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

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.