Theoretical Analysis of Molecular Diffusion in Pressure-Driven Laminar Flow in Microfluidic Channels

The T-sensor is a microfluidic analytical device that operates at low Reynolds numbers to ensure entirely laminar flow. Diffusion of molecules between streams flowing side by side may be observed directly. The pressure-driven velocity profile in the duct-shaped device influences diffusive transport in ways that affect the use of the T-sensor to measure molecular properties. The primary effect is a position-dependent variation in the extent of diffusion that occurs due to the distribution of residence time among different fluid laminae. A more detailed characterization reveals that resultant secondary concentration gradients yield variations in the scaling behavior between diffusive displacement and elapsed time in different regions of the channel. In this study, the time-dependent evolution of analyte distribution has been quantified using a combination of one- and two-dimensional models. The results include an accurate portrayal of the shape of the interdiffusion region in a representative T-sensor assay, calculation of the diffusive scaling law across the width of the channel, and quantification of artifacts that occur when making diffusion coefficient measurements in the T-sensor.