Interdiffusion and Hydrodynamic Dispersion in a Y-Shaped Geometry

Microfluidics is a very promising tool to measure the dynamics of different processes: diffusion of a solute, protein folding, kinetics of chemical reactions… In most of these experiments, two streams of miscible liquids are brought at a junction to flow side-by-side within a Y-shaped microchannel, allowing solutes to diffuse from one stream to the other and possibly react. Since flows are laminar given the small length scales and velocities involved, the liquids only mix by transverse diffusion, and one can relate the distance downstream in the channel to the time elapsed since the two streams were put into contact. Such devices are widely used experimentally to perform chemical reactions, and to extract kinetic parameters from the reaction-diffusion dynamics. The precise control of the mixing due to the small length scales allows us to perform stationary measurements of kinetics down to time scales of a few tens of milliseconds. In this context, we focussed our researches on two different problems: (i) the hydrodynamic dispersion coming from the parabolic Poiseuille velocity profile along the channel, (ii) and the interdiffusion of two fluids having different viscosities. These two common problems were investigated using both numerics and experiments using Raman confocal imaging. We also provided simple analytical arguments to understand the hydrodynamic dispersion, and also the effect of the viscosity difference on the interdiffusion process