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

Verma, S and Toley, BJ (2024) Saturation Equation: An Analytical Expression for Partial Saturation during Wicking Flow in Paper Microfluidic Channels. In: Langmuir .

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Abstract

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. © 2024 American Chemical Society.

Item Type:	Journal Article
Publication:	Langmuir
Publisher:	American Chemical Society
Additional Information:	The copyright for this article belongs to American Chemical Society
Keywords:	Analytical models; Fluidic devices; Microfluidics; Normal distribution; Solute transport, Analytical expressions; Fluid-flow; Microfluidics channels; Microfluidics devices; Model fluids; Paper-based microfluidics; Partial saturation; Richards Equation; Saturation equations; Wicking flow, Flow of fluids
Department/Centre:	Division of Interdisciplinary Sciences > Centre for Biosystems Science and Engineering Division of Mechanical Sciences > Chemical Engineering
Date Deposited:	29 Jul 2024 05:11
Last Modified:	29 Jul 2024 05:11
URI:	http://eprints.iisc.ac.in/id/eprint/85198

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