Mass diffusion coefficient measurements at the microscale: Imaging a transient concentration profile using TIRF microscopy

This article describes a new method to measure the mass diffusion coefficient of a fluorescent dye in a liquid, inside a millichannel geometry. The proposed method, based on Total Internal Reflection Fluorescence (TIRF) microscopy, enables the measurement of the diffusion coefficient for mass transport parallel to the millichannel wall. It determines the diffusion coefficient that provides the best fit of measured concentration profiles as a function of position and time, following a Heaviside-shaped initial concentration profile. A thorough description of the methodology is provided, including the mathematics of dye diffusion as well as fluorescence imaging considerations. In particular, we carefully develop the explicit relationship between acquired images by TIRF microscopy and actual dye concentration profiles inside the millichannel, which leads to the experimental determination of the dye diffusion coefficient. This is followed by the presentation of validation experiments with rhodamine 6G in deionized water. An average diffusion coefficient of 3.3 × 10−10 m2/s is obtained, which is in good agreement with previously reported values.