Abstract : Recent works have shown that steady laminar flows through 3D porous media can spontaneously generate Lagrangian chaos at pore scale, with strong implications for a range of transport, reactive, and biological processes in nature and industry. Lagrangian (deterministic) chaos induces the exponential stretching of neighboring fluid particles, impacting solutes mixing rates, dispersivity and chemical reactivity. Imaging 3D transport processes in opaque porous environments is an outstanding challenge. We present a novel experimental technique based upon high-resolution imaging of the scalar signature produced by push-pull flows through natural porous samples (beads, gravels, sandstones) at high Péclet number. We show that this method provides a direct image of the invariant unstable manifold of the chaotic flow, and allows for a precise quantification of the incompleteness of mixing at pore scale. In the limit of large Péclet numbers, we demonstrate that the decay rate of the scalar variance is directly related to the Lyapunov exponent of the chaotic flow. Thus, this new push-pull method has the potential to provide a complete characterization of chaotic mixing dynamics in a large class of opaque porous materials.

Reference :
J. Heyman, D. R. Lester, and T. Le Borgne, Phys. Rev. Lett. 126, 034505, https://doi.org/10.1103/PhysRevLett.126.034505