Chaos in flatland: mixing in unsteady two dimensional porous media flow

Solute mixing is efficient in a steady three dimensional porous media flow, since filaments of solute elongate exponentially fast in time. This "chaotic" elongation enables molecular diffusion to rapidly distribute solute concentrations. In two dimensional steady flows, such as through thin fractures in rock, existing knowledge indicates that filaments of solute elongate much more slowly than exponentially, meaning the mixing is far less efficient. Here, we present experimental evidence that when porous media flows are instead unsteady, two dimensional mixing becomes chaotic.  Using 3D printed model porous media with steady longitudinal and oscillating transverse flow components, we measure Lyapunov exponents of filament elongation and quantify solute stretching and folding statistics as a function of the frequency and amplitude of the transverse flow. We find resonances in mixing frequency which are consistent with numerical simulations of the model geometry. These findings improve our understanding of mixing in geological systems and provide insights which may be useful to design efficient geologically-inspired mixing devices in the future.