Disorder-induced topological transition in porous media flow networks

Abstract

We introduce spectral Morse–Smale analysis as a robust method to identify topological phase transitions in disordered continuous media. Combining microfluidic experiments with large-scale, pore-resolved simulations of porous media flow, we demonstrate that invariants of Morse–Smale graphs of flow speed provide a well-defined measure of the effects of spatial disorder on fluid transport. By systematically perturbing a microfluidic lattice, the fluid flow topology undergoes a phase transition from periodic to filamentous flow structure, which corresponds to a change in the spectral density of the Morse–Smale graphs and carries important implications for advective transport and front dispersion. Due to its generic formulation, spectral Morse–Smale analysis can be applied to detect and characterize topological transformations in a wide range of complex physical, chemical or biological fluid systems.