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

Area of Science:

• Microfluidics
• Materials Science
• Fluid Dynamics

Background:

• Paper-based microfluidic devices rely on understanding fluid flow in porous membranes.
• Partial saturation, where pores aren't fully filled, is a key challenge in wicking flow.
• Existing models like the Richards equation are complex and require specialized software.

Purpose of the Study:

• To develop a simple, accessible analytical model for partial saturation in paper membranes.
• To provide a user-friendly tool for the microfluidics and lateral flow assay community.
• To enable better design of paper-based microfluidic devices by accounting for partial saturation.

Main Methods:

• Modeling paper as parallel capillaries with a log-normal pore size distribution.
• Applying the Washburn equation to determine fluid front distribution.
• Deriving an explicit analytical expression, the "saturation equation," for 1D wicking flow.

Main Results:

• The derived "saturation equation" provides an explicit calculation of saturation over space and time.
• Experimental data from four paper types were used to parameterize the model.
• The analytical model's results closely matched experimental data and numerical simulations from the Richards equation.

Conclusions:

• The new analytical model offers a simplified yet accurate approach to partial saturation in paper wicking.
• This accessible "saturation equation" can be readily integrated into the design of paper microfluidic devices.
• The model facilitates improved performance and reliability of assays using paper-based platforms.