application of this technology in the area of medical diagnosis, energy generation, environmental monitoring, and food quality control. This review also presents the theoretical analysis of fluid flow in porous media for the efficient handling and control of fluids. The limitations of PAD have also been discussed with an emphasis to concern on the transformation of such devices from laboratory to the consumer.