Topological inversions in coalescing granular media control fluid-flow regimes.

Sintering-or coalescence-of viscous droplets is an essential process in many natural and industrial scenarios. Current physical models of the dynamics of sintering are limited by the lack of an explicit account of the evolution of microstructural geometry. Here, we use high-speed time-resolved x-ray tomography to image the evolving geometry of a sintering system of viscous droplets, and use lattice Boltzmann simulations of creeping fluid flow through the reconstructed pore space to determine its permeability. We identify and characterize a topological inversion, from spherical droplets in a continuous interstitial gas, to isolated bubbles in a continuous liquid. We find that the topological inversion is associated with a transition in permeability-porosity behavior, from Stokes permeability at high porosity, to percolation theory at low porosity. We use these findings to construct a unified physical description that reconciles previously incompatible models for the evolution of porosity and permeability during sintering.