Mathematical model for mixing in a paper-based channel and applications to the generation of a concentration gradient

A paper-based channel is a useful platform for the facile development of analytical devices implementing various chemical or biological reactions. To improve the analytical performance for various applications, it was necessary to analyze the detailed mixing characteristics within a paper-based channel. In this paper, we proposed a mathematical model to predict a concentration field created as a result of the imbibition of multiple fluids within a porous material. Interestingly, we found that the model exhibited a constant interdiffusion width within a paper-based channel even though the flow front velocity decreased over time. We were able to verify that our model accurately predicted the concentration field by comparing the experimental and numerical results for mixing in a 2 inlet-channel. Finally, we designed and fabricated paper-based channels to generate two (linear and non-linear) concentration gradients based on predictions made by the model. Both the experimental and numerical results were in good agreement, demonstrating that our model was accurate and useful for developing a paper-based analytical device utilizing the mixing characteristics of a sample and reagent flow system.