Fluid Flow Dynamics in Partially Saturated Paper

Abstract

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.

Keywords

• fluid dynamics
• saturated paper substrate
• numerical modeling
• capillary flow
• porosity
• pore size