# Experiment and modeling of concentration-dependent diffusion in a solution with dual transport-phase flow for paper-based sensing

## TL;DR

This paper studies how different concentrations affect fluid flow in paper-based sensors and uses experiments and a mathematical model to explain the process.

## Contribution

The study introduces a new mathematical model and video processing technique to analyze concentration-dependent dual-phase transport in paper-based sensors.

## Key findings

- A video processing algorithm was developed to automatically track fluid flow distance in paper strips.
- A mathematical model successfully explained the concentration-dependent two-phase flow observed in experiments.
- The model showed good agreement with experimental trends, aiding in the design of paper-based sensors.

## Abstract

Paper-based sensors are promising as low-cost, passive devices for point-of-care clinical diagnostics, food quality assessment, and environmental monitoring. The diffusion process in paper-based sensors, and component detection through multistage transport or multiphase solution flow (e.g., in chromatography) have been studied in literature. However, observation or analysis of concentration dependent analyte flow in such systems has not been considered. In this work, we performed a set of experiments on concentration dependent liquid-flow in paper strips, developed a video processing technique for automatic fluid-flow-distance detection, and explained the observation through a mathematical model. We use KMnO4 solutions – such solutes which have weak bonds with water (solvent) can have decoupled transport-phases: (i) water flow, followed by (ii) analyte diffusion. We have presented a video processing algorithm to automatically extract the time-series analyte and water flow distance measurements by analyzing the pixel values frame-by-frame of the recorded experiment videos. This ensures consistency in distance measurements among the experiments. We finally explain the physical process of the flow using a corresponding mathematical model to describe the concentration effects in paper-like materials. The model includes how analyte undergoes drift force (due to water flow velocity) along with diffusion. We found that the numerical solution of the model agrees with the trends seen in the experimental results. This can help us better understand the liquid-wicking behavior in different concentrations through a mathematical model and provide guidance in the design and optimization of paper-based sensors.

(A) Video processing to automatically detect fluid-flow-distance. (B) Concentration dependent two-transport-phase flow distance explained using experiments and a mathematical model. (C) Studied for different source conditions and device orientations.