A space-spanning network structure is a basic morphology in phase separation of soft and biomatter, alongside a droplet one. Despite its fundamental and industrial importance, the physical principle underlying such network-forming phase separation remains elusive. Here, we study the network coarsening during gas-liquid-type phase separation of colloidal suspensions and pure fluids, by hydrodynamic and molecular dynamics simulations, respectively. For both, the detailed analyses of the pore sizes and strain field reveal the self-similar network coarsening and the unconventional power-law growth more than a decade according to ℓ ∝ t1/2, where ℓ is the characteristic pore size and t is the elapsed time. We find that phase-separation dynamics is controlled by mechanical relaxation of the network-forming dense phase, whose limiting process is permeation flow of the solvent for colloidal suspensions and heat transport for pure fluids. This universal coarsening law would contribute to the fundamental physical understanding of network-forming phase separation.

Numerical prediction of out-of-equilibrium processes in soft and bio matter containing liquids is highly desirable. However, it is quite challenging primarily because the motions of the components at different hierarchical levels (e.g., large colloids and small solvent molecules) are spatio-temporally coupled in a complicated manner via momentum conservation. Here we critically examine the predictability of numerical simulations for colloidal phase separation as a prototype example of self-organization of soft materials containing a liquid. We use coarse-grained hydrodynamic simulations to tackle this problem, and succeed in almost perfectly reproducing the structural and topological evolution experimentally observed by three-dimensional confocal microscopy without any adjustable parameters. Furthermore, comparison with non-hydrodynamic simulations shows the fundamental importance of many-body hydrodynamic interactions in colloidal phase separation. The predictive power of our computational approach may significantly contribute to not only the basic understanding of the dynamical behavior and self-organization of soft, bio and active matter but also the computer-aided design of colloidal materials.