To analyze the time-dependent spectral data and convert it into a DOSY spectrum, we solve the diffusion equation to obtain an expression for the time-dependent absorption (see Supporting Information for the mathematical details). Sufficiently far away from the entrance and exit of the channel, the diffusion is effectively 1-dimensional. At t = 0, the spatial profile of the concentration is a step function, and the subsequent evolution of the position-and time-dependent concentration is described by the diffusion equation: