Relative Peclet number determines the transient dynamics of miscible fluids in porous media

Mixing and diffusion at the interface of two miscible fluids in porous media play a critical role in many chemical and environmental processes, such as contaminant transport in groundwater and the dissolution of rock minerals during underground carbon dioxide sequestration. In our experiments, we characterize the mixing of glycerol and dyed water solutions as they simultaneously flow into a porous medium. Using soft lithography, we fabricate two-dimensional porous microfluidic devices and control the co-injection of fluids with syringe pumps. We investigate the impact of the advection rates of each fluid on transport properties across the medium. Using optical microscopy, we directly observe the resulting flow and quantify dyed water concentration throughout the medium. We find that the total dye content in the medium reaches a steady state. This is attributed to the damping effects of the porous medium. The transition time to a steady state is determined by the relative Peclet number of the two fluids. Interestingly, the volume of the mixing zone is only determined by the flow rate of the high viscosity fluid.